Electromagnetic Energy Momentum Thruster Using Tapered Cavity Resonator Evanescent Modes

Abstract

An electromagnetic energy momentum thruster has a cavity resonator and an electromagnetic radiation source for emitting an electromagnetic wave in evanescence into the cavity resonator. The electromagnetic wave produces a greater electromagnetic field amplitude and a greater electromagnetic radiation pressure on a primary interior surface area of the cavity resonator than on a secondary interior surface area of the cavity resonator. The difference between the electromagnetic field amplitude on the primary interior surface area and on the secondary interior surface area of the cavity resonator forms a highly directional electromagnetic energy momentum tensor and provides a highly directional general relativistic metric tensor. As a result, a force is produced on the cavity resonator in the form of a thrust or an acceleration that propels the device in a direction substantially perpendicular to the primary interior surface area.

Claims

1. An electromagnetic energy momentum thruster comprising: a) a cavity resonator forming a cavity having a base interior surface and a tapered interior surface, the tapered interior surface converging to an apex point; and b) an electromagnetic radiation source in communication with the cavity resonator, the electromagnetic radiation source configured to emit an electromagnetic wave having a frequency between about 1.0 MHz to about 1000 THz into the cavity resonator.

2. The thruster of claim 1, wherein the electromagnetic radiation source is configured to produce the frequency of the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude, the maximum field amplitude being at, or adjacent to, the base interior surface, the asymptotic field amplitude being at, or adjacent to, one or both the tapered interior surface and the apex point.

3. The thruster of claim 1, wherein the electromagnetic radiation source is configured to produce the frequency of the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude, the maximum field amplitude being at, or adjacent to, one or both the tapered interior surface and the apex point, and the asymptotic field amplitude being at, or adjacent to, the base interior surface.

4. The thruster of claim 1, wherein the cavity includes an overall interior surface that includes the base and tapered interior surfaces, substantially the entire overall interior surface being electrically conductive, wherein the cavity resonator has a quality factor between about 10{circumflex over ( )}3 to about 10{circumflex over ( )}9.

5. The thruster of claim 1, wherein the cavity includes an overall interior surface that includes the base and tapered interior surfaces, the overall interior surface comprises aluminum, antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum, scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin, titanium, tungsten, vanadium, yttrium, zinc, zirconium, or any combination thereof.

6. The thruster of claim 1, wherein the cavity includes an overall interior surface that includes the base and tapered interior surfaces, substantially the entire overall interior surface being superconductive, wherein the cavity resonator has a quality factor between about 10{circumflex over ( )}6 to about 10{circumflex over ( )}15.

7. The thruster of claim 1, wherein the cavity includes an overall interior surface that includes the base and tapered interior surfaces, the overall interior surface comprises aluminum, barium, beryllium, bismuth, cadmium, calcium, copper, gallium, gadolinium, germanium, lanthanum, lead, lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS, V.sub.3Ga, NbN, V.sub.3Si, Nb.sub.3Sn, Nb.sub.3Al, Nb.sub.3(AlGe), Nb.sub.3Ge, Bi.sub.2Sr.sub.2CuO.sub.6, Bi.sub.2Sr.sub.2CaCu.sub.2O.sub.8, Bi.sub.2Sr.sub.2Ca.sub.2Cu.sub.3O.sub.10, YBa.sub.2Cu.sub.3O.sub.7, YBa.sub.2Cu.sub.4O.sub.8, Y.sub.2Ba.sub.4Cu.sub.7O.sub.15, Y.sub.3Ba.sub.5Cu.sub.8O.sub.18, T.sub.12Ba.sub.2CuO.sub.6, Tl.sub.2Ba.sub.2CaCu.sub.2O.sub.8, Tl.sub.2Ba.sub.2Ca.sub.2Cu.sub.3O.sub.10, TlBa.sub.2Ca.sub.3Cu.sub.4O.sub.11, HgBa.sub.2CuO.sub.4O.sub.11, HgBa.sub.2CaCu.sub.2O.sub.6, HgBa.sub.2Ca.sub.2Cu.sub.3O.sub.8, or any combination thereof.

8. The thruster of claim 1, wherein the cavity comprises a vacuum with a pressure between about 10{circumflex over ( )}−24 Torr to about 10{circumflex over ( )}3 Torr.

9. The thruster of claim 1, wherein the cavity comprises a thermal reservoir with a temperature between about 10{circumflex over ( )}−3 Kelvin to about 10{circumflex over ( )}3 Kelvin.

10. The thruster of claim 1, wherein the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2.

11. The thruster of claim 1, wherein the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Various novel features of the disclosure are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present disclosure will be obtained by reference to the following detailed description that sets forth illustrative embodiments and the accompanying drawings.

[0072] FIG. 1 is an exemplary schematic diagram of a non-limiting electromagnetic energy momentum thruster.

[0073] FIG. 2 is an exemplary perspective view of a non-limiting conical cavity resonator.

[0074] FIG. 3 is an exemplary perspective cross section view of a non-limiting conical cavity resonator.

[0075] FIG. 4 is an exemplary perspective view of a non-limiting truncated conical cavity resonator.

[0076] FIG. 5 is an exemplary perspective cross section view of a non-limiting truncated conical cavity resonator.

[0077] FIG. 6 is an exemplary perspective view of a non-limiting pyramidal cavity resonator.

[0078] FIG. 7 is an exemplary perspective cross section view of a non-limiting pyramidal cavity resonator.

[0079] FIG. 8 is an exemplary perspective view of a non-limiting truncated pyramidal cavity resonator.

[0080] FIG. 9 is an exemplary perspective cross section view of a non-limiting truncated pyramidal cavity resonator.

[0081] FIG. 10 is an exemplary cross section view of a non-limiting tapered cavity resonator.

[0082] FIG. 11 is an exemplary cross section view of a non-limiting tapered cavity resonator comprising a substantially flat base interior surface.

[0083] FIG. 12 is an exemplary cross section view of a non-limiting tapered cavity resonator comprising a base radiation source.

[0084] FIG. 13 is an exemplary cross section view of a non-limiting tapered cavity resonator comprising a substantially flat base interior surface and a base radiation source.

[0085] FIG. 14 is an exemplary cross section view of a non-limiting tapered cavity resonator comprising a side radiation source.

[0086] FIG. 15 is an exemplary cross section view of a non-limiting tapered cavity comprising a substantially flat base interior surface and a side radiation source.

[0087] FIG. 16 is an exemplary cross section view of a non-limiting truncated tapered cavity resonator.

[0088] FIG. 17 is an exemplary cross section view of a non-limiting truncated tapered cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0089] FIG. 18 is an exemplary cross section view of a non-limiting truncated tapered cavity resonator comprising a base radiation source.

[0090] FIG. 19 is an exemplary cross section view of a non-limiting truncated tapered cavity resonator comprising a substantially flat base and truncated interior surfaces, and a base radiation source.

[0091] FIG. 20 is an exemplary cross section view of a non-limiting truncated tapered cavity resonator comprising a side radiation source.

[0092] FIG. 21 is an exemplary cross section view of a non-limiting truncated tapered cavity resonator comprising a substantially flat base and truncated interior surfaces, and a side radiation source.

[0093] FIG. 22 is a non-limiting exemplary plot of a first azimuthal eigenfunction of a conical cavity resonator.

[0094] FIG. 23 is a non-limiting exemplary plot of a second azimuthal eigenfunction of a conical cavity resonator.

[0095] FIG. 24 is a non-limiting exemplary plot of a first transverse magnetic polar eigenfunction of a conical cavity resonator.

[0096] FIG. 25 is a non-limiting exemplary plot of a second transverse magnetic polar eigenfunction of a conical cavity resonator.

[0097] FIG. 26 is a non-limiting exemplary plot of a first transverse magnetic radial eigenfunction of a conical cavity resonator.

[0098] FIG. 27 is a non-limiting exemplary plot of a second transverse magnetic radial eigenfunction of a conical cavity resonator.

[0099] FIG. 28 is a non-limiting exemplary plot of a first transverse magnetic evanescent radial eigenfunction of a conical cavity resonator.

[0100] FIG. 29 is a non-limiting exemplary plot of a second transverse magnetic evanescent radial eigenfunction of a conical cavity resonator.

[0101] FIG. 30 is a non-limiting exemplary plot of a first transverse electric polar eigenfunction of a conical cavity resonator.

[0102] FIG. 31 is a non-limiting exemplary plot of a second transverse electric polar eigenfunction of a conical cavity resonator.

[0103] FIG. 32 is a non-limiting exemplary plot of a first transverse electric radial eigenfunction of a conical cavity resonator.

[0104] FIG. 33 is a non-limiting exemplary plot of a second transverse electric radial eigenfunction of a conical cavity resonator.

[0105] FIG. 34 is a non-limiting exemplary plot of a first transverse electric evanescent radial eigenfunction of a conical cavity resonator.

[0106] FIG. 35 is a non-limiting exemplary plot of a second transverse electric evanescent radial eigenfunction of a conical cavity resonator.

[0107] FIG. 36 is a non-limiting exemplary plot of a first azimuthal eigenfunction of a pyramidal cavity resonator.

[0108] FIG. 37 is a non-limiting exemplary plot of a second azimuthal eigenfunction of a pyramidal cavity resonator.

[0109] FIG. 38 is a non-limiting exemplary plot of a first transverse magnetic polar eigenfunction of a pyramidal cavity resonator.

[0110] FIG. 39 is a non-limiting exemplary plot of a second transverse magnetic polar eigenfunction of a pyramidal cavity resonator.

[0111] FIG. 40 is a non-limiting exemplary plot of a first transverse magnetic radial eigenfunction of a pyramidal cavity resonator.

[0112] FIG. 41 is a non-limiting exemplary plot of a second transverse magnetic radial eigenfunction of a pyramidal cavity resonator.

[0113] FIG. 42 is a non-limiting exemplary plot of a first transverse magnetic evanescent radial eigenfunction of a pyramidal cavity resonator.

[0114] FIG. 43 is a non-limiting exemplary plot of a second transverse magnetic evanescent radial eigenfunction of a pyramidal cavity resonator.

[0115] FIG. 44 is a non-limiting exemplary plot of a first transverse electric polar eigenfunction of a pyramidal cavity resonator.

[0116] FIG. 45 is a non-limiting exemplary plot of a second transverse electric polar eigenfunction of a pyramidal cavity resonator.

[0117] FIG. 46 is a non-limiting exemplary plot of a first transverse electric radial eigenfunction of a pyramidal cavity resonator.

[0118] FIG. 47 is a non-limiting exemplary plot of a second transverse electric radial eigenfunction of a pyramidal cavity resonator.

[0119] FIG. 48 is a non-limiting exemplary plot of a first transverse electric evanescent radial eigenfunction of a pyramidal cavity resonator.

[0120] FIG. 49 is a non-limiting exemplary plot of a second transverse electric evanescent radial eigenfunction of a pyramidal cavity resonator.

[0121] FIG. 50 is an exemplary perspective view of a first three-dimensional electric field vector plot of a non-limiting conical cavity resonator.

[0122] FIG. 51 is an exemplary perspective view of a first three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0123] FIG. 52 is an exemplary axial cross section view of a first electric field density plot of a non-limiting conical cavity resonator.

[0124] FIG. 53 is an exemplary axial cross section view of a first magnetic field vector plot of a non-limiting conical cavity resonator.

[0125] FIG. 54 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting conical cavity resonator.

[0126] FIG. 55 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0127] FIG. 56 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting conical cavity resonator.

[0128] FIG. 57 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0129] FIG. 58 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting truncated conical cavity resonator.

[0130] FIG. 59 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0131] FIG. 60 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting truncated conical cavity resonator.

[0132] FIG. 61 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0133] FIG. 62 is an exemplary perspective view of a second three-dimensional electric field vector plot of a non-limiting conical cavity resonator.

[0134] FIG. 63 is an exemplary perspective view of a second three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0135] FIG. 64 is an exemplary axial cross section view of a second electric field density plot of a non-limiting conical cavity resonator.

[0136] FIG. 65 is an exemplary axial cross section view of a second magnetic field vector plot of a non-limiting conical cavity resonator.

[0137] FIG. 66 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting conical cavity resonator.

[0138] FIG. 67 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0139] FIG. 68 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting conical cavity resonator.

[0140] FIG. 69 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0141] FIG. 70 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting truncated conical cavity resonator.

[0142] FIG. 71 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0143] FIG. 72 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting truncated conical cavity resonator.

[0144] FIG. 73 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0145] FIG. 74 is an exemplary perspective view of a third three-dimensional electric field vector plot of a non-limiting conical cavity resonator.

[0146] FIG. 75 is an exemplary perspective view of a third three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0147] FIG. 76 is an exemplary axial cross section view of a third electric field vector plot of a non-limiting conical cavity resonator.

[0148] FIG. 77 is an exemplary axial cross section view of a third magnetic field vector plot of a non-limiting conical cavity resonator.

[0149] FIG. 78 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting conical cavity resonator.

[0150] FIG. 79 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0151] FIG. 80 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting conical cavity resonator.

[0152] FIG. 81 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0153] FIG. 82 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting truncated conical cavity resonator.

[0154] FIG. 83 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0155] FIG. 84 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting truncated conical cavity resonator.

[0156] FIG. 85 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0157] FIG. 86 is an exemplary perspective view of a first three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator.

[0158] FIG. 87 is an exemplary perspective view of a first three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0159] FIG. 88 is an exemplary axial cross section view of a first electric field density plot of a non-limiting pyramidal cavity resonator.

[0160] FIG. 89 is an exemplary axial cross section view of a first magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0161] FIG. 90 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting pyramidal cavity resonator.

[0162] FIG. 91 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0163] FIG. 92 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting pyramidal cavity resonator.

[0164] FIG. 93 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0165] FIG. 94 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting truncated pyramidal cavity resonator.

[0166] FIG. 95 is an exemplary radial cross section view of a first electric field vector plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0167] FIG. 96 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting truncated pyramidal cavity resonator.

[0168] FIG. 97 is an exemplary radial cross section view of a first magnetic field density plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0169] FIG. 98 is an exemplary perspective view of a second three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator.

[0170] FIG. 99 is an exemplary perspective view of a second three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0171] FIG. 100 is an exemplary axial cross section view of a second electric field density plot of a non-limiting pyramidal cavity resonator.

[0172] FIG. 101 is an exemplary axial cross section view of a second magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0173] FIG. 102 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting pyramidal cavity resonator.

[0174] FIG. 103 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0175] FIG. 104 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting pyramidal cavity resonator.

[0176] FIG. 105 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0177] FIG. 106 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting truncated pyramidal cavity resonator.

[0178] FIG. 107 is an exemplary radial cross section view of a second electric field vector plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0179] FIG. 108 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting truncated pyramidal cavity resonator.

[0180] FIG. 109 is an exemplary radial cross section view of a second magnetic field density plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0181] FIG. 110 is an exemplary perspective view of a third three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator.

[0182] FIG. 111 is an exemplary perspective view of a third three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0183] FIG. 112 is an exemplary axial cross section view of a third electric field density plot of a non-limiting pyramidal cavity resonator.

[0184] FIG. 113 is an exemplary axial cross section view of a third magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0185] FIG. 114 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting pyramidal cavity resonator.

[0186] FIG. 115 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0187] FIG. 116 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0188] FIG. 117 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0189] FIG. 118 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting truncated pyramidal cavity resonator.

[0190] FIG. 119 is an exemplary radial cross section view of a third electric field vector plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0191] FIG. 120 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting truncated pyramidal cavity resonator.

[0192] FIG. 121 is an exemplary radial cross section view of a third magnetic field vector plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0193] FIG. 122 is an exemplary perspective view of a non-limiting environmental control apparatus.

[0194] FIG. 123 is an exemplary cross-section view of a non-limiting environmental control apparatus.

DETAILED DESCRIPTION OF THE FIGURES

[0195] Disclosed herein, per FIG. 1, is an electromagnetic energy momentum thruster comprising a tapered cavity resonator 10 and an electromagnetic radiation source 20 in communication with the cavity resonator 10. In some embodiments, the electromagnetic radiation source 20 is configured to emit an electromagnetic wave into the cavity resonator 10. In some embodiments, the electromagnetic radiation source 20 is configured to emit an electromagnetic wave into the cavity resonator 10 via a transmission line 30. In some embodiments, the electromagnetic wave has a frequency between about 1.0 MHz to about 1000 THz. In some embodiments, the cavity resonator 10 is confined within an environmental control apparatus 40.

Conical Cavity Resonator Thruster

[0196] Provided herein per FIGS. 2, 3, and 10-15 is an electromagnetic energy momentum thruster comprising a conical cavity resonator 100 and a base electromagnetic radiation source 600a or a side electromagnetic radiation source 600b. In some embodiments, the cavity resonator 100 forms a cavity 180 having a base interior surface 110 and a tapered interior surface 120, wherein the tapered interior surface converges to an apex point 130.

[0197] In some embodiments, the base electromagnetic radiation source 600a is configured to emit an electromagnetic wave into the cavity 180 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz. In some embodiments, the side electromagnetic radiation source 600b is configured to emit an electromagnetic wave into the cavity 180 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz.

[0198] In some embodiments, the base electromagnetic radiation source 600a is configured to produce the frequency of the electromagnetic wave in evanescence, so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, the base interior surface 110, and the asymptotic field amplitude is at, or adjacent to, one or both the tapered interior surface 120 and the apex point 130. In some embodiments, the side electromagnetic radiation source 600b is configured to produce the frequency of the electromagnetic wave in evanescence, so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, one or both the tapered interior surface 120 and the apex point 130, and the asymptotic field amplitude is at, or adjacent to, the base interior surface 110.

[0199] In some embodiments, the cavity 180 includes an overall interior surface comprising the base interior surface 110 and the tapered interior surface 120. In some embodiments, substantially the entire overall interior surface of the cavity 180 is electrically conductive. In some embodiments, substantially the entire overall interior surface of the cavity 180 is superconductive. In some embodiments, substantially the entire overall interior surface of the cavity 180 is electrically conductive, and has a quality factor between about 10{circumflex over ( )}3 to about 10{circumflex over ( )}9. In some embodiments, substantially the entire overall interior surface of the cavity 180 is superconductive, and has a quality factor between about 10{circumflex over ( )}6 to about 10{circumflex over ( )}15.

[0200] In some embodiments, substantially the entire overall interior surface of the cavity 180 comprises aluminum, antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum, scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin, titanium, tungsten, vanadium, yttrium, zinc, zirconium, or any combination thereof. In some embodiments, substantially the entire overall interior surface of the cavity 180 comprises aluminum, barium, beryllium, bismuth, cadmium, calcium, copper, gallium, gadolinium, germanium, lanthanum, lead, lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS, V.sub.3Ga, NbN, V.sub.3Si, Nb.sub.3Sn, Nb.sub.3Al, Nb.sub.3(AlGe), Nb.sub.3Ge, Bi.sub.2Sr.sub.2CuO.sub.6, Bi.sub.2Sr.sub.2CaCu.sub.2O.sub.8, Bi.sub.2Sr.sub.2Ca.sub.2Cu.sub.3O.sub.10, YBa.sub.2Cu.sub.3O.sub.7, YBa.sub.2Cu.sub.4O.sub.8, Y.sub.2Ba.sub.4Cu.sub.7O.sub.15, Y.sub.3BasCu.sub.8O.sub.18, Tl.sub.2Ba.sub.2CuO.sub.6, Tl.sub.2Ba.sub.2CaCu.sub.2O.sub.8, Tl.sub.2Ba.sub.2Ca.sub.2Cu.sub.3O.sub.10, TlBa.sub.2Ca.sub.3Cu.sub.4O.sub.11, HgBa.sub.2CuO.sub.4, HgBa.sub.2CaCu.sub.2O.sub.6, HgBa.sub.2Ca.sub.2Cu.sub.3O.sub.8, or any combination thereof.

[0201] In some embodiments, the cavity 180 is empty. In some embodiments, the cavity 180 comprises a vacuum with a pressure between about 10{circumflex over ( )}−24 Torr to about 10{circumflex over ( )}3 Torr. In some embodiments, the cavity 180 comprises a vacuum with a pressure of about 10{circumflex over ( )}−24 Torr, about 10{circumflex over ( )}−21 Torr, about 10{circumflex over ( )}−18 Torr, about 10{circumflex over ( )}−15 Torr, about 10{circumflex over ( )}−12 Torr, about 10{circumflex over ( )}−9 Torr, about 10{circumflex over ( )}−6 Torr, about 10{circumflex over ( )}−3 Torr, about 1.0 Torr, or about 10{circumflex over ( )}3 Torr.

[0202] In some embodiments, the cavity 180 comprises a thermal reservoir with a temperature between about 10{circumflex over ( )}−3 Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 180 comprises a thermal reservoir with a temperature of about 10{circumflex over ( )}−3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about 10{circumflex over ( )}3 Kelvin.

[0203] In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic radiation source is located inside the cavity 180 at, or adjacent to, a maximum field amplitude of the electromagnetic wave.

[0204] In some embodiments, the cavity 180 has at least one of a width 140 and a height 150 between about 10{circumflex over ( )}−9 meters to about 10{circumflex over ( )}3 meters. In some embodiments, the width 140 is measured as a maximum diameter of the base interior surface 110. In some embodiments, the height 150 is measured as a distance from the base interior surface 110 to the apex point 130. In some embodiments, the tapered interior surface 120 forms an aperture angle 160 between about 5 degrees to about 175 degrees. In some embodiments, the aperture angle 160 is measured as the interior angle of the tapered interior surface 120 at the apex point 130. In some embodiments, the cavity 180 has a wall with a wall thickness 170 between about 10{circumflex over ( )}−9 meters to about 1.0 meter. In some embodiments, the wall thickness 170 is measured as a normal distance between the overall interior surface of the cavity 180 and an exterior of the cavity resonator 100. In some embodiments, the base interior surface 110 has a different wall thickness 170 than the tapered interior surface 120. In some embodiments, the base interior surface 110 has about the same wall thickness 170 as the tapered interior surface 120.

[0205] In some embodiments, the base interior surface 110 is substantially elliptical. In some embodiments, the base interior surface 110 is substantially circular. In some embodiments, the base interior surface 110 is substantially flat.

[0206] In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, the base interior surface 110, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster. In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, one or both the tapered interior surface 120 and the apex point 130, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster.

Truncated Conical Cavity Resonator Thruster

[0207] Provided herein per FIGS. 4, 5, and 16-21 is an electromagnetic energy momentum thruster comprising a truncated conical cavity resonator 200 and a base electromagnetic radiation source 600a or a side electromagnetic radiation source 600b. In some embodiments, the cavity resonator 200 forms a cavity 280 having a base interior surface 210, a tapered interior surface 220, and a truncated interior surface 230 opposing the base interior surface 210, the tapered interior surface 220 being between the base interior surface 210 and the truncated interior surface 230.

[0208] In some embodiments, the base electromagnetic radiation source 600a is configured to emit an electromagnetic wave into the cavity 280 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz. In some embodiments, the side electromagnetic radiation source 600b is configured to emit an electromagnetic wave into the cavity 280 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz.

[0209] In some embodiments, the base electromagnetic radiation source 600a is configured to produce the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, the base interior surface 210, and the asymptotic field amplitude is at, or adjacent to, one or both the tapered interior surface 220 and the truncated interior surface 230. In some embodiments, the side electromagnetic radiation source 600b is configured to produce the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, one or both the tapered interior surface 220 and the truncated interior surface 230, and the asymptotic field amplitude is at, or adjacent to, the base interior surface 210.

[0210] In some embodiments, the cavity 280 includes an overall interior surface comprising the base interior surface 210, the tapered interior surface 220, and the truncated interior surface 230. In some embodiments, substantially the entire overall interior surface of the cavity 280 is electrically conductive. In some embodiments, substantially the entire overall interior surface of the cavity 280 is superconductive. In some embodiments, substantially the entire overall interior surface of the cavity 280 is electrically conductive, and has a quality factor between about 10{circumflex over ( )}3 to about 10{circumflex over ( )}9. In some embodiments, substantially the entire overall interior surface of the cavity 280 is superconductive, and has a quality factor between about 10{circumflex over ( )}6 to about 10{circumflex over ( )}15.

[0211] In some embodiments, substantially the entire overall interior surface of the cavity 280 comprises aluminum, antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum, scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin, titanium, tungsten, vanadium, yttrium, zinc, zirconium, or any combination thereof. In some embodiments, substantially the entire overall interior surface of the cavity 280 comprises aluminum, barium, beryllium, bismuth, cadmium, calcium, copper, gallium, gadolinium, germanium, lanthanum, lead, lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS, V.sub.3Ga, NbN, V.sub.3Si, Nb.sub.3Sn, Nb.sub.3Al, Nb.sub.3(AlGe), Nb.sub.3Ge, Bi.sub.2Sr.sub.2CuO.sub.6, Bi.sub.2Sr.sub.2CaCu.sub.2O.sub.8, Bi.sub.2Sr.sub.2Ca.sub.2Cu.sub.3O.sub.10, YBa.sub.2Cu.sub.3O.sub.7, YBa.sub.2Cu.sub.4O.sub.8, Y.sub.2Ba.sub.4Cu.sub.7O.sub.15, Y.sub.3Ba.sub.5Cu.sub.8O.sub.18, Tl.sub.2Ba.sub.2CuO.sub.6, Tl.sub.2Ba.sub.2CaCu.sub.2O.sub.8, Tl.sub.2Ba.sub.2Ca.sub.2Cu.sub.3O.sub.10, TlBa.sub.2Ca.sub.3Cu.sub.4O.sub.11, HgBa.sub.2CuO.sub.4, HgBa.sub.2CaCu.sub.2O.sub.6, HgBa.sub.2Ca.sub.2Cu.sub.3O.sub.8, or any combination thereof.

[0212] In some embodiments, the cavity 280 is empty. In some embodiments, the cavity 280 comprises a vacuum with a pressure between about 10{circumflex over ( )}−24 Torr to about 10{circumflex over ( )}3 Torr. In some embodiments, the cavity 280 comprises a vacuum with a pressure of about 10{circumflex over ( )}−24 Torr, about 10{circumflex over ( )}−21 Torr, about 10{circumflex over ( )}−18 Torr, about 10{circumflex over ( )}−15 Torr, about 10{circumflex over ( )}−12 Torr, about 10{circumflex over ( )}−9 Torr, about 10{circumflex over ( )}−6 Torr, about 10{circumflex over ( )}−3 Torr, about 1.0 Torr, or about 10{circumflex over ( )}3 Torr.

[0213] In some embodiments, the cavity 280 comprises a thermal reservoir with a temperature between about 10{circumflex over ( )}−3 Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 280 comprises a thermal reservoir with a temperature of about 10{circumflex over ( )}−3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about 10{circumflex over ( )}3 Kelvin.

[0214] In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic radiation source is located inside the cavity 280 at, or adjacent to, a maximum field amplitude of the electromagnetic wave.

[0215] In some embodiments, the cavity 280 has at least one of a width 240 and a height 250 between about 10{circumflex over ( )}−9 meters to about 10{circumflex over ( )}3 meters. In some embodiments, the width 240 is measured as a maximum diameter of the base interior surface 210. In some embodiments, the height 250 is measured as a normal distance from the base interior surface 210 to the truncated interior surface 230. In some embodiments, the tapered interior surface 220 forms an aperture angle 260 between about 5 degrees to about 175 degrees. In some embodiments, the aperture angle 260 is measured as the interior angle of the tapered interior surface 220. In some embodiments, the cavity 280 has a wall with a wall thickness 270 between about 10{circumflex over ( )}−9 meters to about 1.0 meter. In some embodiments, the wall thickness 270 is measured as a normal distance between the overall interior surface of the cavity 280 and an exterior of the cavity resonator 200. In some embodiments, the base interior surface 210 has a different wall thickness 270 than the tapered interior surface 220. In some embodiments, the base interior surface 210 has about the same wall thickness 270 as the tapered interior surface 220. In some embodiments, the truncated interior surface 230 has a different wall thickness 270 than the tapered interior surface 220. In some embodiments, the truncated interior surface 230 has about the same wall thickness 270 the tapered interior surface 220. In some embodiments, the base interior surface 210 has a different wall thickness 270 than the truncated interior surface 230. In some embodiments, the base interior surface 210 has about the same wall thickness 270 as the truncated interior surface 230.

[0216] In some embodiments, one or both the base interior surface 210 and the truncated interior surface 230 is substantially elliptical. In some embodiments, one or both the base interior surface 210 and the truncated interior surface 230 is substantially circular. In some embodiments, one or both the base interior surface 210 and the truncated interior surface 230 is substantially flat.

[0217] In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, the base interior surface 210, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster. In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, one or both the tapered interior surface 220 and the truncated interior surface 230, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster.

Pyramidal Cavity Resonator Thruster

[0218] Provided herein per FIGS. 6, 7, and 10-15 is an electromagnetic energy momentum thruster comprising a pyramidal cavity resonator 300 and a base electromagnetic radiation source 600a or a side electromagnetic radiation source 600b. In some embodiments, the cavity resonator 300 forms a cavity 380 having a base interior surface 310 and at least three tapered interior surfaces 320, the tapered interior surfaces 320 converging to an apex point 330.

[0219] In some embodiments, the base electromagnetic radiation source 600a is configured to emit an electromagnetic wave into the cavity 380 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz. In some embodiments, the side electromagnetic radiation source 600b is configured to emit an electromagnetic wave into the cavity 380 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz.

[0220] In some embodiments, the base electromagnetic radiation source 600a is configured to produce the frequency of the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, the base interior surface 310, and the asymptotic field amplitude is at, or adjacent to, one or more of the at least three tapered interior surfaces 320 and the apex point 330. In some embodiments, the side electromagnetic radiation source 600b is configured to produce the frequency of the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, one or more of the at least three tapered interior surfaces 320 and the apex point 330, and the asymptotic field amplitude is at, or adjacent to, the base interior surface 310.

[0221] In some embodiments, the cavity 380 includes an overall interior surface comprising the base interior surface 310 and the at least three tapered interior surfaces 320. In some embodiments, substantially the entire overall interior surface of the cavity 380 is electrically conductive. In some embodiments, substantially the entire overall interior surface of the cavity 380 is superconductive. In some embodiments, substantially the entire overall interior surface of the cavity 380 is electrically conductive, and has a quality factor between about 10{circumflex over ( )}3 to about 10{circumflex over ( )}9. In some embodiments, substantially the entire overall interior surface of the cavity 380 is superconductive, and has a quality factor between about 10{circumflex over ( )}6 to about 10{circumflex over ( )}15.

[0222] In some embodiments, substantially the entire overall interior surface of the cavity 380 comprises aluminum, antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum, scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin, titanium, tungsten, vanadium, yttrium, zinc, zirconium, or any combination thereof. In some embodiments, substantially the entire overall interior surface of the cavity 380 comprises aluminum, barium, beryllium, bismuth, cadmium, calcium, copper, gallium, gadolinium, germanium, lanthanum, lead, lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS, V.sub.3Ga, NbN, V.sub.3Si, Nb.sub.3Sn, Nb.sub.3Al, Nb.sub.3(AlGe), Nb.sub.3Ge, Bi.sub.2Sr.sub.2CuO.sub.6, Bi.sub.2Sr.sub.2CaCu.sub.2O.sub.8, Bi.sub.2Sr.sub.2Ca.sub.2Cu.sub.3O.sub.10, YBa.sub.2Cu.sub.3O.sub.7, YBa.sub.2Cu.sub.4O.sub.8, Y.sub.2Ba.sub.4Cu.sub.7O.sub.15, Y.sub.3BasCu.sub.8O.sub.18, Tl.sub.2Ba.sub.2CuO.sub.6, Tl.sub.2Ba.sub.2CaCu.sub.2O.sub.8, Tl.sub.2Ba.sub.2Ca.sub.2Cu.sub.3O.sub.10, TlBa.sub.2Ca.sub.3Cu.sub.4O.sub.11, HgBa.sub.2CuO.sub.4, HgBa.sub.2CaCu.sub.2O.sub.6, HgBa.sub.2Ca.sub.2Cu.sub.3O.sub.8, or any combination thereof.

[0223] In some embodiments, the cavity 380 is empty. In some embodiments, the cavity 380 comprises a vacuum with a pressure between about 10{circumflex over ( )}−24 Torr to about 10{circumflex over ( )}3 Torr. In some embodiments, the cavity 380 comprises a vacuum with a pressure of about 10{circumflex over ( )}−24 Torr, about 10{circumflex over ( )}−21 Torr, about 10{circumflex over ( )}−18 Torr, about 10{circumflex over ( )}−15 Torr, about 10{circumflex over ( )}−12 Torr, about 10{circumflex over ( )}−9 Torr, about 10{circumflex over ( )}−6 Torr, about 10{circumflex over ( )}−3 Torr, about 1.0 Torr, or about 10{circumflex over ( )}3 Torr.

[0224] In some embodiments, the cavity 380 comprises a thermal reservoir with a temperature between about 10{circumflex over ( )}−3 Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 380 comprises a thermal reservoir with a temperature of about 10{circumflex over ( )}−3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about 10{circumflex over ( )}3 Kelvin.

[0225] In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic radiation source is located inside the cavity 380 at, or adjacent to, a maximum field amplitude of the electromagnetic wave.

[0226] In some embodiments, the cavity 380 has at least one of a width 340 and a height 350 between about 10{circumflex over ( )}−9 meters to about 10{circumflex over ( )}3 meters. In some embodiments, the width 340 is measured as a maximum diameter of the base interior surface 310. In some embodiments, the height 350 is measured as a distance from the base interior surface 310 to the apex point 330. In some embodiments, two or more of the at least three tapered interior surfaces 320 form an aperture angle 360 between about 5 degrees to about 175 degrees. In some embodiments, the aperture angle 360 is measured as an internal angle between two or more of the at least three tapered interior surfaces 320 at the apex point 330. In some embodiments, the cavity has a wall with a wall thickness 370 between about 10{circumflex over ( )}−9 meters to about 1.0 meter. In some embodiments, the wall thickness 370 is measured as a normal distance between the overall interior surface of the cavity 380 and an exterior of the cavity resonator 300. In some embodiments, the base interior surface 310 has a different wall thickness 370 than as at least one of the at least three the tapered interior surfaces 320. In some embodiments, the base interior surface 310 has about the same wall thickness 370 as at least one of the at least three the tapered interior surfaces 320.

[0227] In some embodiments, the base interior surface 310 comprises 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or more sides. In some embodiments the base interior surface 310 is substantially equilateral. In some embodiments, the base interior surface 310 is substantially flat.

[0228] In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, the base interior surface 310, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster. In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, one or more of the at least three tapered interior surfaces 320 and the apex point 330, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster.

Truncated Pyramidal Cavity Resonator Thruster

[0229] Provided herein per FIGS. 8, 9, and 16-21 is an electromagnetic energy momentum thruster comprising a truncated pyramidal cavity resonator 400 and a base electromagnetic radiation source 600a or a side electromagnetic radiation source 600b. In some embodiments, the cavity resonator 400 forms a cavity 480 having a base interior surface 410, at least three tapered interior surfaces 420, and a truncated interior surface 430 opposing the base interior surface 410, the at least three tapered interior surfaces 420 being between the base interior surface 410 and truncated interior surfaces 430.

[0230] In some embodiments, the base electromagnetic radiation source 600a is configured to emit an electromagnetic wave into the cavity 480 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz. In some embodiments, the side electromagnetic radiation source 600b is configured to emit an electromagnetic wave into the cavity 480 having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz.

[0231] In some embodiments, the base electromagnetic radiation source 600a is configured to produce the frequency of the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, the base interior surface 410, and the asymptotic field amplitude is at, or adjacent to, one or more of the at least three tapered interior surfaces 420 and the truncated interior surface 430. In some embodiments, the side electromagnetic radiation source 600b is configured to produce the frequency of the electromagnetic wave in evanescence so that the electromagnetic wave has a maximum field amplitude and an asymptotic field amplitude. In some embodiments, the maximum field amplitude is at, or adjacent to, one or more of the at least three tapered interior surfaces 420 and the truncated interior surface 430, and the asymptotic field amplitude is at, or adjacent to, the base interior surface 410.

[0232] In some embodiments, the cavity 480 includes an overall interior surface comprising the base interior surface 410, the at least three tapered interior surfaces 420, and the truncated interior surface 430. In some embodiments, substantially the entire overall interior surface of the cavity 480 is electrically conductive. In some embodiments, substantially the entire overall interior surface of the cavity 480 is superconductive. In some embodiments, substantially the entire overall interior surface of the cavity 480 is electrically conductive, and has a quality factor between about 10{circumflex over ( )}3 to about 10{circumflex over ( )}9. In some embodiments, the entire overall interior surface of the cavity 480 is superconductive, and has a quality factor between about 10{circumflex over ( )}6 to about 10{circumflex over ( )}15.

[0233] In some embodiments, substantially the entire overall interior surface of the cavity 480 comprises aluminum, antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum, scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin, titanium, tungsten, vanadium, yttrium, zinc, zirconium, or any combination thereof. In some embodiments, substantially the entire overall interior surface of the cavity 480 comprises aluminum, barium, beryllium, bismuth, cadmium, calcium, copper, gallium, gadolinium, germanium, lanthanum, lead, lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS, V.sub.3Ga, NbN, V.sub.3Si, Nb.sub.3Sn, Nb.sub.3Al, Nb.sub.3(AlGe), Nb.sub.3Ge, Bi.sub.2Sr.sub.2CuO.sub.6, Bi.sub.2Sr.sub.2CaCu.sub.2O.sub.8, Bi.sub.2Sr.sub.2Ca.sub.2Cu.sub.3O.sub.10, YBa.sub.2Cu.sub.3O.sub.7, YBa.sub.2Cu.sub.4O.sub.8, Y.sub.2Ba.sub.4Cu.sub.7O.sub.15, Y.sub.3Ba.sub.5Cu.sub.8O.sub.18, Tl.sub.2Ba.sub.2CuO.sub.6, Tl.sub.2Ba.sub.2CaCu.sub.2O.sub.8, Tl.sub.2Ba.sub.2Ca.sub.2Cu.sub.3O.sub.10, TlBa.sub.2Ca.sub.3Cu.sub.4O.sub.11, HgBa.sub.2CuO.sub.4, HgBa.sub.2CaCu.sub.2O.sub.6, HgBa.sub.2Ca.sub.2Cu.sub.3O.sub.8, or any combination thereof.

[0234] In some embodiments, the cavity 480 is empty. In some embodiments, the cavity 480 comprises a vacuum with a pressure between about 10{circumflex over ( )}−24 Torr to about 10{circumflex over ( )}3 Torr. In some embodiments, the cavity 480 comprises a vacuum with a pressure of about 10{circumflex over ( )}−24 Torr, about 10{circumflex over ( )}−21 Torr, about 10{circumflex over ( )}−18 Torr, about 10{circumflex over ( )}−15 Torr, about 10{circumflex over ( )}−12 Torr, about 10{circumflex over ( )}−9 Torr, about 10{circumflex over ( )}−6 Torr, about 10{circumflex over ( )}−3 Torr, about 1.0 Torr, or about 10{circumflex over ( )}3 Torr.

[0235] In some embodiments, the cavity 480 comprises a thermal reservoir with a temperature between about 10{circumflex over ( )}−3 Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 480 comprises a thermal reservoir with a temperature of about 10{circumflex over ( )}−3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about 10{circumflex over ( )}3 Kelvin.

[0236] In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse magnetic wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N1 and an azimuthal mode number of N2, where N1 and N2 are an integers from 0 to 1000, and N1 is greater than or equal to N2. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of 0, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic wave comprises a transverse electric wave with a polar mode number of N and an azimuthal mode number of N, where N is an integer from 0 to 1000. In some embodiments, the electromagnetic radiation source is located inside the cavity 480 at, or adjacent to, a maximum field amplitude of the electromagnetic wave.

[0237] In some embodiments, the cavity 480 has at least one of a width 440 and a height 450 between about 10{circumflex over ( )}−9 meters to about 10{circumflex over ( )}3 meters. In some embodiments, the width 440 is measured as a normal width of the base interior surface 410. In some embodiments, the height 450 is measured as a normal distance from the base interior surface 410 to the truncated interior surface 430. In some embodiments, two or more of the at least three tapered interior surfaces 420 form an aperture angle 460 between about 5 degrees to about 175 degrees. In some embodiments, the aperture angle 460 is measured as an internal angle between two or more of the at least three tapered interior surfaces 420. In some embodiments, the cavity 480 has a wall with a wall thickness 470 between about 10{circumflex over ( )}−9 meters to about 1.0 meter. In some embodiments, the wall thickness 470 is measured as a normal distance between the overall interior surface of the cavity 480 and an exterior of the cavity resonator 400. In some embodiments, the base interior surface 410 has a different wall thickness 470 than at least one of the three or more tapered interior surfaces 420. In some embodiments, the base interior surface 410 has about the same wall thickness 470 as at least one of the three or more tapered interior surfaces 420. In some embodiments, the truncated interior surface 430 has a different wall thickness 470 than at least one of the three or more tapered interior surfaces 420. In some embodiments, the truncated interior surface 430 has about the same wall thickness 470 as at least one of the three or more tapered interior surfaces 420. In some embodiments, the base interior surface 410 has a different wall thickness 470 than the truncated interior surface 430. In some embodiments, the base interior surface 410 has about the same wall thickness 470 as the truncated interior surface 430.

[0238] In some embodiments, one or both the base interior surface 410 and the truncated interior surface 430 comprises 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or more sides. In some embodiments, one or both the base interior surface 410 and the truncated interior surface 430 is substantially equilateral. In some embodiments, one or both the base interior surface 410 and the truncated interior surface 430 is substantially flat.

[0239] In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, the base interior surface 410, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster. In some embodiments, the electromagnetic wave forms an electromagnetic energy momentum tensor with an amplitude maximum at, or adjacent to, one or more of the at least three tapered interior surfaces 420 and the truncated interior surface 430, which results in one or more of a metric tensor curvature, a thrust, and an acceleration of the thruster.

Electromagnetic Radiation Source

[0240] Provided herein is an electromagnetic energy momentum thruster comprising a cavity resonator forming a cavity, and an electromagnetic radiation source.

[0241] In some embodiments, per FIGS. 12 and 13, the electromagnetic energy momentum thruster comprises a tapered cavity resonator 500 and a base electromagnetic radiation source 600a. In some embodiments, per FIGS. 14 and 15, the electromagnetic energy momentum thruster comprises a tapered cavity resonator 500 and a side electromagnetic radiation source 600b.

[0242] In some embodiments, per FIGS. 18 and 19, the electromagnetic energy momentum thruster comprises a truncated tapered cavity resonator 550 and a base electromagnetic radiation source 600a. In some embodiments, per FIGS. 20 and 21, the electromagnetic energy momentum thruster comprises a truncated tapered cavity resonator 550 and a side electromagnetic radiation source 600b.

[0243] In some embodiments, the tapered cavity resonator 500 comprises a pyramidal or a conical cavity resonator. In some embodiments, the truncated tapered cavity resonator 550 comprises a truncated pyramidal or a truncated conical cavity resonator.

[0244] In some embodiments, the base radiation source 600a emits the electromagnetic wave from the base interior surface of the tapered cavity resonator 500 or the truncated tapered cavity resonator 550. In some embodiments, the base radiation source 600a is affixed to the base interior surface of the tapered cavity resonator 500 or the truncated tapered cavity resonator 550. In some embodiments, the side radiation source 600b emits the electromagnetic wave from the tapered interior surface of the tapered cavity resonator 500 or the truncated tapered cavity resonator 550. In some embodiments, the side radiation source 600b is affixed to the tapered interior surface of the tapered cavity resonator 500 or the truncated tapered cavity resonator 550.

[0245] In some embodiments, the base electromagnetic radiation source 600a is configured to emit an electromagnetic wave into the cavity resonator having a frequency between about 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz. In some embodiments, the side electromagnetic radiation source 600b is configured to emit an electromagnetic wave into the cavity resonator having a frequency between about 10{circumflex over ( )}1 MHz to about 10{circumflex over ( )}9 MHz.

[0246] Environmental Control Apparatus

[0247] Provided herein, per FIGS. 122 and 123, is an exemplary environmental control apparatus 1000. In some embodiments, the environmental control apparatus 1000 comprises a transmission line 1001, an instrumentation channel 1002, a coolant input 1003, and a coolant output 1004. In some embodiments, the coolant comprises a gaseous coolant, a liquid coolant, a cryogen coolant, or any combination thereof.

[0248] In some embodiments, the exemplary environmental control apparatus 1000 comprises at least one of a clamp, a clasp, a cam, a handle, a gasket, an insulator, and a probe.

EXAMPLES

[0249] The following illustrative examples are representative of embodiments of the hardware applications, systems, and methods described herein and are not meant to be limiting in any way. Exemplary plots of the transverse magnetic waves and the transverse electric waves of a non-limiting conical cavity resonator, a non-limiting truncated conical cavity resonator, a non-limiting pyramidal cavity resonator, and a non-limiting truncated pyramidal cavity resonator are shown in FIGS. 22-121.

Example 1—Transverse Electric Wave Frequency of a Conical Cavity Resonator

[0250] In some embodiments, a frequency of a hollow conical cavity resonator is calculated per the equations below:

[0251] For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . . .

[0252] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), and a polar wave equation (P.sub.l.sup.m(cos θ)) of the resonator:

[00001]${\left[\frac{d}{d\theta }\left[P_l^m\left(\cos \theta \right)\right]\right]}_{\theta ={\theta }_0}=0$

[0253] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[(kr)j.sub.l(kr)].sub.r=0=0 and [(kr)j.sub.l(kr)].sub.r=r.sub.l=0

[0254] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[00002]${\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=0}=0{\mathrm{or}\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=r_1}=0$

[0255] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00003]$f=\frac{kc}{2\pi }$

[0256] FIGS. 22 and 23 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a conical cavity resonator, respectively. FIGS. 30 and 31 are non-limiting exemplary plots of a first and a second transverse electric polar eigenfunction of a conical cavity resonator, respectively. FIGS. 32 and 33 are non-limiting exemplary plots of a first and a second transverse electric radial eigenfunction of a conical cavity resonator, respectively. FIGS. 34 and 35 are non-limiting exemplary plots of a first and a second transverse electric evanescent radial eigenfunction of a conical cavity resonator, respectively.

[0257] FIG. 74 is an exemplary perspective view of a first transverse electric three-dimensional electric field vector plot of a non-limiting conical cavity resonator. FIG. 75 is an exemplary perspective view of a first transverse electric three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0258] FIG. 76 is an exemplary axial cross section view of a first electric field transverse electric vector plot of a non-limiting conical cavity resonator. FIG. 77 is an exemplary axial cross section view of a first magnetic field transverse electric vector plot of a non-limiting conical cavity resonator.

[0259] FIG. 78 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting conical cavity resonator. FIG. 79 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0260] FIG. 80 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting conical cavity resonator. FIG. 81 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0261] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting conical cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from the base interior surface.

Example 2—Transverse Magnetic Wave Frequency of a Conical Cavity Resonator

[0262] In some embodiments, a frequency of a hollow conical cavity resonator is calculated per the equations below:

[0263] For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . . .

[0264] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), and a polar wave equation (P.sub.l.sup.m(cos θ)) of the resonator:

[(P.sub.l.sup.m(cos θ)].sub.θ=θ.sub.0=0

[0265] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[00004]${\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=0}=0{\mathrm{and}\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=r_1}=0$

[0266] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[(kr)j.sub.l(kr)].sub.r=0=0 or [(kr)j.sub.l(kr)].sub.r=r.sub.1=0

[0267] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00005]$f=\frac{kc}{2\pi }$

[0268] FIGS. 22 and 23 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a conical cavity resonator, respectively. FIGS. 24 and 25 are non-limiting exemplary plots of a first and a second transverse magnetic polar eigenfunction of a conical cavity resonator, respectively. FIGS. 26 and 27 are non-limiting exemplary plots of a first and a second transverse magnetic radial eigenfunction of a conical cavity resonator, respectively. FIGS. 28 and 29 are non-limiting exemplary plots of a first and a second transverse magnetic evanescent radial eigenfunction of a conical cavity resonator, respectively.

[0269] FIG. 50 is an exemplary perspective view of a first transverse magnetic three-dimensional electric field vector plot of a non-limiting conical cavity resonator. FIG. 51 is an exemplary perspective view of a first transverse magnetic three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0270] FIG. 52 is an exemplary axial cross section view of a first electric field transverse magnetic density plot of a non-limiting conical cavity resonator. FIG. 53 is an exemplary axial cross section view of a first magnetic field transverse magnetic vector plot of a non-limiting conical cavity resonator.

[0271] FIG. 54 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting conical cavity resonator. FIG. 55 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0272] FIG. 56 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting conical cavity resonator. FIG. 57 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0273] FIG. 62 is an exemplary perspective view of a second transverse magnetic three-dimensional electric field vector plot of a non-limiting conical cavity resonator. FIG. 63 is an exemplary perspective view of a second transverse magnetic three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0274] FIG. 64 is an exemplary axial cross section view of a second electric field transverse magnetic density plot of a non-limiting conical cavity resonator. FIG. 65 is an exemplary axial cross section view of a second magnetic field transverse magnetic vector plot of a non-limiting conical cavity resonator.

[0275] FIG. 66 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting conical cavity resonator. FIG. 67 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0276] FIG. 68 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting conical cavity resonator. FIG. 69 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting conical cavity resonator comprising a substantially flat base interior surface.

[0277] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting conical cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from the tapered interior surface.

Example 3—Transverse Electric Wave Frequency of a Truncated Conical Cavity Resonator

[0278] In some embodiments, a frequency of a hollow conical cavity resonator is calculated per the equations below:

[0279] For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . . .

[0280] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), and a polar wave equation (P.sub.l.sup.m(cos θ)) of the resonator:

[00006]${\left[\frac{d}{d\theta }\left[P_l^m\left(\cos \theta \right)\right]\right]}_{\theta ={\theta }_0}=0$

[0281] For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radial length (r.sub.0), a radial length (r.sub.1), and a radial wave equation (h.sub.l(kr)) of the resonator:

[(kr)h.sub.l(kr)].sub.r=0=0 and [(kr)h.sub.l(kr)].sub.r=r.sub.1=0

[0282] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), a truncated radial length (r.sub.0), and a radial wave equation (h.sub.l(kr)) of the resonator:

[00007]${\left[\frac{d}{dr}\left[\left(kr\right)h_l\left(kr\right)\right]\right]}_{r=r_0}=0{\mathrm{or}\left[\frac{d}{dr}\left[\left(kr\right)h_l\left(kr\right)\right]\right]}_{r=r_1}$

[0283] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00008]$f=\frac{kc}{2\pi }$

[0284] FIGS. 22 and 23 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a conical cavity resonator, respectively. FIGS. 30 and 31 are non-limiting exemplary plots of a first and a second transverse electric polar eigenfunction of a conical cavity resonator, respectively. FIGS. 32 and 33 are non-limiting exemplary plots of a first and a second transverse electric radial eigenfunction of a conical cavity resonator, respectively. FIGS. 34 and 35 are non-limiting exemplary plots of a first and a second transverse electric evanescent radial eigenfunction of a conical cavity resonator, respectively.

[0285] FIG. 74 is an exemplary perspective view of a first transverse electric three-dimensional electric field vector plot of a non-limiting conical cavity resonator. FIG. 75 is an exemplary perspective view of a first transverse electric three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0286] FIG. 76 is an exemplary axial cross section view of a first electric field transverse electric vector plot of a non-limiting conical cavity resonator. FIG. 77 is an exemplary axial cross section view of a first magnetic field transverse electric vector plot of a non-limiting conical cavity resonator.

[0287] FIG. 82 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting truncated conical cavity resonator. FIG. 83 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0288] FIG. 84 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting truncated conical cavity resonator. FIG. 85 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0289] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting conical cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from the base interior surface.

Example 4—Transverse Magnetic Wave Frequency of a Truncated Conical Cavity Resonator

[0290] In some embodiments, a frequency of a hollow conical cavity resonator is calculated per the equations below:

[0291] For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . . .

[0292] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), and a polar wave equation (P.sub.l.sup.m(cos θ)) of the resonator:

[(P.sub.l.sup.m(cos θ)].sub.θ=θ.sub.0=0

[0293] For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radial length (r.sub.0), a radial length (r.sub.1), and a radial wave equation (h.sub.l(kr)) of the resonator:

[00009]${\left[\frac{d}{dr}\left[\left(kr\right)h_l\left(kr\right)\right]\right]}_{r=r_0}=0{\mathrm{and}\left[\frac{d}{dr}\left[\left(kr\right)h_l\left(kr\right)\right]\right]}_{r=r_1}=0$

[0294] For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radial length (r.sub.0), a radial length (r.sub.1), and a radial wave equation (h.sub.l(kr)) of the resonator:

[(kr)h.sub.l(kr)].sub.r=r.sub.0=0 or [(kr)h.sub.l(kr)].sub.r=r.sub.1=0

[0295] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00010]$f=\frac{kc}{2\pi }$

[0296] FIGS. 22 and 23 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a conical cavity resonator, respectively. FIGS. 24 and 25 are non-limiting exemplary plots of a first and a second transverse magnetic polar eigenfunction of a conical cavity resonator, respectively. FIGS. 26 and 27 are non-limiting exemplary plots of a first and a second transverse magnetic radial eigenfunction of a conical cavity resonator, respectively. FIGS. 28 and 29 are non-limiting exemplary plots of a first and a second transverse magnetic evanescent radial eigenfunction of a conical cavity resonator, respectively.

[0297] FIG. 50 is an exemplary perspective view of a first transverse magnetic three-dimensional electric field vector plot of a non-limiting conical cavity resonator. FIG. 51 is an exemplary perspective view of a first transverse magnetic three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0298] FIG. 52 is an exemplary axial cross section view of a first electric field transverse magnetic density plot of a non-limiting conical cavity resonator. FIG. 53 is an exemplary axial cross section view of a first magnetic field transverse magnetic vector plot of a non-limiting conical cavity resonator.

[0299] FIG. 58 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting truncated conical cavity resonator. FIG. 59 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0300] FIG. 60 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting truncated conical cavity resonator. FIG. 61 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0301] FIG. 62 is an exemplary perspective view of a second transverse magnetic three-dimensional electric field vector plot of a non-limiting conical cavity resonator. FIG. 63 is an exemplary perspective view of a second transverse magnetic three-dimensional magnetic field vector plot of a non-limiting conical cavity resonator.

[0302] FIG. 64 is an exemplary axial cross section view of a second electric field transverse magnetic density plot of a non-limiting conical cavity resonator. FIG. 65 is an exemplary axial cross section view of a second magnetic field transverse magnetic vector plot of a non-limiting conical cavity resonator.

[0303] FIG. 70 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting truncated conical cavity resonator. FIG. 71 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0304] FIG. 72 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting truncated conical cavity resonator. FIG. 73 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting truncated conical cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0305] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting conical cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from one or both the tapered interior surface and the truncated interior surface.

Example 5—Transverse Electric Wave Frequency of a Pyramidal Cavity Resonator

[0306] In some embodiments, a frequency of a hollow pyramidal cavity resonator is calculated per the equations below:

[0307] For an azimuthal eigenvalue (m) and a taper angle (φ.sub.0) of the resonator:

[00011]$m=\frac{n\pi }{{\phi }_0}\mathrm{where}n=0,1,2,\mathrm{.Math.}$

[0308] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), a polar wave equation (P.sub.l.sup.m(cos θ)), and a polar wave equation (Q.sub.l.sup.m(cos θ)) of the resonator:

[00012]${\left[\frac{d}{d\theta }\left[P_l^m\left(\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(-\cos \frac{{\theta }_0}{2}\right)-P_l^m\left(-\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(\cos \frac{{\theta }_0}{2}\right)\right]\right]}_{\theta ={\theta }_0}=0$

[0309] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[(kr)j.sub.l(kr)].sub.r=0=0 and [(kr)j.sub.l(kr)].sub.r=r.sub.1=0

[0310] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[00013]${\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=0}=0{\mathrm{or}\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=r_1}=0$

[0311] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00014]$f=\frac{kc}{2\pi }$

[0312] FIGS. 36 and 37 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 44 and 45 are non-limiting exemplary plots of a first and a second transverse electric polar eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 46 and 47 are non-limiting exemplary plots of a first and a second transverse electric radial eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 48 and 49 are non-limiting exemplary plots of a first and a second transverse electric evanescent radial eigenfunction of a pyramidal cavity resonator, respectively.

[0313] FIG. 110 is an exemplary perspective view of a first transverse electric three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator. FIG. 111 is an exemplary perspective view of a first transverse electric three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0314] FIG. 112 is an exemplary axial cross section view of a first electric field transverse electric density plot of a non-limiting pyramidal cavity resonator. FIG. 113 is an exemplary axial cross section view of a first magnetic field transverse electric vector plot of a non-limiting pyramidal cavity resonator.

[0315] FIG. 114 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting pyramidal cavity resonator. FIG. 115 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting pyramidal resonator comprising a substantially flat base interior surface.

[0316] FIG. 116 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting pyramidal cavity resonator. FIG. 117 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0317] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting pyramidal cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from the base interior surface.

Example 6—Transverse Magnetic Wave Frequency of a Pyramidal Cavity Resonator

[0318] In some embodiments, a frequency of a hollow pyramidal cavity resonator is calculated per the equations below:

[0319] For an azimuthal eigenvalue (m) and a taper angle (φ.sub.0) of the resonator:

[00015]$m=\frac{n\pi }{{\phi }_0}\mathrm{where}n=0,1,2,\mathrm{.Math.}$

[0320] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), a polar wave equation (P.sub.l.sup.m(cos θ)), and a polar wave equation (Q.sub.l.sup.m(cos θ)) of the resonator:

[00016]${\left[P_l^m\left(\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(-\cos \frac{{\theta }_0}{2}\right)-P_l^m\left(-\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(\cos \frac{{\theta }_0}{2}\right)\right]}_{\theta ={\theta }_0}=0$

[0321] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[00017]${\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=0}=0{\mathrm{and}\left[\frac{d}{dr}\left[\left(kr\right)j_l\left(kr\right)\right]\right]}_{r=r_1}=0$

[0322] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), and a radial wave equation (j.sub.l(kr)) of the resonator:

[(kr)j.sub.l(kr)].sub.r=0=0 or [(kr)j.sub.l(kr)].sub.r=r.sub.1=0

[0323] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00018]$f=\frac{kc}{2\pi }$

[0324] FIGS. 36 and 37 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 38 and 39 are non-limiting exemplary plots of a first and a second transverse magnetic polar eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 40 and 41 are non-limiting exemplary plots of a first and a second transverse magnetic radial eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 42 and 43 are non-limiting exemplary plots of a first and a second transverse magnetic evanescent radial eigenfunction of a pyramidal cavity resonator, respectively.

[0325] FIG. 86 is an exemplary perspective view of a first transverse magnetic three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator. FIG. 87 is an exemplary perspective view of a first transverse magnetic three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0326] FIG. 88 is an exemplary axial cross section view of a first electric field transverse magnetic density plot of a non-limiting pyramidal cavity resonator. FIG. 89 is an exemplary axial cross section view of a first magnetic field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator.

[0327] FIG. 90 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator. FIG. 91 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0328] FIG. 92 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting pyramidal cavity resonator. FIG. 93 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0329] FIG. 98 is an exemplary perspective view of a second transverse magnetic three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator. FIG. 99 is an exemplary perspective view of a second transverse magnetic three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0330] FIG. 100 is an exemplary axial cross section view of a second electric field transverse magnetic density plot of a non-limiting pyramidal cavity resonator. FIG. 101 is an exemplary axial cross section view of a second magnetic field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator.

[0331] FIG. 102 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator. FIG. 103 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0332] FIG. 104 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting pyramidal cavity resonator. FIG. 105 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting pyramidal cavity resonator comprising a substantially flat base interior surface.

[0333] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting pyramidal cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from one or more of the at least three tapered interior surfaces.

Example 7—Transverse Electric Wave Frequency of a Truncated Pyramidal Cavity Resonator

[0334] In some embodiments, a frequency of a hollow pyramidal cavity resonator is calculated per the equations below:

[0335] For an azimuthal eigenvalue (m) and a taper angle (φ.sub.0) of the resonator:

[00019]$m=\frac{n\pi }{{\phi }_0}\mathrm{where}n=0,1,2,\mathrm{.Math.}$

[0336] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), a polar wave equation (P.sub.l.sup.m(cos θ)), and a polar wave equation (Q.sub.l.sup.m(cos θ)) of the resonator:

[00020]${\left[\frac{d}{d\theta }\left[P_l^m\left(\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(-\cos \frac{{\theta }_0}{2}\right)-P_l^m\left(-\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(\cos \frac{{\theta }_0}{2}\right)\right]\right]}_{\theta ={\theta }_0}=0$

[0337] For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radial length (r.sub.0), a radial length (r.sub.1), and a radial wave equation (h.sub.l(kr)) of the resonator:

[(kr)h.sub.l(kr)].sub.r=r.sub.0=0 and [(kr)h.sub.l(kr)].sub.r=r.sub.1=0

[0338] For a radial eigenvalue (k), a polar eigenvalue (l), a radial length (r.sub.1), a truncated radial length (r.sub.0), and a radial wave equation (h.sub.l(kr)) of the resonator:

[00021]${\left[\frac{d}{dr}\left[\left(kr\right)h_l\left(kr\right)\right]\right]}_{r=0}=0{\mathrm{or}\left[\frac{d}{dr}\left[\left(kr\right)h_l\left(kr\right)\right]\right]}_{r=r_1}$

[0339] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00022]$f=\frac{kc}{2\pi }$

[0340] FIGS. 36 and 37 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 44 and 45 are non-limiting exemplary plots of a first and a second transverse electric polar eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 46 and 47 are non-limiting exemplary plots of a first and a second transverse electric radial eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 48 and 49 are non-limiting exemplary plots of a first and a second transverse electric evanescent radial eigenfunction of a pyramidal cavity resonator, respectively.

[0341] FIG. 110 is an exemplary perspective view of a first transverse electric three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator. FIG. 111 is an exemplary perspective view of a first transverse electric three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0342] FIG. 112 is an exemplary axial cross section view of a first electric field transverse electric density plot of a non-limiting pyramidal cavity resonator. FIG. 113 is an exemplary axial cross section view of a first magnetic field transverse electric vector plot of a non-limiting pyramidal cavity resonator.

[0343] FIG. 118 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting truncated pyramidal cavity resonator. FIG. 119 is an exemplary radial cross section view of a first electric field transverse electric vector plot of a non-limiting truncated pyramidal resonator comprising a substantially flat base and truncated interior surfaces.

[0344] FIG. 120 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting truncated pyramidal cavity resonator. FIG. 121 is an exemplary radial cross section view of a first magnetic field transverse electric vector plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0345] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting pyramidal cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from the base interior surface.

Example 8—Transverse Magnetic Wave Frequency of a Truncated Pyramidal Cavity Resonator

[0346] In some embodiments, a frequency of a hollow pyramidal cavity resonator is calculated per the equations below:

[0347] For an azimuthal eigenvalue (m) and a taper angle (φ.sub.0) of the resonator:

[00023]$m=\frac{n\pi }{{\phi }_0}\mathrm{where}n=0,1,2,\mathrm{.Math.}$

[0348] For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle (θ.sub.0), a polar wave equation (P.sub.l.sup.m(cos θ)), and a polar wave equation (Q.sub.l.sup.m(cos θ)) of the resonator:

[00024]${\left[P_l^m\left(\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(-\cos \frac{{\theta }_0}{2}\right)-P_l^m\left(-\cos \frac{{\theta }_0}{2}\right)Q_l^m\left(\cos \frac{{\theta }_0}{2}\right)\right]}_{\theta ={\theta }_0}=0$

[0349] For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radial length (r.sub.0), a radial length (r.sub.1), and a radial wave equation (h.sub.l(kr)) of the resonator:

[00025]${\left[\frac{d}{dr}\left[\left(\mathrm{kr}\right)h_l\left(kr\right)\right]\right]}_{r=r_0}=0{\mathrm{and}\left[\frac{d}{dr}\left[\left(kr\right)h_l\left(kr\right)\right]\right]}_{r=r_1}=0$

[0350] For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radial length (r.sub.0), a radial length (r.sub.1), and a radial wave equation (h.sub.l(kr)) of the resonator:

[(kr)h.sub.l(kr)].sub.r=r.sub.0=0 or [(kr)h.sub.l(kr)].sub.r=r.sub.1=0

[0351] For a frequency (f), a radial eigenvalue (k), and a speed of light (c) of the resonator:

[00026]$f=\frac{kc}{2\pi }$

[0352] FIGS. 36 and 37 are non-limiting exemplary plots of a first and a second azimuthal eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 38 and 39 are non-limiting exemplary plots of a first and a second transverse magnetic polar eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 40 and 41 are non-limiting exemplary plots of a first and a second transverse magnetic radial eigenfunction of a pyramidal cavity resonator, respectively. FIGS. 42 and 43 are non-limiting exemplary plots of a first and a second transverse magnetic evanescent radial eigenfunction of a pyramidal cavity resonator, respectively.

[0353] FIG. 86 is an exemplary perspective view of a first transverse magnetic three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator. FIG. 87 is an exemplary perspective view of a first transverse magnetic three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0354] FIG. 88 is an exemplary axial cross section view of a first electric field transverse magnetic density plot of a non-limiting pyramidal cavity resonator. FIG. 89 is an exemplary axial cross section view of a first magnetic field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator.

[0355] FIG. 94 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting truncated pyramidal cavity resonator. FIG. 95 is an exemplary radial cross section view of a first electric field transverse magnetic vector plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0356] FIG. 96 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting truncated pyramidal cavity resonator. FIG. 97 is an exemplary radial cross section view of a first magnetic field transverse magnetic density plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0357] FIG. 98 is an exemplary perspective view of a second transverse magnetic three-dimensional electric field vector plot of a non-limiting pyramidal cavity resonator. FIG. 99 is an exemplary perspective view of a second transverse magnetic three-dimensional magnetic field vector plot of a non-limiting pyramidal cavity resonator.

[0358] FIG. 100 is an exemplary axial cross section view of a second electric field transverse magnetic density plot of a non-limiting pyramidal cavity resonator. FIG. 101 is an exemplary axial cross section view of a second magnetic field transverse magnetic vector plot of a non-limiting pyramidal cavity resonator.

[0359] FIG. 106 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting truncated pyramidal cavity resonator. FIG. 107 is an exemplary radial cross section view of a second electric field transverse magnetic vector plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0360] FIG. 108 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting truncated pyramidal cavity resonator. FIG. 109 is an exemplary radial cross section view of a second magnetic field transverse magnetic density plot of a non-limiting truncated pyramidal cavity resonator comprising a substantially flat base and truncated interior surfaces.

[0361] As the size of the arrows in the above figures are positively correlated with an electric field and an electric field density, or with a magnetic field and a magnetic field density, the non-limiting pyramidal cavity resonator exhibits one or both a highly asymmetric electric field and a highly asymmetric electric field density, and a highly asymmetric magnetic field and a highly asymmetric magnetic field density, wherein the electric field and the electric field density, and the magnetic field and the magnetic field density, are more concentrated away from one or more of the at least three tapered interior surfaces and the truncated interior surface.

Terms and Definitions

[0362] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.

[0363] As used herein, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.

[0364] As used herein, the term “about” refers to an amount that is near the stated amount by about 10%, 5%, or 1%, including increments therein.

[0365] The embodiments of the invention described above are intended to be merely exemplary; numerous variations and modifications will be apparent to those skilled in the art. Such variations and modifications are intended to be within the scope of the present invention as defined by any of the appended claims.