OPTICAL STRUCTURE FOR IMPARTING A DISTRIBUTED PHASE SHIFT TO AN OPTICAL SIGNAL, ELECTRO-OPTIC MODULATOR INCORPORATING SUCH STRUCTURE FOR REDUCED SIZE, LOW SIGNAL LOSS, AND HIGH EXTINCTION RATIO, AND RELATED SYSTEM AND METHOD

Abstract

An embodiment of an optical structure includes a core having first and second ends and a first side with a first grating profile having a first phase shift distributed between the first and second ends, and a cladding disposed around the core. Such an optical structure can be used in an electro-optic modulator (EOM), and can render the EOM smaller in size than currently available EOMs.

Claims

1. An optical structure, comprising: a core having first and second ends and a first side with a first grating profile having a first phase shift distributed between the first and second ends; and a cladding disposed around the core.

2. The optical structure of claim 1 wherein: the core includes lithium niobate; and the cladding includes silicon dioxide.

3. The optical structure of claim 1 wherein the first grating profile includes a sinusoidal grating profile.

4. The optical structure of claim 1 wherein the first phase shift is 180 of a spatial wavelength of the first grating profile.

5. The optical structure of claim 1 wherein the first grating profile has one half of the first phase shift distributed between the first end of the core and a midpoint between the first and second ends of the core, and has another half of the first phase shift distributed between the midpoint and the second end of the core.

6. The optical structure of claim 1 wherein the first phase shift is distributed linearly between the first and second ends of the core.

7. The optical structure of claim 1 wherein the core includes a second side with a second grating profile having a second phase shift distributed between the first and second ends of the core.

8. The optical structure of claim 1 wherein the core includes a second side with the first grating profile.

9. The optical structure of claim 1 wherein the first grating profile has a uniform amplitude between the first and second ends of the core.

10. A electro-optic modulator, comprising: an optical structure, including first and second ends, a core having a first side with a first grating profile having a first phase shift distributed between the first and second ends, and a cladding disposed around the core; a first electrode disposed adjacent to the first side of the core; and a second electrode disposed adjacent to a second side of the core, the second side being opposite the first side.

11. The electro-optic modulator of claim 10 wherein the second side of the core has a second grating profile having a second phase shift distributed between the first and second ends of the optical cavity.

12. The electro-optic modulator of claim 11 wherein: the second grating profile is approximately the same as the first grating profile; the second phase shift is approximately the same as the first phase shift; and the second phase shift is distributed between the first and second ends in a manner similar to a manner in which the first phase shift is distributed between the first and second ends.

13. The electro-optic modulator of claim 11 wherein first and second phase shifts are each distributed approximately uniformly between the respective first and second ends.

14. The electro-optic modulator of claim 10 wherein: the optical structure is configured to resonate at an optical frequency in response to a first voltage between the first and second electrodes; and the optical structure is configured to attenuate an optical signal at the optical frequency in response to a second voltage between the first and second electrodes.

15. The electro-optic modulator of claim 10, further comprising: a first reflector disposed at the first end of the optical structure and configured to impart a second phase shift to an optical signal propagating in the structure; a second reflector disposed at the second end of the optical structure and configured to impart a third phase shift to the optical signal; and wherein a combination of the optical structure, the first reflector, and the second reflector is configured to resonate at an optical wavelength in response to a sum of the first, second, and third phase shifts equaling 360 of the optical wavelength.

16. The electro-optic modulator of claim 10, further comprising: a first Bragg reflector disposed at the first end of the optical structure and configured to impart, to an optical signal propagating in the structure, a phase shift of approximately 180 of a spatial wavelength of the first grating profile; a second Bragg reflector disposed at the second end and configured to impart, to the optical signal, a phase shift of approximately 180 of the spatial wavelength of the first grating profile; and wherein the optical structure is configured to impart, to the optical signal, a phase shift equal to approximately 180 of the spatial wavelength to the optical signal.

17.-20. (canceled)

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0042] FIG. 1 is a diagram of a binary optical switch that is configured to convert an electrical binary signal to an optical binary signal.

[0043] FIG. 2 is an isometric view of a Phase Shift Bragg resonator that can be used as the electro-optic modulator (EOM) of FIG. 1.

[0044] FIG. 3 is a plot of the grating profile versus position along the core of the Phase Shift Bragg resonator of FIG. 2.

[0045] FIG. 4 is a plot of normalized reflection (loss) of an optical signal propagating in the Phase Shift Bragg resonator of FIG. 2 versus the free-space wavelength of the optical signal.

[0046] FIG. 5 is an isometric view of a Phase Shift Bragg resonator having a core with an apodized grating profile that provides increased values for Q and extinction ratio as compared to the Phase Shift Bragg resonator of FIG. 2.

[0047] FIG. 6 is a plot of the apodized grating profile of the core of the Phase Shift Bragg resonator of FIG. 5 versus position along the core.

[0048] FIG. 7 is a plot of normalized reflection (loss) of an optical signal propagating in the Phase Shift Bragg resonator of FIG. 5 versus the free-space wavelength of the optical signal.

[0049] FIG. 8 is a plot of transmission levels of an optical signal propagating in the Phase Shift Bragg resonator of FIG. 5 versus the free-space wavelength of the optical signal at selected lengths of the apodized core of the resonator.

[0050] FIG. 9 is an isometric view of a distributed-phase-shift resonator, according to an embodiment.

[0051] FIG. 10 is a plot of an embodiment of a grating profile of the core of the distributed-phase-shift resonator of FIG. 9 overlaying the grating profile of the apodized core of the Phase Shift Bragg resonator of FIG. 5.

[0052] FIG. 11 is a plot of transmission levels of an optical signal propagating in the distributed-phase-shift Bragg resonator of FIG. 9 versus the free-space wavelength of the optical signal at selected lengths of the resonator core, according to an embodiment.

[0053] FIG. 12 is a plot of wavelength response of the distributed-phase-shift resonator of FIG. 9, according to an embodiment.

[0054] FIG. 13 is a plot of the intensity level of an optical signal propagating in the distributed-phase-shift resonator of FIG. 9 during a resonant mode versus position along the resonator, according to an embodiment.

[0055] FIG. 14 is diagram of a system including an optical binary switch that incorporates one or more of the distributed-phase-shift resonator of FIG. 9, according to an embodiment.

DETAILED DESCRIPTION

[0056] Unless otherwise noted, a value, quantity, or attribute herein preceded by substantially, approximately, about, a form or derivative thereof, or a similar term, encompasses a range that includes the value, quantity, or attribute 20% of the value, quantity, or attribute, and a range of values preceded by such a term includes the range extended by 20% of the difference between the range endpoints. For example, an approximate range of b to c is a range of b20%.Math.(cb) to c+20%.Math.(cb). Furthermore, the terms a, an, and the can indicate one or more than one of the objects that they modify.

[0057] FIG. 9 is an isometric view of a distributed-phase-shift resonator 90, according to an embodiment. The resonator 90 includes a core 92 having ends 94.sub.a and 94.sub.b, reflectors 96 and 98, electrodes 100 and 102, and a cladding (not shown in FIG. 9) disposed around the core and the reflectors. The core 92 has a sinusoidal distributed-phase-shift grating profile 104 along two sides 106.sub.a and 106.sub.b of the core, and each reflector 96 and 98 has a non-phase-shift grating profile 108 along two sides 110a, 110b, and 112a, 112b, respectively. The combination of the core 92 and the cladding (not shown in FIG. 9) between the core ends 94.sub.a and 94.sub.b forms an optical structure, and the optical structure, and possibly portions of the reflectors 96 and 98 adjacent to the core, form an optical cavity.

[0058] FIG. 10 is a plot 120 of the two instances of the grating profile 104 along the sides 106.sub.a and 106.sub.b of the core 92 of FIG. 9, according to an embodiment, and, two instances of a potential apodized grating profile 122 respectively overlaying the two instances of the grating profile 104 for purposes of comparison (potential indicates that the core 92 does not actually have the apodized grating profile, but if it were to have an apodized grating profile, it could be like the profile 122). In this example, the length l of the core 92 is 8.0 m, the width w of the core between the vertical centers (e.g., zero crossings) of the two instances of the grating profile 104 is 10.0 m, and the thickness, i.e., height h, of the core is 600 nm. Furthermore, the potential apodized grating profile 122 is similar to the apodized grating profile 54 of FIGS. 5-6 in that it has an abrupt phase shift of 180 at a center location 124 and the peak-to-peak amplitude decreases linearly from the right and left sides of the plot 120 toward the center location. Moreover, the spatial wavelengths of the grating profiles 104, 108, and 122 are equal to 1550 nm/2.Math..sub.effective, although the grating profile 108 of the resonators 96 and 98 exhibits no spatial phase shift. In this example, .sub.effective has a value that is between the refractive index .sub.core of the material (e.g., lithium niobate) from which the core 92 is formed and the refractive index .sub.cladding of the material from which the cladding (not shown in FIG. 9) is formed, at the waveguide mode excited by an optical signal having a free-space wavelength of 1550 nm. In addition to depending on the refractive indices .sub.core and .sub.cladding, the value of .sub.effective depends on the geometry of the optical structure (e.g., the shape of the core disregarding the grating profile 104, which shape would be a rectangle l=8 m long, w=10 m wide, and h=600 nm high), the wavelength of the exciting optical signal, and the spatial parameters (e.g., wavelength, amplitude, phase shift) of the grating profile.

[0059] Referring to FIGS. 9-10, major differences between the distributed-phase-shift grating profile 104 and the apodized grating profile 122 include that the distributed-phase-shift grating profile ideally has a uniform peak-to-peak amplitude, and that instead of having an abrupt phase shift of 180, the distributed-phase-shift grating profile has a phase shift of 180 that is linearly distributed over the length l of the core 92. Further to the latter difference, at the 4 m position (end 94.sub.a in FIG. 9) of the core 92, the spatial phases of the grating profiles 104 and 122 are equal; at the center location 124, the apodized grating profile undergoes an abrupt 180 spatial phase shift, while the distributed-phase-shift grating profile has linearly accumulated a spatial phase shift of 90; and at the rightmost +4 m position (end 94.sub.b in FIG. 9) the spatial phase of the distributed-phase-shift grating profile has linearly accumulated another spatial phase shift of 90 such that both the distributed-phase-shift and apodized grating profiles have accumulated the same 180 phase shift relative to their phases at the 4 m position.

[0060] FIG. 11 is a plot 130 of the transmission levels of the distributed-phase-shift resonator 90 of FIG. 9 versus wavelength at selected core lengths l=8 m and l=12 m, according to an embodiment.

[0061] Referring to FIGS. 5, 8, 9, and 11, the core 92, with its distributed-phase-shift grating profile 104, can provide transmission levels of almost unity for core lengths l=8 m and l=12 m, which lengths are, respectively, about half of the core lengths l=16 m and l=20 m that the core 52, with its apodized grating profile 54, needs to provide similarly high transmission levels.

[0062] Consequently, the core 92, with its distributed-phase-shift grating profile 104, can be significantly shorter than the core 52 with its apodized grating profile 54, yet can provide transmission levels equivalent to those provided by the apodized core 52.

[0063] And because it can incorporate a shorter core 92, the distributed-phase-shift resonator 90 can be shorter overall than the apodized Phase Shift Bragg resonator 50 of FIG. 5.

[0064] Therefore, the distributed-phase-shift resonator 90 may be suitable for applications that call for an electro-optic modulator that is smaller than the apodized Phase Shift Bragg resonator 50 of FIG. 5.

[0065] Referring to FIGS. 9 and 11, the resonant free-space wavelength .sub.0,r for which the resonator 90 is designed for a transmission-level voltage (e.g., logic 1, as opposed to a blocking-level voltage, e.g., logic 0) across the electrodes 100 and 102 is slightly different than a sometimes-desired wavelength of 1550 nm, which, in this example, is equal to 2.Math..Math.n.sub.effective, where, as described above, is the spatial wavelength of the grating profile 104. That is, the grating profile 104 having a particular spatial wavelength slightly shifts the actual free-space resonant wavelength .sub.0,r of the resonator 90 from the desired free-space resonant wavelength 2.Math..Math.n.sub.effective. One way to account for this shift in .sub.0,r is to reduce the spatial wavelength of the grating profile 104 to a value that causes the actual resonant wavelength .sub.0,r to equal the desired wavelength, e.g., 1550 nm. Another way to account for this shift in .sub.0,r is to use a tunable light source (e.g., a tunable cavity laser) to generate the input optical signal, and to tune the light source to generate the input optical signal to have the resonant wavelength .sub.0,r of the resonator 90 while the resonator is in a transmissive (resonant) mode.

[0066] Referring to FIGS. 9-10, design and operation of the distributed-phase-shift resonator 90 is described, according to an embodiment.

[0067] First, a designer determines the resonant free-space wavelength .sub.0,r that he/she wants the resonator 90 to have for a transmission-level voltage (e.g., logic 1, as opposed to a blocking-level voltage, e.g., logic 0). The designer determines the length l, width w, and thickness/height h of the core 92, and the respective materials from which he/she wants the core and cladding (not shown in FIGS. 9-10) to be formed. The length l can be of any suitable value, for example, in an approximate range of 4 m-25 m, the width w can be of any suitable value, for example, in an approximate range of 1 m-5 m, and the height h can be of any suitable value, for example, in an approximate range of 300-1000 nm. Furthermore, the core and cladding each can be formed from any suitable material, examples of which include lithium niobate, silicon, silicon nitride, silicon germanium, germanium, gallium nitride, gallium arsenide, and diamond. Next, in response to the dimensions of the core 92 and the cladding, the indices of refraction .sub.pore and .sub.cladding of the materials respectively used to form the core and the cladding, and the desired .sub.0,r, the designer determines, in a conventional manner, the effective refractive index .sub.effective of the resonator 90 without a grating profile.

[0068] Next, the designer sets a value of the spatial wavelength of the grating profile 104 equal to .sub.0,r/(2.Math..sub.effective).

[0069] Then, according to an embodiment, the designer accounts for the grating profile 104 causing the actual value of the resonant wavelength .sub.0,r to be different from the value determined according to the preceding paragraph by specifying that a light source used to excite the resonator 90 be tunable to the actual value of the resonant wavelength .sub.0,r.

[0070] Alternatively, according to another embodiment, using conventional computer-simulation or other analytical techniques, the designer determines, for the grating profile 104, a value of the spatial wavelength that is slightly different (e.g., within 1%) than the desired value .sub.0,r/(2.Math..sub.effective) but that causes .sub.0,r to have the desired value. Said another way, the designer uses computer simulation or other analytical techniques to tweak the spatial wavelength of the grating profile 104 so that the resonator 90 has a resonant wavelength equal to the desired resonant wavelength .sub.0,r (e.g., 1550 nm)

[0071] Then, the designer determines the dimensions of the sinusoidal grating profile 104. The designer sets the spatial wavelength as described in the preceding paragraphs. The designer sets the peak-to-peak amplitude of the grating profile 104 to any suitable value, such as a value in an approximate range of 500 nm-5000 nm, where the maximum allowable value of the peak-to-peak amplitude depends on the width w of the core 92. And the designer determines how to distribute the 180 phase shift of the grating profile 104 across the length l of the core 92. For example, the phase shift may be distributed linearly as shown in FIGS. 9-10. Examples of other phase distributions include exponential phase distribution, sinusoidal phase distribution, and discrete-step phase distribution.

[0072] Next, the designer determines the dimensions and other parameters of the reflectors 96 and 98. For example, each reflector 96 has the same width w and height h as the core 92, and the grating profile 108 has the same spatial wavelength as the grating profile 104 of the core, but without a phase shift. The designer determines other parameters of each of the reflectors 96 and 96, such as the length, materials, refractive indices of the materials, and arrangement of the materials in a conventional manner. For example, each reflector 96 and 98 may be a Bragg reflector having a length that is much greater than the length l of the core 92.

[0073] Then, if he/she has not already done so, the designer chooses a cladding material for disposition around the core 92 and reflectors 96 and 98. Examples of cladding material include silicon dioxide, silicon nitride, gallium nitride, and diamond. As described above, to increase the precision of the determination of , the designer may choose the cladding material before determining the value for so that the designer can consider any effect that the cladding material or its effective refractive index may have on .

[0074] Referring to FIG. 9, operation is described for an embodiment of the resonator 90 in which the core 92 has the following parameters: l=8 m, w=2.0 m, h=600 nm, desired resonant transmission wavelength is 2.Math..Math..sub.effective=1550 nm, actual resonant wavelength .sub.0,r=1552.5 nm, and a 180 phase shift linearly distributed between the ends 94.sub.a and 94.sub.b of the core.

[0075] During a transmission mode of operation, a drive circuit (not shown in FIG. 11) applies a transmission-level voltage (e.g., a logic 1 level) across the electrodes 100 and 102 to configure the resonator 90 to resonate at .sub.0,r=1552.5 nm.

[0076] A wave front of an optical signal (e.g., from a tunable cavity laser) having a free-space wavelength of 1552.5 nm enters one of the reflectors 96 and 98, for example, the reflector 96.

[0077] The wave front accumulates an approximate 180 phase shift as it propagates through the core 92 to the reflector 98.

[0078] The reflector 98 redirects a portion of the wave front signal back into the core 92, and imparts to the redirected portion a phase shift of either approximately 0 or 180, depending upon its structure. As is known, the reflector 98 may not redirect all of the redirected signal energy of the wave front at the interface between the core 92 and the reflector; portions of the wave front may propagate respective distances into the reflector before being redirected. These redirected portions effectively interfere with one another at the interface between the reflector 98 and the core 92 to form a redirected wave front that propagates back into the core.

[0079] The remaining portion of the wave front of the optical signal continues propagating through the reflector 98 and to, for example, an output port of a binary switch, such as the output port 24 of the optical switch 10 of FIG. 1.

[0080] The once-redirected portion of the wave front of the optical signal accumulates another approximately 180 of phase shift as it propagates back through the core 92.

[0081] Upon reaching the end 94.sub.a of the core 92, the reflector 96 redirects a portion of the once-redirected wave front back into the core in a manner similar to that described above for the reflector 98, and imparts to the twice-redirected wave front a phase shift of either approximately 0 or 180 such that the twice-redirected wave front has accumulated a total phase shift of m.Math.360, where m=1 or 2. Because the twice-redirected portion of the wave front constructively interferes with, and, therefore, reinforces, the optical signal entering the core 92 from the optical source (not shown in FIG. 9) via the reflector 96, an oscillation, or resonance, occurs within the core 92, and potentially within portions of the reflectors 96 and 96 adjacent to the core for reasons described above. It is these portions of the reflectors 96 and 98 in which resonance occurs, along with the core 92 and the cladding material around the core and the reflector portions, that forms a resonant optical cavity.

[0082] A result of this resonant operation, or resonant waveguide mode, is that propagating out from the reflector 98 in a direction away from the core 92 is an output optical signal having an output power that is approximately the same as the input power minus signal loss incurred in the resonator 90.

[0083] Furthermore, during resonant operation, little or no signal power is redirected by the core 92 back through the reflector 96 toward the optical source (not shown in FIG. 9).

[0084] Consequently, the extinction ratio of output power/redirected power is relatively high as is desired.

[0085] During a blocking mode of operation, the drive circuit (not shown in FIG. 11) applies a blocking-level voltage (e.g., a logic 0 level) across the electrodes 100 and 102 to configure the resonator 90 to resonate at a wavelength that is significantly different from .sub.0,r=1552.5 nm.

[0086] An optical signal (e.g., from a tunable cavity laser) having a free-space wavelength of 1552.5 nm enters one of the resonators 96 and 98, for example, the resonator 96.

[0087] The core 92 acts as a high impedance to the optical signal, and, therefore, redirects most of the energy of the optical signal back into the reflector 96 such that little or no optical energy propagates to and out through the reflector 98.

[0088] Therefore, propagating out from the reflector 98 in a direction away from the core 92 is an output optical signal having an output power that is approximately zero.

[0089] Furthermore, most of the signal power is redirected by the core 92 back through the reflector 96 toward the optical source (not shown in FIG. 9) and, for example, out of a signal-coupled port such as the port 22 of the binary switch 10 of FIG. 1.

[0090] Consequently, as in the transmission mode, in the blocking mode the extinction ratio redirected power/output power is relatively high as is desired.

[0091] Referring to FIGS. 9-11, alternate embodiments of the distributed-phase-shift Bragg resonator 90 are contemplated. For example, although shown as being sinusoidal, the grating profile 104 can have a shape other than sinusoidal. Furthermore, the respective amount of phase shift that each of the core 92 and reflectors 96 and 98 impart to the optical signal can be different than described above as long as the round-trip phase shift from one point back to the same point is an integer multiple of 360. Moreover, although the grating profile 104 is shown as being the same on both sides 106.sub.a and 106.sub.b of the core 92, the grating profile can be on only one side, or each side can have a different grating profile. In addition, one or both of the top and bottom of the core 92 can be grated. Similarly, although the grating profile 108 is shown as being the same on both sides of each reflector 96 and 98, the grating profile can be on only one side, or each side can have a different grating profile. Furthermore, one or both of the top and bottom of each reflector 96 and 98 can be grated.

[0092] FIG. 12 is a plot 140 of the wavelength response of the distributed-phase-shift resonator 90 of FIG. 9, according to an embodiment where .sub.0,r=1550 nm. Because the resonator 90 effectively has only a single defect (the core 92 imparts a 180 phase shift), the resonator supports only a single resonant mode in the vicinity of .sub.0,r.

[0093] FIG. 13 is a plot 150 of field intensity versus position along the core 92 and reflectors 96 and 98 of the distributed-phase-shift resonator 90 of FIG. 9 during a transmission mode, according to an embodiment in which the length 1 of the core 92 is 8 m. Most of the resonant behavior (higher levels of signal intensity) occurs within the core 92, although some resonant behavior occurs up to a distance of about 1 m into each of the reflectors 96 and 98. The distance into the reflectors 96 and 98 in which resonant behavior occurs is a function of the construction of the reflectors, and a designer can make this distance smaller or larger than 1 m by appropriately configuring the resonators in a conventional manner.

[0094] FIG. 14 is a diagram of a system 160 including one or more of an optical binary switch 162, which incorporates the distributed-phase-shift resonator 90 of FIG. 9, according to an embodiment.

[0095] The system 160 includes a subsystem 164. Examples of the system 160 include a vehicle such as an aircraft, spacecraft, watercraft, submarine, land vehicle, unmanned vehicle such as a drone, or a missile. Examples of the subsystem 164 include a navigation subsystem, flight-management subsystem, communications subsystem, and sensor subsystem.

[0096] The subsystem 164 includes one or more of the optical binary switch 162, which may be similar to the optical binary switch 10 of FIG. 1 except that the switch 162 includes the distributed-phase-shift resonator 90 of FIG. 9 as the electro-optic modulator 26. For example, an optical binary switch 162 may be disposed on an integrated circuit and may provide communications between the integrated circuit and an apparatus or device external to the integrated circuit.

[0097] From the foregoing, it will be appreciated that, although specific embodiments have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the disclosure. Furthermore, where an alternative is disclosed for a particular embodiment, this alternative may also apply to other embodiments even if not specifically stated. Moreover, the circuit components described above may be disposed on a single or multiple integrated-circuit (IC), a digital signal processor (DSP), a filter and detect (FAD) circuit, integrated-photonic (IP) dies, or radio-frequency-over-glass (RFOG) dies to form one or more ICs/IPs/RFOGs/DSP/FAD, where these one or more ICs/IPs/RFOGs/DSP/FAD may be coupled to one or more other ICs/IPs/RFOGs/DSP/FAD. Furthermore, one or more components of a described apparatus or system may have been omitted from the description for clarity or another reason. Moreover, one or more components of a described apparatus or system that have been included in the description may be omitted from the apparatus or system.

Example Embodiments

[0098] What is Exampleed is:

[0099] Example 1 includes an optical structure, comprising: a core having first and second ends and a first side with a first grating profile having a first phase shift distributed between the first and second ends; and a cladding disposed around the core.

[0100] Example 2 includes the optical structure of Example 1 wherein: the core includes lithium niobate; and the cladding includes silicon dioxide.

[0101] Example 3 includes the optical structure of any of Examples 1-2, wherein the first grating profile includes a sinusoidal grating profile.

[0102] Example 4 includes the optical structure of any of Example 1-3, wherein the first phase shift is 180 of a spatial wavelength of the first grating profile.

[0103] Example 5 includes the optical structure of any of Examples 1-4, wherein the first grating profile has one half of the first phase shift distributed between the first end of the core and a midpoint between the first and second ends of the core, and has another half of the first phase shift distributed between the midpoint and the second end of the core.

[0104] Example 6 includes the optical structure of any of Examples 1-5, wherein the first phase shift is distributed linearly between the first and second ends of the core.

[0105] Example 7 includes the optical structure of any of Examples 1-6, wherein the core includes a second side with a second grating profile having a second phase shift distributed between the first and second ends of the core.

[0106] Example 8 includes the optical structure of any of Examples 1-7, wherein the core includes a second side with the first grating profile.

[0107] Example 9 includes the optical structure of any of Examples 1-8, wherein the first grating profile has a uniform amplitude between the first and second ends of the core.

[0108] Example 10 includes A electro-optic modulator, comprising: an optical structure, including first and second ends, a core having a first side with a first grating profile having a first phase shift distributed between the first and second ends, and a cladding disposed around the core; a first electrode disposed adjacent to the first side of the core; and a second electrode disposed adjacent to a second side of the core, the second side being opposite the first side.

[0109] Example 11 includes the electro-optic modulator of Example 10, wherein the second side of the core has a second grating profile having a second phase shift distributed between the first and second ends of the optical cavity.

[0110] Example 12 includes the electro-optic modulator of any of Examples 10-11, wherein: the second grating profile is approximately the same as the first grating profile; the second phase shift is approximately the same as the first phase shift; and the second phase shift is distributed between the first and second ends in a manner similar to a manner in which the first phase shift is distributed between the first and second ends.

[0111] Example 13 includes the electro-optic modulator of any of Examples 10-12, wherein first and second phase shifts are each distributed approximately uniformly between the respective first and second ends.

[0112] Example 14 includes the electro-optic modulator of any of Examples 10-13, wherein: the optical structure is configured to resonate at an optical frequency in response to a first voltage between the first and second electrodes; and the optical structure is configured to attenuate an optical signal at the optical frequency in response to a second voltage between the first and second electrodes.

[0113] Example 15 includes the electro-optic modulator of any of Examples 10-14, further comprising: a first reflector disposed at the first end of the optical structure and configured to impart a second phase shift to an optical signal propagating in the structure; a second reflector disposed at the second end of the optical structure and configured to impart a third phase shift to the optical signal; and wherein a combination of the optical structure, the first reflector, and the second reflector is configured to resonate at an optical wavelength in response to a sum of the first, second, and third phase shifts equaling 360 of the optical wavelength.

[0114] Example 16 includes the electro-optic modulator of any of Examples 10-15, further comprising: a first Bragg reflector disposed at the first end of the optical structure and configured to impart, to an optical signal propagating in the structure, a phase shift of approximately 180 of a spatial wavelength of the first grating profile; a second Bragg reflector disposed at the second end and configured to impart, to the optical signal, a phase shift of approximately 180 of the spatial wavelength of the first grating profile; and wherein the optical structure is configured to impart, to the optical signal, a phase shift equal to approximately 180 of the spatial wavelength to the optical signal.

[0115] Example 17 includes A method, comprising: causing an optical structure to pass an optical signal by causing a wavelength of the optical signal in the optical structure to be approximately equal to twice a spatial wavelength of a grating profile of a side of a core of the optical structure, the grating profile having a phase shift distributed along the side of the core; and causing the optical structure to block the optical signal by causing the wavelength of the optical signal in the optical structure to be different from twice the spatial wavelength.

[0116] Example 18 includes the method of Example 17, wherein: causing the optical structure to pass the optical signal includes generating a first voltage across the optical structure; and causing the optical structure to block the optical signal includes generating a second voltage across the optical structure.

[0117] Example 19 includes the method of any of Examples 17-18, wherein: causing the optical structure to pass the optical signal includes causing the wavelength of the optical signal to equal a resonant wavelength of the structure; and causing the optical structure to block the optical signal includes causing the wavelength of the optical signal to be different than the resonant wavelength of the structure.

[0118] Example 20 includes the method of any of Examples 17-19, wherein: causing the optical structure to pass the optical signal includes gradually shifting a phase of the optical signal by 180 as the optical signal propagates from one end of the optical structure to another end of the optical structure; and causing the optical structure to block the optical signal includes gradually shifting the phase of the optical signal by other than 180 as the optical signal propagates from one end of the optical structure to the other end of the optical structure.

[0119] Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement, which is calculated to achieve the same purpose, may be substituted for the specific embodiments shown. Therefore, it is manifestly intended that this invention be limited only by the claims and the equivalents thereof.