Electromagnetic waveguide transmission modulation device

Abstract

A plasmonic switching device and method of providing a plasmonic switching device. An example device includes a resonant cavity and an electromagnetic radiation feed arranged to couple electromagnetic radiation into the resonant cavity and at least one plasmonic mode. The resonant cavity is arranged to be switchable between: a first state in which the resonant cavity has an operational characteristic selected to allow resonance of the electromagnetic radiation at a frequency of the at least one plasmonic mode; and a second state in which the operational characteristic of the resonant cavity is adjusted to inhibit resonance of the electromagnetic radiation at a frequency of the at least one plasmonic mode.

Claims

1. An electromagnetic waveguide transmission modulation device comprising: at least one hyperbolic metamaterial element coupleable to a waveguide, wherein said at least one hyperbolic metamaterial element is configured to control an excitation of surface waves along said waveguide by being arranged to be adjustable between: a first mode in which said at least one hyperbolic metamaterial element is configured to support a resonant mode matched to a propagation vector of a waveguide transmission mode supported by said waveguide such that propagation of said waveguide transmission mode along said waveguide is affected; and a second mode in which said at least one hyperbolic metamaterial element is configured to inhibit support of said resonant mode matched to said propagation vector of said waveguide transmission mode, such that interruption of propagation of said waveguide transmission mode along said waveguide is prevented.

2. The device according to claim 1, wherein said at least one hyperbolic metamaterial element is arranged to be adjustable between said first mode and said second mode by means of modification of optical properties of said at least one hyperbolic metamaterial element.

3. The device according to claim 1, further comprising an adjuster, wherein said at least one hyperbolic metamaterial element is arranged to be adjustable between said first mode and said second mode by electro-optical, magneto-optical, acousto-optical or nonlinear optical interaction by said adjuster.

4. The device according to claim 1, wherein said at least one hyperbolic metamaterial element is coupled to said waveguide in a manner which enables dynamic control over transmission, reflection and/or absorption properties of said waveguide.

5. The device according to claim 1, wherein said at least one hyperbolic metamaterial element is integrally formed with said waveguide.

6. The device according to claim 1, wherein said at least one hyperbolic metamaterial element is formed adjacent said waveguide.

7. The device according to claim 1, wherein said at least one hyperbolic metamaterial element is formed in-line with said waveguide.

8. The device according to claim 1, wherein said at least one hyperbolic metamaterial element comprises: a structure comprising a support and a plurality of nanostructure elements comprising a metallic material, wherein said plurality of nanostructure elements are configured on said support to allow said structure to act as a hyperbolic metamaterial, wherein said nanostructure elements are configured to cause a change in permittivity of said hyperbolic metamaterial on application of an external trigger to adjust said device between said first mode and said second mode.

9. The device according to claim 8, wherein said hyperbolic metamaterial comprises an electromagnetic metamaterial.

10. The device according to claim 8, wherein said hyperbolic metamaterial comprises an optical metamaterial.

11. The device according to claim 8, wherein adjacent nanostructure elements are configured on said support such that they are electromagnetically coupled.

12. The device according to claim 8, wherein the plurality of nanostructure elements are configured such that the electromagnetic field of one nanostructure element spatially overlaps that of adjacent nanostructure elements.

13. The device according to claim 12, wherein said plurality of nanostructure elements are configured as an array on said support.

14. The device according to claim 13, wherein said array comprises a substantially regular array.

15. The device according to claim 14, wherein said plurality of nanostructure elements comprise a plurality of metallic nanorods.

16. The device according to claim 15, wherein said plurality of nanostructure elements are embedded within a dielectric matrix.

17. The device according claim 1, wherein the at least one hyperbolic metamaterial element comprises a plurality of hyperbolic metamaterial elements.

18. A method of providing an electromagnetic waveguide transmission modulation device comprising: coupling at least one hyperbolic metamaterial element to a waveguide; configuring said at least one hyperbolic metamaterial element to control an excitation of surface waves along said waveguide by arranging said at least one hyperbolic metamaterial element to be adjustable between: a first mode in which said at least one hyperbolic metamaterial element is configured to support a resonant mode matched to a propagation vector of a waveguide transmission mode supported by said waveguide such that propagation of said waveguide transmission mode along said waveguide is affected; and a second mode in which said at least one hyperbolic metamaterial element is configured to inhibit support of said resonant mode matched to said propagation vector of said waveguide transmission mode, such that interruption of propagation of said waveguide transmission mode along said waveguide is prevented.

19. The method of claim 18: wherein arranging said at least one hyperbolic metamaterial element to be adjustable to be adjustable between said first mode and said second mode comprises arranging said at least one hyperbolic metamaterial element by means of modification of optical properties of said at least one hyperbolic metamaterial element; and further comprising modifying said optical properties of said at least one hyperbolic metamaterial element to adjust between said first mode and said second mode.

20. An electromagnetic waveguide transmission modulation device comprising: a pair of metamaterial elements arranged in-line within a waveguide, wherein said pair of metamaterial elements are configured to control an excitation of surface waves along said waveguide by being arranged to be adjustable between: a first state in which said pair of metamaterial elements operate as ENZ metamaterial elements and form a resonant cavity within said waveguide having a transmission function which allows electromagnetic radiation of a selected frequency propagating along said waveguide to pass through said resonant cavity substantially unimpeded; and a second state in which operation of at least one of said pair of metamaterial elements as an ENZ metamaterial is prevented and the transmission function of the waveguide is modulated.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the present invention will now be described further, with reference to the accompanying drawings, in which:

(2) FIG. 1a illustrates schematically main features of a device according to one embodiment as a cross-section;

(3) FIG. 1b is a schematic top view of the device shown in FIG. 1a; FIG. 2a illustrates schematically a device such as that illustrated in FIG. 1a when in an on state;

(4) FIG. 2b illustrates schematically a device such as that illustrated in FIG. 1a when in an off state;

(5) FIG. 2c illustrates one possible example of extinction ratios obtained as a refractive index in an optical cavity of a device such as that shown in FIG. 1a is varied;

(6) FIG. 2d is a schematic illustration of a device according to one embodiment, in which electrical operation can be implemented to offer an extinction ratio in the region of between 1-2 dB if 2V is applied across a multilayer surface as illustrated;

(7) FIG. 3a illustrates schematically a device according to one embodiment;

(8) FIG. 3b illustrates schematically an example of directionality for a double slit structure such as that shown in FIG. 3a as cavity length varies;

(9) FIG. 4a illustrates schematically a multilayer system for use in a device in accordance with one embodiment;

(10) FIG. 4b illustrates schematically a device such as that illustrated in FIG. 4a when in an on state;

(11) FIG. 4c illustrates schematically a device such as that illustrated in FIG. 4a when in an off state;

(12) FIG. 4d illustrates an example of extinction ratios obtained as applied voltage is varied in a device such as that illustrated in FIG. 4a;

(13) FIG. 5a is a 3-dimensional representation of a modulator according to one embodiment;

(14) FIG. 5b illustrates schematically the modulator of FIG. 5a when in an off state;

(15) FIG. 5c illustrates schematically the modulator of FIG. 5a when in an on state;

(16) FIG. 6 is a 3-dimensional representation of a modulator according to an alternative embodiment;

(17) FIG. 7 illustrates schematically main components of a device according to one arrangement;

(18) FIG. 8 is a perspective view of a schematic representation of a device according to one arrangement;

(19) FIG. 9 is a graphic representation of optical properties of a device according to one arrangement;

(20) FIG. 10 is a graphic representation of real and imaginary parts of epsilon z according to one arrangement; and

(21) FIG. 11 is a graphic representation of optical properties of a device according to one arrangement.

DETAILED DESCRIPTION

(22) According to some aspects and embodiments, a device based on a resonant cavity structure is provided. The device is arranged such that active control of a plasmonic signal is permitted. That control is achieved by exploiting the presence of electromagnetic cavity modes in the cavity structure.

(23) FIG. 1a illustrates schematically main features of a device 10 according to one embodiment as a cross-section and FIG. 1b is a schematic top view of the device shown in FIG. 1a. According to one embodiment, the device may generally comprise: two parallel metallic films 20a, 20b, separated by a spacer layer 30. In the embodiment shown, the metallic films comprise gold films. According to this embodiment, a slit 40 is provided in the lower gold film 20a, and that slit is illuminated from beneath at normal incidence. It will be appreciated that in some embodiments, the slit need not be illuminated at normal incidence. The upper gold film 20b has a length W and width B and is spaced from the lower film 20a by a distance S. It will be understood that the example shown is substantially 2-dimensional, but that a 3-dimensional configuration may also be implemented.

(24) FIG. 2a illustrates schematically a device such as that illustrated in FIG. 1a when in an on state. FIG. 2b illustrates schematically a device such as that illustrated in FIG. 1a when in an off state. FIG. 2c illustrates one possible example of extinction ratios obtained as a refractive index in an optical cavity of a device such as that shown in FIG. 1a is varied and FIG. 2d is a schematic illustration of a device according to one embodiment, in which electrical operation can be implemented to offer an extinction ratio in the region of between 1-2 dB if 2V is applied across a multilayer structure as illustrated. Further detail regarding operation of a device as shown in FIGS. 2a to 2d is set out below:

(25) Optical Cavity

(26) A device in accordance with described aspects and embodiments may function by utilising either optical or plasmonic resonances, in dependence upon device dimensions. One method of operation comprises taking appropriate steps to inhibit the coupling of electromagnetic radiation, for example, radiation in the optical region of the spectrum, to SPPs which exist at the surface of a device surface, by employing optical Fabry Perot modes which can be supported by the cavity structure of the device. Such Fabry Perot modes can be supported by the cavity structure when feed radiation in the optical region of the spectrum is introduced into the cavity, provided the separation (S) between reflective surfaces of the cavity, for example, gold layers, is sufficiently large (typically in the range of 200 nm to micrometers).

(27) It will be understood by those skilled in the art that, in an embodiment of a device such as that shown in FIG. 2a, if a slit 40 is illuminated by electromagnetic radiation 50 in the optical region of the spectrum, light may couple directly to SPPs 60 on the lower gold film surface 20a by scattering from the slit. As a result of destructive interference between two scattering amplitudes from the slit and Fabry-Perot cavity, the SPP intensity exhibits sharp minima at or close to the resonant frequencies of the optical cavity modes. That phenomenon may be understood in terms of a Fano resonance, which describes interaction between coupled scattering channels. The effect arises whenever scattering via two pathways interferes. In this case, the two channels correspond to the scattering from the slit and the scattering from the Fabry-Perot cavity.

(28) According to one implementation, and as described in relation to FIG. 2a and FIG. 2b, minima in the plasmonic signal may be used to define an off state of a switch and it will be understood that the cavity structure of a device according to some embodiments effectively acts to inhibit SPP generation. The minima in a monitored plasmonic signal will typically be below the level of a background signal when the device is in the off state.

(29) To attain an on state, as shown in FIG. 2a, the optical path inside the cavity, perpendicular to the gold films, is constructed or formed such that it is tuned to reduce destructive interference. Active control may be achieved by, for example, utilising a nonlinear Kerr effect. By incorporating a nonlinear material into the cavity, the refractive index of the material inside the cavity may be optically modulated to change the optical path inside the cavity and yield the desired switching. That arrangement is illustrated schematically in FIG. 2c and FIG. 2d.

(30) In some embodiments, the switching of the device may be operated electrically. For example, in some embodiments, utilising refractive index modulation which stems from an increase in carrier concentration in a conductive material (oxide), for example, Indium Tin Oxide (ITO), can be successfully used as a switching mechanism. In order to employ such an effect, embodiments may be provided according to which a thin multilayer 200 replaces the upper reflector 20b of the embodiment shown generally in FIG. 1. In one embodiment, such as the embodiment shown in FIG. 2d, the thin multilayer 200 may comprise two optically transparent gold films separated by a layer of each of Indium Tin Oxide (ITO) and Hafnium Oxide (HfO). When a voltage is applied, the index modulation enhances reflection from the interface, hence effectively modifying the resonance condition of the cavity. It will be appreciated that other switch triggers are possible, including, for example, mechanical pressure.

(31) In some embodiments (not shown) a grating or other optical source can be arranged to both feed the cavity and generate SPPs. That structure may replace the slit shown in the embodiment of FIG. 1. In some embodiments, a hemispherical upper reflector can be used to provide the necessary conditions for switching. It will be appreciated that the embodiment shown in FIG. 1 is a substantially 2-dimensional device and that in such an arrangement, a feed slit is most appropriate. In the case of a 3-dimensional device, a suitable feed may comprise an opening in the form of a hole, rather than an elongate opening such as a slit.

(32) FIG. 3a illustrates schematically a device according to one embodiment and FIG. 3b illustrates schematically an example of directionality for a double slit structure such as that shown in FIG. 3a as cavity length varies. Directionality is defined as the ratio of SPP intensity in a unique direction to the total SPP intensity; Directionality=1 corresponds to SPPs excited only to the left, 0: only to the right, and 0.5 equates to symmetric coupling.

(33) In the embodiment shown in FIG. 3a, two feed slits are provided 40a and 40b in the lower gold film 20a. Those two slits are asymmetrically located in length W of the device and have differing slit widths as shown. It will be appreciated that the lineshape of the Fano resonance is heavily dependent on the dimensions of the resonant cavity structure and illumination conditions. That is to say, an asymmetry parameter can be controlled by altering the effective coupling parameter between the continuum and the discrete channel, in addition to varying the phase between the two channels. In some embodiments, the phase change associated with the optical resonance can be harnessed to modify the phase of the SPPs launched by the slit, thus allowing for a degree of control over the direction of SPP excitation when phase matching structures, for example, double slits of different widths, are employed.

(34) Plasmonic Cavity

(35) FIG. 4a illustrates schematically a multilayer system for with a device having a plasmonic cavity. As shown in FIG. 4a, a device 10 generally comprises: two parallel metallic films 20a, 20b, separated by a spacer 30, which in the embodiment shown comprises two spacer layers 30a, 30b. In the embodiment shown, the metallic films comprise gold films and the spacer layers a layer of each of Indium Tin Oxide (ITO) and HfO. According to this embodiment, a slit 40 is provided in the lower gold film 20a, and that slit is illuminated from beneath at normal incidence.

(36) FIG. 4b illustrates schematically a device such as that illustrated in FIG. 4a when in an on state in which a plasmonic resonance present in the cavity, located either side of the slit, generates single interface SPPs outside the cavity. FIG. 4c illustrates schematically a device such as that illustrated in FIG. 4a when in an off state in which losses experienced by the plasmonic modes in the cavity inhibit the excitation of SPPs on the adjacent gold film.

(37) FIG. 4d illustrates an example of extinction ratios obtained as applied voltage is varied in a device such as that illustrated in FIG. 4a.

(38) It will be appreciated that in some embodiments, a mode of operation may be implemented which reduces separation between the two gold films of a cavity structure such as that shown schematically in FIG. 1, such that the structure is arranged to act as a plasmonic resonator. According to such embodiments, one possible implementation being shown in FIG. 4a, spacing between reflective surfaces of the cavity, S, is typically in the region of 10 to 50 nm. According to such embodiments, a device is operable to support Fabry-Perot resonances based on plasmonic slot modes, which are able to generate single interface SPPs external to the cavity and enhanced excitation occurs at the slot mode resonance. According to such embodiments, the plasmonic slot mode resonances are parallel to the reflective surfaces, for example, gold films in an arrangement such as that shown schematically in FIG. 1, and thus the width of the cavity (W) must be tuned to ensure resonance conditions are achieved. It will be appreciated that in this case, there may be no need to provide a feed. Plane wave excitation may be sufficient to provide a workable device. Furthermore, it will be appreciated that the position of a feed, for example, an opening in the form of a slit, or hole, may be tuned to provide a desired device

(39) It will be appreciated that, in a manner similar to that described above in relation to a photonic cavity, incorporating layers of conductive oxide and a dielectric, for example, ITO and HfO.sub.2, in the reflective wall structure of a cavity can facilitate switching of a signal with an applied voltage. Such an implementation is shown in FIG. 4a. In this case, incorporation of appropriate spacer layers and application of an appropriate voltage can increase losses experienced by the slot modes as a result of increased electron density at the semiconductor/dielectric interface.

(40) The cavity structure of aspects and embodiments described herein can offer high extinction ratios, together with reduced dimensions when compared to similar systems. The structures of aspects and embodiments described herein can be tailored for integration with VCSELs, which offer an efficient platform for SPP excitation, allowing the realisation of an on-chip, plasmonic switch. It will be appreciated that aspects and embodiments described herein may be used in applications including, for example, plasmonic switches and modulators, pressure sensors, acoustic wave sensors and similar devices.

(41) FIG. 5a is a 3-dimensional representation of a modulator according to one embodiment. According to one embodiment of a modulator, a device geometry such as that shown in FIG. 5a may be provided. Such an embodiment may be configured to be coupled to a waveguide. The device of the embodiment shown is based upon use of a metallic nanorod array metamaterial as coupled to a silicon (Si) waveguide. It will be appreciated that it is possible to implement arrangements which are provided for non-silicon waveguides. The metamaterial in the embodiment shown comprises a plurality of metallic nanorods of tunable diameter, length, and spacing distance which are aligned with respect to one another and embedded in a dielectric matrix. The geometric tunability of the metamaterial provides extensive control over both the bandwidth and the operating frequency of the device. In the embodiment illustrated, thin layers of gold and Tantalum oxide (Ta.sub.2O.sub.5) are introduced in the bottom of the metamaterial element.

(42) It will be appreciated that the metamaterial of the device can be integrated into or onto a Si-waveguide to form the device whose purpose is to enable a dynamical control over transmission, reflection and/or absorption of an adjacent silicon waveguide.

(43) It has been found that the transmittance of the Si waveguide as a function of the optical properties of the device demonstrates strong transmission modulation via modification of optical properties of the embedding matrix of the metamaterial by, for example, electro-optical, magneto-optical, acousto-optical or nonlinear optical interactions, or by using other nonlinearity of the metamaterial itself. A device in accordance with some aspects and embodiments can be configured or designed to operate at a frequency close to an inflection point of the transmission versus frequency characteristics. In a configuration where a device is in the off position, for example, the transmission of the device can be chosen to be maximal/minimal or intermediate in dependence upon an envisaged application. If the transmission is maximal, the propagation of light in the waveguide is not altered by the presence of the device, since the device is configured such that the impedance of the waveguide and device is matched. It will be appreciated that small changes in the optical properties of a device will then affect the transmission of the waveguide. FIG. 5b illustrates schematically the modulator of FIG. 5a when in an off state; and FIG. 5c illustrates schematically the modulator of FIG. 5a when in an on state.

(44) When used as a sensor for example, a material or property to be sensed in the form of a gas, liquid or solid, may permeate the structure of the metamaterial such that the optical properties of the metamaterial are changed or modified, that modification impacting transmission of the waveguide.

(45) In one embodiment, in which a waveguide including a metamaterial in accordance with aspects and embodiments described, is configured to operate as a modulator, ultrafast, for example, picosecond thermal properties of both free and bound electron density in the metallic nanorods of a structure such as that shown in FIG. 5a can be used to modulate the transmission/reflection/absorption of the waveguide.

(46) Alternative ultrafast mechanisms based on optical properties of the embedding medium in interaction with the nanorods may also be implemented. For example, in some embodiments, the embedding material may comprise an oxide or suitably chosen resonant or non-resonant material.

(47) It will be appreciated that a device in accordance with aspects and embodiments may be integrated into ultrafast photonic switches, and may be silicon-photonics compatible. Furthermore, such a device may be used to form part of an integrated bio- or chemical sensor.

(48) FIG. 6 is a 3-dimensional representation of a modulator according to an alternative embodiment. In the embodiment shown in FIG. 6, the metamaterial element is formed in-line and integrally with the waveguide, rather than being located adjacent a wave guide as in the embodiment shown in FIG. 5.

(49) FIG. 7 illustrates schematically the main components of a device according to one arrangement. The device geometry of the arrangement shown comprises: two ENZ metamaterial elements arranged in-line within a silicon waveguide. The ENZ metamaterial elements in the arrangement shown are integrated into a waveguide. The ENZ metamaterial elements may be substantially planar and are arranged to lie substantially transverse to the longitudinal axis of the waveguide. The planes of the ENZ metamaterial elements may be substantially aligned, or parallel with respect to each other and can be embedded in a dielectric matrix. The dielectric matrix may comprise the waveguide.

(50) It will be appreciated that an ENZ metamaterial structure can be fabricated in various ways. A suitable metamaterial structure will typically comprise a plurality of metallic nanostructure elements arranged within a dielectric. A metamaterial satisfying ENZ conditions occurs in anisotropic media between hyperbolic and elliptic regimes. In the hyperbolic regime a material typically exhibits high reflectivity at an interface with another material but has large losses. In the elliptic regime a material typically exhibits low reflectivity at an interface with another material with no losses. An ENZ metamaterial may be constructed to balance the two properties to offer a material which has a large reflectivity at an interface with another material yet low losses. As a result, an ENZ metamaterial mirror may perform as a perfect mirror or at least the best mirror possible given selected composition materials.

(51) It will be appreciated that a modulation device in accordance with the arrangement shown in FIG. 7 represents a Fabry-Perot cavity where the two end-mirrors comprise thin layers of metamaterial, enclosing a section of the waveguide of determined length. The geometric tunability of the metamaterial (which can be a multilayer) provides extensive control over both the bandwidth and the operating frequency of the device. ENZ materials provide extensive spectral tunability, low material losses (the mirror formed is an effective medium with low lossy material content), and strong ultrafast response, due to the nanostructured composition of the mirrors.

(52) The metamaterial elements enable ultrafast dynamic control over the transmission, reflection and/or absorption properties of the waveguide. In particular, the transmittance of the Si waveguide as a function of the optical properties of the device demonstrates strong transmission modulation via the modification of the optical properties of the metamaterial by electro-optical, magneto-optical, acousto-optical or nonlinear optical interactions.

(53) A device can be designed to work at a frequency close to an inflection point of the device transmission versus frequency plot. In a configuration where the device is in the off position, for example, the transmission of the device can be chosen to be maximal/minimal or intermediate depending on a selected device application. If the transmission is maximal, the propagation of a selected frequency of electromagnetic radiation in the waveguide may be such that is not altered by the presence of the device. The impedance of the device is matched to the impedance of the waveguide. Small changes in the optical properties of the device affect the transmission of the waveguide. When used as a sensor, for example, a material to be sensed (gas, liquid, solid) may permeate or be in the vicinity of the metamaterial, modify its optical properties and affect the transmission of the waveguide. In a simple configuration as a modulator, the ultrafast (femtosecond) thermal properties of both the free and bound electron density in, for example, the metallic nanostructures provided in the ENZ metamaterial can be used to modulate the transmission/reflection/absorption of the waveguide. In some arrangements alternative ultrafast mechanisms based on the optical properties of the embedding medium in interaction with the metallic nanostructures forming the metamaterial may also be utilised.

(54) It will be appreciated that when forming a device in accordance with arrangements, the ENZ metamaterial elements may be located within a waveguide at a spacing selected in relation to a frequency of interest. That is to say, the gap between ENZ mirrors can be selected to provide a resonant cavity at a frequency of interest.

(55) Similarly, it will be appreciated that in order to perform acceptably, the thickness of the ENZ elements provided may impact upon device operation. In particular, it will be appreciated that with increasing mirror thickness the losses increase and therefore the value of the total transmission at the Fabry-Perot resonance decreases, thus increasing insertion loss. Thus a thinner ENZ metamaterial element can be beneficial. It will be appreciated that as the thickness of an ENZ material is reduced, the ability of the material to perform as an ENZ metamaterial may be compromised. Thus a balance must be struck between minimising losses and the ability of the device to function as intended.

(56) In the general arrangement shown schematically in FIG. 7, both metamaterial elements are configurable to operate in an ENZ condition, which means the metamaterial elements can be switched between operating as a mirror being arranged to have a transmission close to 1. The closer the transmission is to 1 in the Fabry-Perot cavity the lower the insertion loss and the better the modulator may operate.

(57) FIG. 8 is a 3-dimensional representation of a modulator according to one embodiment. In the arrangement shown in FIG. 2 the ENZ mirrors are formed from metallic rods in a dielectric material. The ENZ metamaterial elements in the arrangement shown each comprise a metallic nanorod array. The ENZ metamaterial elements are formed from a plurality of metallic nanorods. The dimensions and arrangement of the nanorods and of the metamaterial elements within the waveguide may be chosen to perform according to a proposed application of a device. Such tunability of a device to an envisaged application can be achieved in relation to the ENZ metamaterial elements since the metallic nanorods forming the ENZ metamaterial elements may have, for example: a tunable diameter, length and/or spacing distance.

(58) As described in relation to the general arrangement shown in FIG. 7, an interesting behaviour is exhibited by waveguide structures comprising consecutive nanorod slabs. At the ENZ condition, the metamaterial element slab becomes highly reflective (as n=0 reflection coefficient=1) which leads to the creation of standing waves within the device. Such an arrangement can allow high transmission through the device in the same manner as a Fabry-Perot resonator. In reality, the ENZ metamaterial comprises a metallic nanorod structure, which can have large losses. The standing waves cannot be supported unless the losses are sufficiently small. One way to reduce losses is to reduce the number of rods needed (thus reducing the amount of metal) to create an ENZ slab.

(59) Consider, for example, the structure shown schematically in FIG. 8. For a certain value of the gap, the transmission of the structure is 1 for a given frequency due to the creation of a standing wave within the device (Fabry-Perot resonance). The thickness of the ENZ metamaterial elements (slabs) can lead to significant losses. Losses can be minimized by reducing the length (thickness) of the ENZ material, although care must be taken since typically an ENZ structure will be fabricated in accordance with conditions derived from an effective medium theory of an infinite slab and therefore the length of the slab should not be reduced further than a single unit of the effective medium (in this case one nanorod diameter).

(60) The structure shown schematically in FIG. 8 comprises two ENZ metamaterial elements. The ENZ elements comprise a plurality of gold nanostructure rods embedded in a dielectric medium.

(61) FIGS. 9 to 11 illustrate graphically a mathematical analysis of the transmission of a structure such as that shown in FIG. 8. The analysis assumes an effective medium theory for a metamaterial slab having a length of one nanorod diameter (50 nm) the model allows both the rod diameter and gap between ENZ elements to be changed to scan the effective permittivity of the medium through the ENZ condition and to obtain the condition for maximum transmission. A simple transfer matrix method (TMM) analysis is implemented to calculate the transmission of the device. In relation to FIG. 9 the surface plot represents the transmittance of the modulator as a function of inter-rod distance and rod diameter. The 2-D plots illustrate the real and imaginary parts of the z-component of the permittivity tensor as a function of rod diameter. The x,y components are positive and not dispersive. ENZ conditions are achieved for a rod diameter of around 35 nm.

(62) The structure shown in FIG. 8 is simulated fully in 3D, accounting for the nanostructured geometry of the metamaterial using COMSOL, and its transmission is calculated for a first TM-like mode (transverse magnetic) and plotted against rod diameter and gap. In the simulated structure a glass substrate is assumed, together with a mode frequency corresponding to a free space wavelength of 1.5 um. The waveguide simulated is 300 nm wide and 340 nm high.

(63) FIG. 9 illustrates the transmission of one device against both rod gap and diameter using TMM. In the mathematical example shown, a mathematical model comprising nanorods embedded within silicon having n=3.48 is used to allow for comparison with real fabricated devices. In other words, the mathematical model can be compared with empirical results from fabricated prototypes formed in accordance with those parameters. The real and imaginary part of eps_z are also plotted in FIG. 9 for ease of reference.

(64) FIG. 10 illustrates the transmission against both gap and diameter for the case of the 3D simulation. The gap in the finite element 3D model is different to the gap in the TMM in the sense that while in the TMM the minimum length of the slab is related to the size of a unit cell (given by the period of a nanorod array), whereas in the model of FIG. 10 the nanorods can be as close as desired, subject to the diameter of the nanorod, and analysis can be performed.

(65) For a rod diameter of 35 nm and a spacing of 80 nm which corresponds to the increased transmission in FEM simulations, the wavelength behaviour was calculated and is shown in FIG. 11. The blue transmission profile corresponds to a full 3D finite element (FEM) calculation of the modulator. The TMM plot refers to an equivalent effective medium theory calculation.

(66) Simulations reveal that for a single cell of effective medium the losses are higher than for a single real cell (comprising a single rod inside a waveguide). This can be understood since in the example arrangements considered the single cell is geometrically closer to a gold layer of few nanometers (related to the diameter of the rod) than to an array of rods with an effective loss. Such an analysis can explain the increased transmission in the case of FEM.

(67) Calculations were also done to simulate use of a AAO instead of silicon as an embedding medium. Although stronger resonances are seen in simulations of such an arrangement, the simulation also indicates that mismatch between a propagating mode in silicon and in AAO, can lead to a drop in transmission through a real nanostructured component. A waveguide made of AAO is likely to give better results, although an AAO waveguide typically requires a larger height of the waveguide and longer rods (in the order of 500 or 600 nm). The size of the device can be as large as 180 nm from the FEM simulation, and simulations indicate that with a drop in the total transmission of 0.17, the device has relatively small insertion losses and integrability. Furthermore, if the device is used as a modulator: in the ON state it has low transmission and in the OFF state it has large transmission. Therefore this device may be particularly energy efficient when integrated into an optical circuit compared to alternative modulator arrangements.

(68) For the case investigated using gold nanorods, it has been determined that the maximum transmission at the Fabry-Perot resonance condition is 0.86 dropping down to 0.5 under optical pumping. It will be appreciated that other materials may provide an improved performance.

(69) Use of rods in the illustrated example gives a tuned ENZ condition at the selected working wavelength (1.5 um). In the case of the illustrated simulated modulator the anisotropic nature of the rods have the result that the switchable ENZ behaviour will only work for TM polarized modes (electric field along the longitudinal axis of the rod) however for TE polarized modes (electric field perpendicular to the longitudinal axis of the rod) the permittivity is not zero but close to that of the silicon waveguide and therefore it will be transparent at this polarization. Such an effect can, in some arrangements, then be used for polarization modulation.

(70) General Structure

(71) It will be appreciated that it is possible to implement arrangements which are provided for non-silicon waveguides. The metamaterial in the embodiment shown comprises a plurality of metallic nanorods of tunable diameter, length, and spacing distance which are aligned with respect to one another and embedded in a dielectric matrix. The geometric tunability of the metamaterial provides extensive control over both the bandwidth and the operating frequency of the device.

(72) It will be appreciated that a device in accordance with aspects and embodiments may be integrated into ultrafast photonic switches, and may be silicon-photonics compatible. Furthermore, such a device may be used to form part of an integrated bio- or chemical sensor.

(73) Although illustrative embodiments of the invention have been disclosed in detail herein, with reference to the accompanying drawings, it is understood that the invention is not limited to the precise embodiment and that various changes and modifications can be effected therein by one skilled in the art without departing from the scope of the invention as defined by the appended claims and their equivalents.