Photonic devices having degenerate spectral band edges and methods of using the same

Provided herein are photonic devices configured to display photonic band gap structure with a degenerate band edge. Electromagnetic radiation incident upon these photonic devices can be converted into a frozen mode characterized by a significantly increased amplitude, as compared to that of the incident wave. The device can also be configured as a resonance cavity with a giant transmission band edge resonance. In an exemplary embodiment, the photonic device is a periodic layered structure with each unit cell comprising at least two anisotropic layers with misaligned anisotropy. The degenerate band edge at given frequency can be achieved by proper choice of the layers' thicknesses and the misalignment angle. In another embodiment, the photonic device is configured as a waveguide periodically modulated along its axis.

FIELD OF THE INVENTION

The invention relates generally to the field of photonic devices, and more particularly to systems and methods for transmitting and storing electromagnetic radiation in a photonic device with inhomogeneous spatially periodic structure.

BACKGROUND INFORMATION

The manipulation of electromagnetic energy can be advantageous to numerous applications within many industries. For instance, much effort has been focused on reducing the velocity of electromagnetic energy, such as light and microwave pulses. The reduced velocity of electromagnetic energy can facilitate manipulation of electromagnetic waves. It can also enhance the light-matter interaction essential in numerous optical and microwave applications. One approach to reducing the electromagnetic energy velocity is through the use of spatially inhomogeneous periodic media displaying strong spatial dispersion at operational frequencies. Spatial inhomogeneity results in strong nonlinear relation between the frequency ω of propagating electromagnetic wave and the respective Bloch wave number k. The relation ω(k) is referred to as dispersion relation or, equivalently, as k-ω diagram. At certain frequencies, the wave group velocity v=dω/dk vanishes implying extremely low energy velocity.

One common photonic device exploiting spatial inhomogeneity is a photonic crystal. This device is typically composed of multiple repeating segments (unit cells) arranged in a periodic manner. Electromagnetic frequency spectrum of a typical photonic crystal develops frequency bands separated by forbidden frequency gaps. The frequency separating a photonic band from adjacent photonic gap is referred to as a (photonic) band edge, or simply a band edge. At frequencies close to a photonic band edge, the relationship between the frequency ω and the wave number k can be approximated as
ω−ωg∝(k−kg)2(1)
implying that the respective group velocity
v=dω/dk∝k−kg∝√{square root over (ω−ωg)}  (2)
vanishes as ω approaches the band edge frequency ωg. This creates conditions for very slow pulse propagation. Another common photonic device exploiting spatial inhomogeneity and providing conditions for slow energy propagation is a periodic array of weakly coupled resonators. There exist many different physical realizations of the individual resonators connected into the periodic chain.

One common drawback of current photonic devices employing spatial inhomogeneity is that only a small fraction of the incident electromagnetic radiation is converted into the slow electromagnetic mode, resulting in low efficiency of the device. Another common drawback of current photonic devices is the necessity to employ a large number of the said segments (unit cells) in order to achieve a desirable slowdown of electromagnetic energy. Accordingly, improved photonic devices are needed having smaller dimensions and allowing for more efficient manipulation of the incident electromagnetic radiation.

SUMMARY

The devices, systems and methods described in this section are done so by way of exemplary embodiments that are not intended to limit these devices, systems and methods in any way.

In one exemplary embodiment, a photonic system is provided that includes a photonic device configured to display a degenerate band edge, the photonic device including a first end, a second end, a first surface located on the first end and a plurality of segments coupled together between the first and second ends. Each segment can include a first anisotropic layer, a second anisotropic layer misaligned with the first anisotropic layer, and a third layer. The photonic device can be configured to convert an electromagnetic wave incident on the first surface into a frozen mode, where the electromagnetic wave operates at a frequency in proximity with the degenerate band edge.

In another exemplary embodiment, a photonic system is provided that includes a photonic device configured to display a degenerate band edge, the photonic device including a first end, a second end, a first surface located on the first end and a plurality of periodic segments coupled together between the first and second ends. Each segment can include a first anisotropic layer having a first thickness and a second anisotropic layer misaligned with the first anisotropic layer and having a second thickness different from the first thickness. The photonic device can be configured to convert an electromagnetic wave incident on the first surface into a frozen mode, when the electromagnetic wave operates at a frequency in proximity with the degenerate band edge.

DETAILED DESCRIPTION

Photonic devices and systems having degenerate spectral band edges and methods for using the same are described herein. These devices, systems and methods are based on the physical idea of using spatially periodic structures displaying a degenerate band edge
ω−ωd∝(k−kd)4(3)
rather then the regular band edge described by equation (1). Unlike the regular band edge (1), display of the degenerate band edge (3) allows for the frozen mode regime, accompanied by a complete conversion of the incident radiation into a slow mode with a drastically enhanced amplitude. In addition, a resonance cavity incorporating a photonic device displaying a degenerate band edge can have much smaller relative dimensions compared to those incorporating existing photonic devices.

Light transmitting periodic structures that can be configured to display the degenerate band edge (3) include, but are not limited to: (i) photonic crystals, such as periodic layered structures, as well as structures with two and three dimensional periodicity, (ii) spatially modulated optical and microwave waveguides and fibers, and (iii) arrays of coupled resonators. The embodiments discussed below are directed towards periodic arrays of anisotropic dielectric layers; however, it is important to emphasize that the underlying reason for the enhanced performance of the photonic device as described herein lies in the existence of a degenerate band edge (3) in the respective frequency spectrum. Specific physical realization of the periodic structure displaying such a spectrum is determined by practical needs, i.e., one of ordinary skill in the art will readily recognize how to implement spatially modulated optical and microwave waveguides and fibers, arrays of coupled resonators and other desired structural configurations based on the embodiments described herein.

FIG. 1is a block diagram depicting one exemplary embodiment of a photonic device101configured to display a degenerate spectral band edge (3).FIG. 1depicts an electromagnetic wave102incident a surface111of device101. In this embodiment, photonic device101includes a plurality of segments (unit cells)105coupled together between a first end103and a second end104of the device101. Each segment105can include a first anisotropic layer106, a second anisotropic layer107, and a third optional layer108. The third layer108can be made of either isotropic or anisotropic material, or it can be omitted entirely. The Z direction is normal to layers106-108. The thickness of segment105in the Z direction is preferably of the same order of magnitude as the wavelength of the incident wave102. Each of the three layers106-108has a plane-parallel configuration with a uniform thickness (measured in the Z direction) and composition, although these conditions may not be necessary. The thickness of each of layers106-108can be different from each other in accordance with the needs of the application.

In this embodiment, the structure of photonic device101is periodic along the Z direction perpendicular to layers106-108, which are parallel to the X-Y plane. The X, Y and Z directions are perpendicular to each other like that of a standard Cartesian coordinate system. Photonic device101is also preferably homogeneous in the in-plane directions X and Y, although photonic device101can also be inhomogeneous in the directions X, Y, or both, if desired. The total number N of repeating segments105in photonic device101depends on the specific application and usually varies between three and several hundred, although device101is not limited to this range of segments105.

The anisotropy axes of anisotropic layers106and107preferably have misaligned orientation in the X-Y plane with the misalignment angle φ being different from 0 and π/2. In this embodiment, anisotropic layers106and107are composed of the same anisotropic dielectric material and have a variable misalignment angle. The dielectric permittivity tensors of the three constitutive layers106,107and108can be chosen as follows:

ɛA⁢⁢1=[ɛ+δ000ɛ-δ000ɛzz],⁢ɛA⁢⁢2=[ɛ+δcos⁢⁢2⁢φδsin⁢⁢2⁢φ0δsin⁢⁢2⁢φɛ-δcos⁢⁢2⁢φ000ɛzz],⁢ɛB=[100010001],(6)
where ∈A1, ∈A2and ∈B, are the dielectric permittivity tensors for the layers106,107and108, respectively. The choice (6) for the material tensor ∈Bcorresponds to the case where layer108is an empty gap between the adjacent pairs of anisotropic layers106and107. If desired, optional layer108can also be filled with either anisotropic or isotropic material, such as glass, air, active or nonlinear medium, etc., or it can be left vacant (e.g., as a vacuum), depending on the specific practical needs of the application. The quantity δ in (6) describes inplane anisotropy of the A-layers106and107, essential for the existence of degenerate band edge. The parameter φ in (6) designates the misalignment angle between anisotropic layers106and107. It can be chosen anywhere between 0 and π, which provides additional tunability of the photonic device. The k-ω diagram of the photonic device inFIG. 1can develop degenerate band edge (3) only if the misalignment angle φ is other than 0 and π/2. A typical value for the misalignment angle φ is π/4. If desired, the tensor anisotropy (6) of layers106and107can be replaced with similar shape anisotropy of the respective X-Y cross sections, i.e., anisotropy can be induced with only isotropic materials through the shape or configuration of the X-Y cross section of the respective layers (e.g., the X-Y cross section is shaped as a, rectangle, ellipse or the like). Additional exemplary embodiments with modulated X-Y cross-sections are described with respect toFIGS. 10-13.

FIG. 2is a block diagram depicting another exemplary embodiment of photonic device101configured to display the degenerate band edge. This embodiment is similar to the embodiment described with respect toFIG. 1except each layer108is omitted. In this case, anisotropic layers106and107preferably have different thicknesses and/or different permittivity tensors

ɛA⁢⁢1=[ɛ1+δ1000ɛ1-δ1000ɛ1⁢zz],⁢ɛA⁢⁢2=[ɛ2+δ2⁢cos⁢⁢2⁢φδ2⁢sin⁢⁢2⁢φ0δ2⁢sin⁢⁢2⁢φɛ2-δ2⁢cos⁢⁢2⁢φ000ɛ2⁢zz].(7)
Otherwise, the characteristics of this embodiment inFIG. 2would be very similar to that of the embodiment described with respect toFIG. 1.

FIGS. 3A-Dare graphs depicting the k-ω diagram for the embodiment of photonic device101described with respect toFIG. 1for four different values of the thickness of the B layer108, respectively. In the graph depicted inFIG. 3B, the upper dispersion curve develops degenerate band edge d described in (3) and associated with the frozen mode regime. (InFIG. 3B, the frequencies above band edge d can be referred to as the frequency gap or photonic gap, while frequencies below band edge d can be referred to as the frequency band or photonic band.) The embodiment of photonic device101described with respect toFIG. 1can develop degenerate band edge d, provided that the misalignment angle φ between the adjacent anisotropic layers106and107is different from 0 and π/2. If the physical parameters, such as the layer thicknesses and/or the misalignment angle φ, of photonic device101deviate from those corresponding to the situation depicted inFIG. 3B, the degenerate band edge d turns into a regular band edge g described in (1) and depicted inFIGS. 3A,3C and3D. The k-ω diagram depicted inFIG. 3Dcorresponds to the case where the B layers108are absent.

FIGS. 4A-Care schematic diagrams depicting a photonic device101during three stages of the frozen mode regime. Photonic device101shown here is configured similar to that of the photonic device embodiment described with respect toFIG. 1. Here, the frozen mode regime occurs for an incident electromagnetic pulse102with a central frequency close to that of the degenerate band edge d depicted inFIG. 3B.FIG. 4Adepicts incident pulse102propagating towards the surface111of photonic device101.FIG. 4Bdepicts the situation after pulse102has reached surface111and has been transmitted into device101and converted into the frozen mode pulse401. Here, the frozen mode401is characterized by an enhanced pulse amplitude and compressed pulse length, compared to those of the incident pulse102.FIG. 4Cdepicts the situation after the frozen pulse401exits the photonic device101and turns into a reflected wave402. The distance404through which the frozen mode pulse102is transmitted inside photonic device101, as well the degree of amplitude enhancement, are strongly dependent on the pulse bandwidth and the central frequency. The frozen mode amplitude will typically increase with decreasing bandwidth and lesser difference between the central frequency and the degenerate band edge.

FIG. 5is a graph depicting an exemplary smoothed frozen mode profile at the steady-state frozen mode regime. In this example, the amplitude of the incident wave is unity. The point z=0 coincides with surface111.

FIG. 6is a graph depicting a smoothed profile of a typical surface electromagnetic wave. Here, the field amplitude decays exponentially with the distance z from surface111.

FIG. 7is a graph depicting a smoothed profile of an exemplary abnormal surface wave associated with the degenerate band edge (3) of the electromagnetic spectrum. In this example, the field amplitude sharply rises inside photonic device101, before decaying as the distance z from surface111further increases. The magnitude and the location of the field amplitude maximum sharply depend on the wave frequency. Remarkably, the maximal amplitude of an abnormal surface wave can be reached at a significant distance from surface111. The latter circumstance can suppress the energy leakage outside photonic device101.

FIG. 8is a graph depicting a typical transmission dispersion of photonic device101with the k-ω diagram depicted inFIG. 3B. Here, N=16 (inFIG. 8A) and N=32 (inFIG. 8B) is the total number of segments105in device101and ωdis the degenerate band edge frequency. The sharp peaks in the device transmittance correspond to giant cavity resonances, their exact position being dependent on the number N.

FIG. 9is a graph depicting the smoothed field distribution A2(z) in photonic device101at the frequency of the rightmost giant transmission resonance closest to the degenerate band edge frequency ωddepicted inFIG. 8, N=16 (inFIG. 9A) and N=32 (inFIG. 9B). The amplitude of the incident plane wave is unity, implying that the field enhancement in the case N=16 reaches 2000, while in the case N=32, the filed enhancement reaches 35000. To achieve similar performance in a common periodic array of isotropic layers, one would generally need at least several hundred layers in a stack.

FIG. 10is a block diagram depicting another exemplary embodiment of photonic device101. Here, device101is a spatially periodic structure configured to display an electromagnetic k-ω diagram with a degenerate band edge (3). In this embodiment, device101is configured as a waveguide with an X-Y cross-section periodically modulated along the waveguide axis Z. In this embodiment, waveguide101includes a plurality of segments (unit cells)605coupled together between a first end603and a second end604of waveguide101. Only the rightmost and the leftmost segments605are shown inFIG. 10. Each segment605has a variable cross-section depending on the coordinate Z, as shown inFIG. 11. The end cross-sections6051and6052are identical, to ensure smooth connection of adjacent segments605in the waveguide. At least at some Z, the X-Y cross-section of segment605is anisotropic in the X-Y plane. The term “anisotropic in the X-Y plane” implies that the axis Z of the waveguide is not an n-fold symmetry axis of this particular cross-section with n>2. The length of each segment605in the Z direction depends on operational frequency and is of the order of the respective electromagnetic wavelength.

In one exemplary embodiment, each segment605can be subdivided into three adjacent portions606-608, as depicted inFIG. 12(portions606-608are shown here spaced apart from each other, although this would not be the case in the actual implementation). Portion606can be viewed as a circular section of the waveguide squeezed in the Y direction, so that its cross-section in the middle has an elliptical shape, as seen inFIGS. 12 and 13A. Portion607inFIGS. 12 and 13Bcan be similar to portion606, but rotated about the Z axis by an angle φ, preferably different from 0 and π/2. In the embodiments depicted inFIGS. 10-13C, the misalignment angle φ is chosen π/4, although it is not limited to such. A third, optional portion608, depicted inFIGS. 12 and 13C, can have circular, or any other cross-section, or it can be omitted altogether. The cross-sections at both ends of each of the three portions606-608are identical to ensure their smooth interface in the waveguide. In this example, the end cross-section is circular, although any desired shape can be used. One can view the shape anisotropy of portions606,607, shown in FIGS.12and13A-B, as being analogous to the dielectric anisotropy (6) of the respective layers106,107of the embodiment of the periodic layered structure101described with respect toFIG. 1. Portion608with a circular cross-section could be viewed as analogous to isotropic layer108inFIG. 1.

Again, waveguide101as depicted inFIG. 10can be configured to display a degenerate band edge at desired frequency. By way of example, display of the degenerate band edge can be done as follows: (i) by adjusting the variable X-Y cross-section as a function of the axial coordinate Z, or (ii) by the proper choice of dielectric or other low-absorption materials filling the waveguide. It should be noted that waveguide101can display the electromagnetic band gap structure with a degenerate band edge in any manner and is not limited to just these two examples.

The input electromagnetic wave602enters waveguide101inFIG. 10at end603, similar to the embodiments described with respect toFIGS. 1-2. The optimal number of segments605in the device601can vary between three and several hundred or more, depending on the specific application.

If this embodiment of waveguide101is empty, or if it is filled with a uniform dielectric substance, the misaligned cross-section anisotropy of portions606and607may become required for the existence of degenerate band edge. But if the filling material is not distributed uniformly, as shown in the exemplary embodiments ofFIGS. 14-15C, the variable cross-section can also be circular, square, or any other.

FIGS. 14-15Cdepict another exemplary embodiment of photonic device101as a waveguide configured to display the degenerate band edge in the electromagnetic k-ω diagram. In this exemplary embodiment, the effect of misaligned cross-sectional anisotropy of waveguide101is achieved by a non-uniform filling of waveguide101, rather than by anisotropy of the shape of the external X-Y cross-section. Here, the non-uniform filling is provided by cylindrical insertions710-711, although any manner of non-uniform filling can be used. In this embodiment with insertions710-711, there are no essential restrictions on the shape of the X-Y cross-section of waveguide101, for example, it can be circular, square, or any other. In this embodiment, the cross-section shape is circular and independent of Z (i.e., there is no periodic external shape modulation along the Z-direction, as in the exemplary embodiments described with respect toFIGS. 10-13). The photonic band gap structure in this case is created by a non-uniform filling (insertions710-711) of waveguide101. InFIG. 14, a single segment (unit cells)705of waveguide101is shown. The entire structure of waveguide101is obtained by repeating segment705in a periodic fashion along the waveguide axis, similar to the embodiments described with respect toFIGS. 1,2and10.

In the exemplary embodiment depicted inFIG. 14, a single segment (a unit cell)705includes three contiguous portions706,707,708, shown also separately inFIGS. 15A-C, respectively. One can view the role of portions706and707as being analogous to that of the respective layers106and107described with respect toFIG. 1, or portions606and607described with respect toFIG. 12. Specifically, portions706and707provide the misaligned structural anisotropy in the X-Y plane and, thereby, create the conditions for degenerate photonic band edge (3). In the embodiment depicted inFIG. 14, the anisotropy is created by misaligned cylindrical insertions710and711, each of which is positioned in the center of the respective section and oriented perpendicular to the waveguide axis Z. The misalignment angle in the X-Y plane between insertions710and711is preferably different from 0 and π/2. It can be set, for example, as π/4, as shown inFIG. 15B, or it can be made variable to provide structural tunability. Portion708can be empty, or it can be filled with a uniform substance with low absorption at operational frequency range, or it can be omitted altogether. Otherwise, the description of photonic device101; one segment105of which is depicted inFIG. 14, is similar to that inFIG. 10.

There can be a practically infinite number of specific waveguide realizations of photonic device101displaying the degenerate band edge (3). In the embodiment inFIG. 10, the desired effect is achieved by the misaligned shape anisotropy of the waveguide cross-section. In the embodiment inFIG. 14, the same effect is achieved by non-uniform filling of the waveguide. One can use any combination of these two embodiments, or one can also exploit the misaligned dielectric anisotropy of a periodic stratified structure, as described with respect toFIGS. 1-2. In any event, the electromagnetic band gap structure (i.e., the k-ω diagram) of photonic device101can develop a degenerate band edge (3) and, thereby, display the frozen mode regime, only if the periodic structure has the proper symmetry and possesses a certain degree of complexity. The embodiments described with respect toFIGS. 1-2and10-15C are only particular solutions or examples. One can use any combination of these embodiments or one can use other configurations not explicitly shown.

Described below are three exemplary methods in which photonic device101can be used. Each of the methods is referred to as an independent regime. It should be noted that operation in any one regime is dependent on the needs of the specific application, and that these regimes do not constitute an exhaustive list of potential uses for photonic device101. In fact, photonic device101can be operated in any one or more of these three regimes as well as other regimes not explicitly described herein.

A first exemplary regime for photonic device101can be referred to as the frozen mode regime at degenerate band edge frequency. In this regime, an incident electromagnetic pulse401with central frequency close to that of the degenerate band edge is transmitted to photonic device101, where it is converted into the frozen mode402having greatly enhanced amplitude and compressed length, similar to the exemplary embodiment described with respect toFIGS. 4A-C. Such a frozen mode does not propagate further through photonic device101than distance404, and after a certain delay pulse is reflected back to space. During the time in which pulse102dwells inside photonic device101, its amplitude can exceed that of the incident wave in air by several orders of magnitude.FIG. 5, which was previously described, depicts the steady-state realization of the frozen mode regime. The fact that the frozen mode amplitude is drastically enhanced compared to that of the incident wave can be used for enhancement of various processes resulting from light-matter interaction, for instance, higher harmonic generation, nonreciprocal Faraday rotation, light amplification by active media, etc. The frozen mode regime at degenerate band edge is fundamentally different from that associated with stationary inflection point and described in A. Figotin et al., U.S. Pat. No. 6,701,048. Indeed, in the case of stationary inflection point, the transmitted frozen mode slowly propagates through the photonic device until it reaches its opposite boundary or gets absorbed by the medium. By contrast, in the case of the degenerate band edge described herein, the incident wave is eventually reflected back to space, as illustrated inFIG. 4C.

A second exemplary regime for photonic device101can be referred to as the abnormal surface wave near degenerate band edge frequency regime. In the embodiments inFIGS. 1 and 2, the surface waves propagate along surface111, normally to the Z direction. Typically, a surface wave rapidly decays with the distance from surface111between the photonic crystal and air, as depicted inFIG. 6. But, if the surface wave frequency is close to that of a degenerate band edge, the surface wave profile can change dramatically. The amplitude of such an abnormal surface wave sharply increases with the distance Z from the interface, before it starts to decay, as depicted inFIG. 7. The abnormal surface wave associated with degenerate band edge is much better confined inside photonic device101reducing the energy leakage outside the system, because the leakage rate is usually proportional to the squared field amplitude A2at the slab/air interface111. This regime of abnormal surface wave is not exhibited in this precise manner in the exemplary embodiments ofFIGS. 10-15Cusing a waveguide setting.

A third exemplary regime for photonic device101can be referred to as giant Fabry-Perot cavity resonance near the degenerate band edge frequency. Periodically modulated waveguides, periodic layered structures, as well as periodic arrays with 2 and 3 dimensional periodicity terminated by plane-parallel boundaries, are known to display sharp transmission cavity resonances at frequencies close to a photonic band edge. This phenomenon has been widely used in resonance cavities for varies practical purposes. In the case of a regular photonic band edge (1), the amplitude A of the resonance field inside the photonic cavity can be estimated as
A∝NA0(4)
where A0is the amplitude of the incident plane wave. Strong cavity resonance can require a large number N of unit cells (e.g., segments105,605and705) in the periodic structure. A similar resonance effect occurs in periodic structures in the vicinity of the degenerate photonic band edge (3), as depicted inFIG. 8. One difference though is that in the latter case, the resonance field amplitude is estimated as
A∝N2A0(5)
and referred to as the giant transmission band edge resonance. This shows that a Fabry-Perot cavity based on photonic device101configured to display the degenerate band edge is much more efficient than previous versions. For instance, a resonance cavity with the degenerate band edge based on an exemplary embodiment of device101having 10 periodic segments (e.g,105,605or705), or unit cells, can perform as well as a regular Fabry-Perot photonic cavity composed of 100 periodic segments. The optimal number of segments (e.g,105,605or705) in the resonance cavity depends on specific application, but in any event, cavities based on photonic device101configured to display the degenerate band edge can be much smaller.

The embodiments described with respect toFIGS. 1-15Cprovide numerous advantages over conventional systems and devices. For instance, photonic device101does not have to include any magnetic components with strong Faraday rotation, as is the case in the devices described in A. Figotin et al., U.S. Pat. No. 6,701,048, entitled “Unidirectional Gyrotropic Photonic Crystal and Applications for the Same,” which is fully incorporated by reference herein. Also, photonic device101can operate without the inclusion of layers with an oblique orientation of the anisotropy axis relative to the normal to the layers, similar to certain devices described in A. Figotin et al., U.S. patent application Ser. No. 10/839,117, filed May 3, 2004 and entitled “Systems and Methods for Transmitting Electromagnetic Energy in a Photonic Device,” which is also fully incorporated by reference herein. In addition, the regime of the giant transmission resonance described above can be realized exclusively in the photonic devices configured to display degenerate photonic band edge (3). Additional information relating to photonic devices101configured to display degenerate band edges is contained in A. Figotin et al., “Gigantic Transmission Band-Edge Resonance in Periodic Stacks of Anisotropic Layers,” Physical Review E 72, 036619, published Sep. 29, 2005, which is also fully incorporated by reference herein.

Photonic device101can be incorporated in numerous photonic systems implemented in a myriad of applications. For instance, photonic device101can be implemented as a tunable delay line, an efficient nonlinear element used for frequency conversion, wave mixing and the like, it can also be used as a high performance resonance cavity in an optical amplifier and in a laser, a host for a multi-dimensional optical network, an incident wave receiver and the like. It should be noted that these examples are not intended to limit, in any way, the systems and methods in which photonic device101can be used. Nor are these examples intended to limit photonic device101to any one type of system, application or technology.

In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention. For example, the reader is to understand that the specific ordering and combination of process actions shown in the process flow diagrams described herein is merely illustrative, unless otherwise stated, and the invention can be performed using different or additional process actions, or a different combination or ordering of process actions. As another example, each feature of one embodiment can be mixed and matched with other features shown in other embodiments. Features and processes known to those of ordinary skill may similarly be incorporated as desired. Additionally and obviously, features may be added or subtracted as desired. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.