Abstract:
Light is processed and, in some instances, generated using an approach involving a photonic crystal resonator arrangement. According to an example embodiment, a photonic crystal resonator array includes an array of defect locations configured for controlling the group velocity of light passing through the photonic crystal resonator array. In one implementation, holes are selectively formed in a membrane, with certain periodic locations in the membrane being substantially free of holes. In other implementations, certain periodic locations as discussed above are characterized by holes having a relatively differently-shaped opening, relative to a plurality of the holes. Still other implementations involve optical delay components, lasers, sensors and other devices implemented with a photonic crystal resonator array.

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to crystal structures and more particularly to the use and implementation of photonic crystal structures with light. 
     BACKGROUND 
     A variety of applications seek to control and/or manipulate the propagation of electromagnetic radiation and many applications are specifically directed to the manipulation and control of light propagation. For instance, lasers, optical delay components, sensors, non-linear optical devices and others manipulate light for use in many different applications. 
     One approach to manipulating light involves the use of crystalline structures and, more particularly, photonic crystals. Photonic crystals are structures typically implemented with dielectric type materials and are used to manipulate the propagation of light in certain applications. In many applications, photonic crystals are implemented with artificial multidimensional periodic structures having periodic variations in dielectric constant, with a period of the order of optical wavelength. These periodic structures tend to prohibit light from propagating under certain conditions. Photonic crystals can be implemented for defining a path for light that can bend sharply with low loss, for facilitating the localization of light and/or for defining small optical cavities for laser applications. 
     Achieving slow (or small) group velocity is useful in a variety of applications, ranging from optical delay components and low-threshold lasers, to sensors and the study of nonlinear optics phenomena. 
     Photonic crystals have been employed for achieving slow group velocities of light at electromagnetic band edges of the crystals. However this approach can be used to achieve slow group velocity for a relatively narrow range of wave vectors in a particular direction. This approach causes a generally large variation of group velocity with a wave vector (i.e., group velocity dispersion) and as a result leads to distortion in the shape of an optical pulse propagating through the structure. 
     Coupled resonator optical waveguides (CROWs) are structures that have been proposed for reducing group velocity. See, e.g., Yariv et al.,  Coupled - resonator optical waveguide: a proposal and analysis , Optics Letters Vol. 24, No. 11 (Jun. 1, 1999). In this case, adjacent defect cavities exhibit electromagnetic fields that couple with one another (due to evanescent Bloch waves), and a slow group velocity is achieved as a result of the tunneling of photons between the cavities. However, the reduction of group velocity is generally limited to a narrow region along the waveguide axis in which the cavities are coupled. As in the case of photonic crystal waveguides, the coupling into such a CROW structure is difficult, since the input (light) beam needs to be aligned in one particular direction. 
     These and other issues have been particularly challenging to the implementation of light in many applications, including applications involving the use of photonic crystals. 
     SUMMARY 
     The present invention is directed to overcoming the above-mentioned challenges and others related to the types of devices and applications discussed above and in other applications. These and other aspects of the present invention are exemplified in a number of illustrated implementations and applications, some of which are shown in the figures and characterized in the claims section that follows. 
     Various aspects of the present invention are applicable to an approach involving a crystalline material with an array of resonators characterized by hole locations with periodic inconsistencies. Such a structure can be used to control the group velocity of light passing in the crystalline material. 
     According to another example embodiment of the present invention, a photonic crystal device includes a substrate and a (e.g., two-dimensional) photonic crystal resonator array. In many instances, such a resonator array may be referred to as a Coupled Photonic Crystal Resonator Array (CPCRA). The resonator array includes a membrane having an arrayed pattern of hole locations, with the membrane defining the hole locations and with periodic inconsistencies introduced into hole patterns; such inconsistencies characterize locations of resonators inside the array. The resonator array is adapted, with the substrate, to control the group velocity of light propagating in an arbitrary crystalline direction of the structure. 
     According to another example embodiment of the present invention, a laser includes a photonic crystal resonator array configured and arranged for controlling the type of light (e.g., the group velocity of light) passed through this array. A membrane is implemented with an arrayed pattern of hole locations including a plurality of holes, and contains an embedded active layer, such as multi-quantum wells, where a stimulated emission of photons occurs. Each hole has boundaries defined by the membrane, with periodic ones of the hole locations having an inconsistency such as a differently-shaped hole or no hole at all. A membrane is suspended over a substrate, and a low-refractive index layer (such as air, oxide, etc.) is placed between the membrane and the substrate, (e.g., to provide a vertical confinement of light in the membrane). An excitation source is arranged and adapted to excite a portion of the active layer into emitting photons, and the photonic crystal resonator array is configured and arranged to couple the emitted photons to output laser light. This coupling may involve, for example, directing a selected wavelength of the photons in a direction substantially perpendicular to a lateral direction of the arrayed pattern. 
     Other example embodiments are directed to sensor implementations of a photonic crystal resonator array, such as that discussed above. 
     Still other example embodiments are directed to an optical delay device that uses a photonic crystal resonator array to cause a delay for optical signal, relative to an optical signal that is not interacting with a photonic crystal resonator array. 
     The above summary is not intended to describe each illustrated embodiment or every implementation of the present invention. The figures and detailed description that follow more particularly exemplify these embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention may be more completely understood in consideration of the detailed description of various embodiments of the invention that follows in connection with the accompanying drawings, in which: 
         FIG. 1  shows a cross-sectional view of a photonic crystal resonator array including a membrane suspended over a substrate, according to an example embodiment of the present invention; 
         FIG. 2  shows a single unit cell resonator for use in a photonic crystal resonator array, according to another example embodiment of the present invention; 
         FIG. 3  shows a top view of an implementation for a multitude of single unit cell resonators, such as that shown in  FIG. 2 , according to another example embodiment of the present invention; 
         FIG. 4  shows a cross-sectional view of a photonic crystal resonator with an InP substrate, according to another example embodiment of the present invention; 
         FIG. 5  shows a cross-sectional view of a photonic crystal resonator array laser at a stage of manufacture, with active material wafer bonded to a photonic crystal structure, according to another example embodiment of the present invention; 
         FIG. 6  shows an active CPCRA sensor with an InP substrate patterned with a resonator array, according to another example embodiment of the present invention; 
         FIG. 7  shows a passive CPCRA sensor, according to another example embodiment of the present invention; 
         FIG. 8  shows an optically pumped CPCRA laser, according to another example embodiment of the present invention; and 
         FIG. 9  shows one possible implementation for an electrically pumped CPCRA laser such as that shown in  FIG. 8  with an InP substrate bonded to a silicon chip, according to another example embodiment of the present invention. 
     
    
    
     While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. 
     DETAILED DESCRIPTION 
     The present invention is believed to be applicable to a variety of different types of devices and processes, and the invention has been found to be particularly suited for controlling the group velocity of light. While the present invention is not necessarily limited to such applications, various aspects of the invention may be appreciated through a discussion of various examples using this context. 
     According to an example embodiment of the present invention, two-dimensional arrays of coupled photonic crystal resonators are configured to exhibit flat electromagnetic bands in all crystalline directions (i.e., electromagnetic bands whose frequency variation with a wave vector is minimized in all directions in a plane in which the arrays are arranged). These relatively flat electromagnetic bands are implemented to reduce the group velocity of light propagating through the resonators, over an entire range of optical wave vectors. Relative to a particular mode (corresponding, e.g., to a field pattern for a particular resonant frequency), group velocity in this context refers generally to the speed at which an electromagnetic field coupled to this particular mode propagates through the resonators. This approach to reducing group velocity is implemented to generally minimize the distortion of an optical pulse propagating through the structure, and to increase the density of optical states. This approach has been found useful for reducing the power threshold of nonlinear optical processes and lasing. 
     In some implementations, the arrays of coupled photonic crystal resonators are implemented with a two-dimensional or three-dimensional arrangement of resonators exhibiting evanescent electromagnetic field coupling in all crystalline directions. In this regard, the mode of each resonator in the array is coupled, with electromagnetic waves being transmitted across the array. The resonant frequency of each resonator falls within the photonic bandgap (forbidden area) of the surrounding array structure, facilitating high quality (high-Q) optical modes. For more information regarding the coupling of electromagnetic bands across adjacent resonators in a one-dimensional chain, reference may be made to the above-discussed document entitled  Coupled - resonator optical waveguide: a proposal and analysis , which is fully incorporated herein by reference. 
     In another example embodiment of the present invention, a coupled photonic crystal resonator array (CPCRA) is employed to build low-threshold photonic crystal lasers to facilitate desirable output power. The CPCRA includes periodic defects that act together to generate coupled electromagnetic fields across the array to reduce group velocity in generally any photonic crystal direction. This reduction in group velocity is implemented to achieve relatively high output power while preserving a generally low lasing threshold (the lowest excitation power level at which a laser&#39;s output is mainly the result of stimulated emission rather than spontaneous emission). For example, a particular mode can be localized in the photonic band gap of the resonator array (as set by defect type and periodicity) to reduce group velocity (i.e., increase the density of optical states), thereby reducing lasing threshold. In addition, the radiative decay time of carriers is also reduced, facilitating a laser that can be modulated at very high speeds. In various implementations, this approach is further implemented with the construction of efficient light-emitting diodes (solid-state light sources), that generally operate below the lasing threshold for stimulated emission and employ a relatively high spontaneous emission rate, achievable in CPCRAs. 
     In connection with some embodiments discussed herein and as mentioned above, the term “spontaneous emission” generally refers to radiation emitted when a quantum mechanical system drops spontaneously from an excited level to a lower level, followed by an emission of photon with energy about equal to the difference between the initial and the final state. This radiation is emitted according to the laws of probability without necessary regard to the simultaneous presence of similar radiation. The rate of spontaneous emission is proportional to the Einstein “A” coefficient and is inversely proportional to the radiative lifetime. 
     Also in connection with some embodiments discussed herein and as mentioned above, the term “stimulated emission” refers to radiation that is similar in origin to spontaneous emission but is determined by the presence of other radiation having the same frequency. The phase and amplitude of the stimulated wave depend on the stimulating wave; thus, this radiation is coherent with the stimulating wave. The rate of stimulated emission is proportional to the intensity of the stimulating radiation. 
     In another example embodiment, arrays of coupled photonic crystal resonators are adapted for the exploration of nonlinear optical effects (e.g., solitons) and/or the construction of optical switching arrays resulting from the optical delay of pulses propagating through the arrays. 
     According to another example embodiment of the present invention, CPCRAs are constructed by periodically modifying array locations in a photonic crystal slab. These modified locations may be formed, for example, by forming generally consistent openings in the slab and, at periodic locations, introducing an opening having a different size and/or shape than the generally consistent openings or, in some instances, eliminating an opening altogether. The crystal slab is suspended over a substrate in a manner that facilitates the passage of light through resonators in the crystal slab. Electromagnetic bands that couple with modified locations are thereby formed and exhibit generally low group velocity. 
       FIG. 1  shows a two-dimensional CPCRA  100  having a repeating defect structure that facilitates electromagnetic field coupling across the CPCRA, according to another example embodiment of the present invention. The CPCRA  100  includes a membrane  120  suspended over a substrate  105  by supporting structures  110  and  112 . The membrane  120  and substrate are arranged such that an undercut air region exists between the membrane and substrate (facilitating, e.g., a guiding mechanism of light in silicon membrane  120  via air (having a relatively low refractive index) above and below the membrane. 
     The membrane  120  has a thickness represented by dimension “d,” and is characterized by a plurality of lattice holes (e.g.,  130 ) in an array. Every third lattice hole in two (x and y) perpendicular directions has been removed to create a defect location (e.g.,  132 ), relative to locations in the array having a hole. 
     The thickness of the CPCRA  100  is selected to fit a particular implementation to which the CPCRA is applied. In one implementation, the CPCRA  100  includes a dielectric slab having a thickness of 0.55 a with a hole radius is of about 0.4 a, where “a” is the inter-hole spacing indicated in  FIG. 1 , with a refractive index of about n=3.5, corresponding to silicon at optical wavelengths. Coupled cavity bands are formed with adjacent tiled patterns of holes and defects as shown in the CPCRA  100 . 
     In another implementation, the CPCRA structure  100  is formed using a silicon on insulator approach for an operating wavelength of about 1550 nm. The desired thickness of the silicon membrane  120  is set using wafer thermal oxidization followed by hydrofluoric (HF) wet etching of oxide formed in the thermal oxidation. Openings are patterned in the silicon membrane  120  by using polymethylmethacrylate (PMMA) layer (molecular weight of about 495 K) that is spun on the silicon membrane  120 . The PMMA layer is baked on a hot plate at about 170° C. for about 30 min to create a PMMA layer having a thickness of about 320 nanometers. Electron-beam lithography is then performed (e.g., in a Raith  150  system at 10 keV) and the exposed PMMA is developed in 3:1 isopropyl alcohol IPA:MIBK mixture for about 50 seconds and rinsed in IPA for 30 seconds. Patterns are subsequently transferred to the silicon using a magnetically induced reactive ion etch with HBr/Cl 2  gas combination, forming the patterned openings shown in  FIG. 1 . After dry etching, remaining PMMA is removed by an O 2  plasma process. Finally, the oxide layer underneath silicon membrane  120  is removed by immersing the sample into the buffered HF, leaving behind portions  110  and  112  of the oxide layer and a freestanding silicon membrane  120 . 
     The substrate material  105  is implemented with different types of materials, depending upon the implementation. In some instances, the substrate material  105  includes a silicon-based material. In other instances, the substrate material is an indium phosphide (InP) type material configured for applications such as those involving lasers. In addition, material having a lower refractive index than the membrane material  120  and the substrate material  105  can be inserted in between the membrane and substrate material and utilized for guiding light in the membrane material  120 . For instance, air, which has the lower refractive index than the membrane material  120  and the substrate material  105 , is used in  FIG. 1 . 
     The arrangement and/or shape of the holes are selected to fit a particular application for which the CPCRA is implemented. As shown in  FIG. 1 , each of the holes is spaced apart from other holes at about an equal distance (represented by distance “a”). However, in various implementations, the hole spacing is varied to suit the needs of the implementation. For instance, by varying the spacing in one or both of x and y (or other) directions, the band in which optical signals are passed can be tuned. Similarly, by selecting the shape of the holes, the band can also be tuned. For instance, the radius “r” of the hole can be increased or decreased, or the holes can be stretched or skewed. The position of a band through which light passes in the CPCRA is thus manipulated within the band gap. This approach increases or decreases the overlap of an electromagnetic field with an air region inside an individual resonator (e.g., in a hole), and leads to an increase or decrease in the mode frequency. In addition, the shown holes can be replaced with other openings having a variety of different shapes (e.g., oval). Each of these approaches is selectively implemented for tuning the band in which optical signals are passed for particular CPCRA functions. 
       FIG. 2  shows a single unit cell resonator  200  for use with a repeating pattern of resonators in a generally square photonic crystal lattice, according to another example embodiment of the present invention. The resonator  200  has directions of high-symmetry points, Γ, X, and M as shown by legend  220 . This unit cell  200  may be implemented, for example, in connection with the repeating defect structure used with the CPCRA  100  shown in  FIG. 1  and discussed above. This structure can be implemented as a two-dimensional (2D) array of single-defect photonic crystal cavities formed by altering and/or removing a single air hole (i.e., by not forming an air hole). This structure supports three types of modes: doubly degenerate dipole, nondegenerate quadrupole, and nondegenerate monopole. 
     The single unit cell resonator  200  includes hole regions  210 – 217 , with a central defect location  218 . While referred here as a defect location, the defect location  218  generally refers to a location having a variation in the hole pattern (i.e., no hole), and does not necessarily imply that the lack of a hole is “defective” in the context of an undesirable characteristic. 
     As the lattice perturbation increases (e.g., a modified, or defect, hole radius decreases), modes are pulled from the air or dielectric band and localized in the band gap. For example when the defect hole radius is decreased (e.g., as with a zero hole radius shown at defect location  218 ), the modes are pulled from the air band into the bandgap. The first mode to be localized in this process is the dipole, and the last is the monopole. In some implementations, the cavity mode with a desirable quality factor (Q-factor) is the quadrupole mode. Here, when implemented with the quadrupole mode, the resonator  200  exhibits magnetic field patterns as represented by regions  230 ,  232 ,  234  and  236 . These bands are generally equal in four directions and couple generally equally to all adjacent resonators (i.e., when arranged in an array as shown in  FIG. 3 ). In other implementations (e.g., where linear polarization is desirable) the dipole mode is localized and used; this mode exhibits a magnetic field pattern with two lobes (relative, e.g., to a quadrupole mode exhibiting four lobes) and is primarily linearly polarized. 
       FIG. 3  shows an array  300  of unit cell resonators, similar to the resonator  200  shown in  FIG. 2 , according to another example embodiment of the present invention. The array  300  includes unit cell resonators in a two-dimensional pattern defined by rows and columns. By way of example, row “R 1 ” is labeled, as are columns “C 1 ” and “C 2 .” In this regard, a single unit cell resonator, similar to unit cell resonator  200  shown in  FIG. 2 , occupies a location defined by the intersection of row “R 1 ” and column “C 1 ,” with an additional unit cell resonator occupying a location in row “R 1 ” but under column “C 2 .” A variety of such arrangements are possible, using different geometrical shapes and further adding a third dimension (e.g., where unit cell resonators, or arrays of unit cell resonators, are stacked). 
     In one implementation, the number of holes between defect locations in the array  300  is increased. For instance, as shown, there are two holes between adjacent defect locations (as defect location  218 ). The number of holes between these locations can be increased by separating adjacent unit cell resonators by a row or column of holes. Referring to columns C 1  and C 2 , an additional column of holes inserted between these columns would increase the distance between defect locations in adjacent unit cells in each column and thereby reduce the coupling between individual resonators. This approach may be implemented to make the coupled-quadrupole band flatter; e.g., the group velocity of light passing through the array  300  is reduced. 
       FIG. 4  shows a cross-sectional view of a photonic crystal resonator  400  with a substrate  405 , according to another example embodiment of the present invention. The resonator  400  is similar to the resonator  100  shown in  FIG. 1 , but without an undercut region as shown between the membrane  120  and the substrate  205 . Various dimensions including a membrane thickness (d) hole radius (r) and spacing (a) are shown as in  FIG. 1 . Here, a substrate  405  is separated from a membrane layer  420  by a low refractive index material  410  such as an oxide-containing material or air. The membrane layer  420  includes an array arrangement of holes and, at periodic intervals, locations without holes for facilitating the selective passing of light as discussed above. This approach may be implemented, for example, with laser and/or sensor applications. 
     The membrane layer  420 , substrate  405  and low refractive index material  410  may be made of a variety of materials. In one instance, one or both of the membrane layer  420  and substrate  405  are made of silicon. In another instance, the low refractive index material  410  is made of silicon dioxide. In another instance, the membrane layer  420  includes InGaAs with an embedded active layer  425  (e.g., as InGaAsP quantum wells and/or InAs quantum dots) at the center of the membrane layer, with the substrate  405  including InP and the low refractive index material  410  including one or more of air, an oxide, an a non-undercut InP material. 
       FIG. 5  shows a cross-sectional view of a photonic crystal resonator array  500  at a stage of manufacture, according to another example embodiment of the present invention. An InP-based (e.g., InGaAs) substrate  520  having an active layer  525  (e.g., InGaAsP quantum wells) is shown in a position for bonding to a silicon-on-insulator (SOI) arrangement  502 , having a silicon substrate  505  separated from an upper silicon layer  530  (e.g., epitaxial silicon) by an insulative layer  510 . The insulative layer  510  includes one or more of a variety of materials, such as SiO 2  (shown) or other materials characterized by a low refractive index. Bonding may be carried out as shown by the arrow labeled “wafer bonding,” with the InP-based substrate being bonded onto the upper silicon layer  530 . The upper silicon layer  530  and the insulative layer  510  are patterned to form an array of holes extending from an upper surface of the silicon layer  530  and into the insulative layer  510 . However, in various instances, the insulating layer  510  is not necessarily patterned. In addition, although the pattern of holes shown in  FIG. 5  corresponds to a hexagonal photonic crystal lattice without defects, the same CPCRA as shown in  FIG. 4  can also be implemented with the approach shown in  FIG. 5 . In this regard, hole sizes are periodically modified (or holes are eliminated) in both x and y directions to form a CPCRA. The embodiment shown in  FIG. 5  can be used, for example, to implement light sources (such as lasers) that are compatible with silicon-based optoelectronics. 
       FIG. 6  shows an active CPCRA sensor  600  with an InP CPCRA  610  having an InP substrate patterned with an array of resonators, according to another example embodiment of the present invention. A pump laser  620  is used to stimulate the InP CPCRA  610  with pumping laser light  622  that is passed through a beamsplitter  630  and a lens arrangement  640  to stimulate the InP substrate. Generally, the pumping laser light hits the InP CPCRA  610 , scatters along the plane of the CPCRA and interacts with an active layer (e.g., quantum dots or quantum wells) embedded inside of it. The light is absorbed by the active layer, which generates electrons and holes (electron-hole pairs) in response to the light. When the electron-hole pairs recombine, photons are emitted (e.g., at a different wavelength and corresponding color and direction than the pumping laser light  622 ). The emitted photons (light) emit along the plane of the InP CPCRA  610  and are coupled to a vertical direction towards the lens arrangement  640 . Implemented as a sensor, the InP CPCRA  610  responds to the pumping laser light  622  by generating light that is passed through the lens arrangement  640 , the beamsplitter  630  and output as signal  616 . In connection with this embodiment, it has been discovered that the lasing wavelength (i.e., a wavelength of emitted light  616 ) is sensitive to the refractive index of the layer  612  deposited on top of the structure; therefore, various bio-chemical reactions in the layer  612  can be monitored by monitoring the wavelength of the emitted light. 
     The coated material  612  can include one or more layers, depending upon the desirable application. For example, when implemented for biological sensing, the InP CPCRA  610  is coated with first material such as an antibody, hormone or enzyme. The InP CPCRA  610  is then coated with a second material, such as a corresponding antigen for antibody sensing, a receptor for hormone sensing or a particular substrate for enzyme sensing. With these types of approaches, the interaction of nucleotides with complementary nucleotides, the interaction of biotinylated albumin serum with streptavidin (protein molecule) and others can be sensed. For example, by observing an optical response (relative to wavelength and time), specific parameters relating to the interaction (i.e., kinetic rates of the interaction) can be detected. 
     In another implementation, characteristics of a coated material  612  (e.g., chemical or biological material) are determined. For example, the refractive index, molar concentration (with known refractive index) or thickness (also with known refractive index) of the coated material  612  can be determined. In connection with this implementation, the operating wavelength of the structure shown in  FIG. 6  has been discovered to be highly sensitive to the refractive index of the medium surrounding the CPCRA sensor  600  (i.e., deposited biological or chemical material  612 ), as described above. A chart for each unknown property (refractive index, molar concentration, thickness) is extracted as function of wavelength for a particular application (and sensor  600 ). The material  612  is coated and the wavelength of light (as signal  616 ) is detected. The detected wavelength is correlated to the chart to determine one or more unknown properties of the material  612 . 
       FIG. 7  shows a passive CPCRA sensor system  700 , according to another example embodiment of the present invention. The system  700  includes an SOI-based CPCRA  710  that responds to light by altering a reflection or transmission type signal (i.e., a peak or dip occurs in the transmitted or reflected signal as the wavelength of an excitation beam changes). The CPCRA  710  may be implemented similarly to the CPCRA shown in one of the above-discussed figures, such as  FIG. 4  or  5 , and is optionally coated with a material as discussed with  FIG. 6 . A pump laser  720  generates a polarized pumping laser light  722  that is passed to the CPCRA  710  via a beamsplitter  730  and a lens arrangement  740 . A portion  724  of the pumping light  722  from the pump laser  720  is optionally used for synchronization, reference or other processing purposes. 
     The CPCRA  710  generates an output signal in a manner similar to that shown in  FIG. 6 , with an output (e.g., “reflected” signal of opposite polarization relative to the excitation)  716  passed through the beamsplitter  730  as well as a polarizing beamsplitter  735 . A transmission signal  750  and the reflection signal of opposite polarization  716  are measured from the CPCRA  710 . These signals ( 750  and  716 ) exhibit changes (i.e., peaks or dips) as a function of the wavelength of the pump laser  722 . The wavelength at which these peaks and dips occur is related to the refractive index of the layer deposited on top of the CPCRA; therefore, variations in the surrounding refractive index are detected and used to monitor reactions including, e.g., biochemical reactions as described above. 
       FIG. 8  shows an optically pumped CPCRA laser arrangement  800 , according to another example embodiment of the present invention. The laser arrangement  800  includes a CPCRA  810  implemented with a substrate such as an InP-type substrate. A pump laser  820  generates pumping laser light  822  that is passed through a beamsplitter  830  and a lens arrangement  840  to the CPCRA  810 . The CPCRA  810  responds to the pumping laser light  822  by generating photons, e.g., as discussed above with electron-hole pair generation. The photons emit generally perpendicular to the plane of the CPCRA  810 , passed through the lens arrangement  840  and the beamsplitter  830  and output as laser emission  816 . 
       FIG. 9  shows an InP-based CPCRA  910  for application as an electrically pumped CPCRA, according to another example embodiment of the present invention. The CPCRA  910  includes an InP substrate  911  bonded to a silicon chip  912 , shown apart for illustrative purposes. An electrical pumping circuit  940  is adapted to apply electrical pumping signals to the CPCRA  910 . In response to the electrical pumping, the CPCRA  910  generates photons that are emitted as laser emission  930 . In various applications, wafer-bonding of InP to silicon is implemented to facilitate the construction of lasers that are compatible with silicon-based optoelectronics. In another implementation, an electrically pumped InP laser includes an approach involving doped layers and electrodes, similar to that shown in  FIG. 4 . 
     While the present invention has been described with reference to several particular example embodiments, those skilled in the art will recognize that many changes may be made thereto without departing from the spirit and scope of the present invention. For example, various resonator shapes and arrangements can be implemented with CPCRAs, using the approaches discussed above, such as by arranging a hexagonal or other shape of defect structure for a lattice (relative, e.g., to the square lattice in  FIG. 1 ). In other applications, rods in square or hexagonal arrays of dielectric rods embedded in air are periodically modified to achieve low group velocity as discussed herein. In this regard, CPCRAs can be formed by periodically modifying unit cells in any two or three dimensional photonic crystal array, in connection with various example approaches and embodiments. In addition, the various example embodiments and implementations discussed herein can be implemented with a variety of devices and approaches, such as those involving one or more of: waveguides, filters, lasers and optical integrated circuits. For example approaches and embodiments that may be implemented in connection with one or more of the embodiments discussed herein, reference may be made to the attached Appendices A and B, respectively entitled “Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays” and “Polarization control and sensing with two-dimensional coupled photonic crystal microcavity arrays.” Furthermore, for general information regarding resonator arrays and for specific information regarding applications to which one or more of the various example embodiments and implementations shown and discussed herein may be applied with or to, reference may be made to Hatice Altug and Jelena Vuckovic, “Two-dimensional coupled photonic crystal resonator arrays,” Applied Physics Letters, Volume 84, Number 2, 12 Jan. 2004, which is fully incorporated herein by reference.