Abstract:
One-dimensional (1D) photonic crystal prisms can separate a beani of polychromatic electromagnetic waves into constituent wavelength components and can utilize unconventional refraction properties for wavelength dispersion over significant portions of an entire photonic band rather than just near the band edges outside the photonic band gaps. Using a 1D photonic crystal simplifies the design and fabrication process and allows the use of larger feature sizes. The prism geometry broadens the useful wavelength range, enables better optical transmission, and exhibits angular dependence on wavelength with reduced non-linearity. The properties of the 1D plhotonic crystal prism can be tuned by varying design parameters such as incidence angle, exit surface angle, and layer widths. The 1D photonic crystal prism can be fabricated in a planar process, and can be used as optical integrated circuit elements.

Description:
The invention described hereunder was made in the performance of work under a NASA contract, and is subject to the provisions of Public Law 96-517 (35 U.S.C. 202) in which the Contractor has elected not to retain title. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to the field of prisms, wavelength division multiplexers, and optical integrated circuits. More specifically, it relates to methods of dispersing a polychromatic electromagnetic wave into its constituent wavelength An components. 
     2. Description of Related Art 
     A photonic crystal is a periodic structure consisting typically of two dielectric materials with high dielectric contrast (e.g., semiconductor and air), and with geometrical feature sizes comparable to or smaller than light wavelengths of interest. As an engineered structure or artificially engineered material, a photonic crystal can exhibit optical properties not commonly found in natural substances. Extensive research has led to the discovery of several classes of photonic crystal structures for which the propagation of electromagnetic radiation is forbidden in certain frequency ranges (photonic band gaps, or PBGs). More recently, it has also been realized that electromagnetic radiation with frequency just outside the photonic band gaps can propagate in photonic crystals with characteristics that are quite different from those of ordinary optical materials. Recently, Kosaka and co-workers, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami published an article titled “Superprism phenomena in photonic crystals: Toward microscale lightwave circuits”,  Journal of Lightwave Technology,  17 (11): 2032-2038 (1999). In the article, Kosaka showed that they had demonstrated a “superprism” phenomenon in a three-dimensional photonic crystal. They reported that two light beams, with slightly different wavelengths (0.99 μm and 1 μm), exhibited a 50° divergence inside the photonic crystal. The same pair of beams entering a conventional optical material at the same angle would diverge by less than 1° after incidence. This unusually large color-dispersion capability is called the superprism or ultra-refractive effect. The photonic crystal that was the subject of the demonstration is a complex three-dimensional (3D) structure consisting of, from bottom to top: (1) a silicon substrate, (2) a silicon dioxide buffer layer patterned with a hexagonal array of holes formed by electron-beam lithography, and (3) alternating layers of amorphous silicon and silicon dioxide sputtered on top of the patterned buffer layer. It is believed that. NEC, NTT, and the Tohoku University in Japan sponsored the work performed. It is believed that the Tohoku University made the devices tested using E-beam (electron-beam) lithography to form a hexagonal lattice pattern on a silicon dioxide buffer layer grown on top of a silicon substrate. That step was followed by the deposition of amorphous silicon and silicon dioxide in alternating layers. A typical structure consists of 20 or so pairs of silicon/silicon dioxide layers. The silicon/silicon dioxide layers follow the contour of the E-beam patterned buffer layer and form a three-dimensional structure. The many steps in the process suggest that the devices produced were made at high cost. 
     The unusual propagation characteristics of electromagnetic waves with frequency just outside the photonic band gaps (PBGs) have been analyzed by a number of researchers. Lin et al. “recognize the highly nonlinear dispersion of PBG materials near Brilluoin zone edges and utilize the dispersion to achieve strong prism action” (“Highly dispersive photonic band-gap prism,” S. Y. Lin, V. M. Hietala, L. 
     Wang and E. D. Jones, Optics Letters, 21(21), pp 1771-1773, 1996). Notomi performed theoretical analysis and demonstrated “that light propagation in strongly modulated two-dimensional (2D)/3D photonic crystals become refractionlike in the vicinity of photonic band gap.” (“Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” M. Notomi, Phys. Rev. B, 62(16), pp 10696-10705, 2000). Miller et al. stated that in “region just outside the main reflection region there is strong group velocity dispersions, causing different wavelength of light to travel at different angles through the dielectric stack.” (“Method for dispersing light using multilayered structures,” D. 
     A. B. Miller et al., U.S. patent application Ser. No. 20020018298). Lin et al. found that “very strong dependence of dielectric constant, and hence index of refraction, on photon energy near the bandgap allows photonic crystals to be used to form highly dispersive prisms and other optical elements.” (S. Y. Lin et al., U.S. patent application No. 20010012149). All of these works recognize the strong dispersion of electromagnetic waves with frequencyjust outside the photonic band gaps (PBGs). 
     SUMMARY OF THE INVENTION 
     The invention shows that strong wavelength dispersion, known as the superprism effect or ultra-refraction, can be found in one-dimensional (one-dimensional) photonic crystals for entire photonic bands rather than near the band edges only. In the lowest frequency photonic band, ultra-refraction occurs near the edge of the Brillouin zone. In higher photonic bands, where wavelengths are always comparable to or shorter than photonic crystal feature sizes, ultra-refraction can be found for the entire band, or a significant portion of the entire band, rather than just near the band edges Oust outside photonic band gaps). The use of full bands rather than only band edges broadens the ultra-refraction wavelength range considerably. The use of full bands is preferred, as transmission tends to diminish near the band edges just outside photonic band gaps where reflection occurs. The use of higher bands also allows the use of photonic crystals with larger feature sizes, thereby reducing fabrication requirements. In a prism-like geometry, electromagnetic waves dispersed by the one-dimensional photonic crystal exhibit angular dependence on wavelength which is much closer to being linear, making this effect much easier to use than the highly non-linear dispersions near the band gap. The properties of the ultra-refractive one-dimensional photonic crystal prism can be tuned by varying design parameters such as incidence angle, exit surface angle, and layer widths. The mathematical analysis of a one-dimensional photonic crystal is well understood, and therefore the design procedure is simple. In addition to the foregoing, a one-dimensional photonic crystal prism is easier to fabricate than a 2D or 3D photonic crystal prisms. For optical and infrared wavelengths, they can be made on semiconductor wafers (e.g., silicon or gallium arsenide), which also allows for the possibility of monolithic integration with other micro optical components. For applications to longer wavelengths (such as millimeter waves), one-dimensional photonic crystal prisms could be made by bonding pre-formed wafers together. 
     An important reason why we are able to exploit fill-band ultra-refraction in one-dimensional photonic crystals is that it is easy to design one-dimensional photonic crystals with simple band structures that monotonically vary with frequency and wave vector. In 2D and 3D photonic crystals, photonic band structure can be considerably more complicated, and can sometimes exhibit features such as crossings or anti-crossings, or a multiplicity of bands, which makes the exploitation of full-band ultra-refraction more difficult. However, appropriately engineered 2D/3D photonic crystals can exhibit fill-band (or at least partial band, rather than band-edge only) ultra-refraction, albeit at a greater cost due to increased complexity. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic side sectional view of the one-dimensional Photonic Crystal; 
     FIG. 2 schematically illustrates how a one-dimensional photonic crystal slab might be used to disperse light of different wavelengths; 
     FIG. 3 shows propagation angle inside a one-dimensional photonic crystal slab as a function of incident beam wavelength; 
     FIG. 4 shows the ratio between lateral displacement (D) and photonic crystal slab thickness (T) as a function of incident wavelength; 
     FIG. 5 schematically illustrates the strongly refractive one-dimensional photonic crystal prism with an angled exit surface used to disperse electromagnetic waves of different wavelengths to three remote targets; 
     FIG. 6 shows exit beam propagation angle, θ out , as a function of incident wavelength, after traversing the strongly refractive one-dimensional photonic crystal prism. Results for four different exit surface angles, θ xs , are plotted; 
     FIG. 7 shows exit beam propagation angle, θ out , as a function of incident wavelength after traversing a strongly refractive one-dimensional photonic crystal prism for three different layer-width combinations; 
     FIG. 8 shows exit beam propagation angle, θ out , as a function of incident wavelength after traversing a strongly refractive one-dimensional photonic crystal prism from three different incidence angles, θ inc ; 
     FIG. 9 schematically illustrates a possible implementation of the strongly refractive one-dimensional photonic crystal prism on a SOI (silicon on insulator) wafer using micro-fabrication techniques; 
     FIG. 10 schematically illustrates a possible implementation of the strongly refractive one-dimensional photonic crystal prism on a GaAs wafer using micro-fabrication techniques; 
     FIG. 11 is a 3-D schematic perspective exploded view of two wafers etched to expose void rectangular regions, the two etched wafers being interleaved between three solid wafers before assembly of the strongly refractive one-dimensional photonic crystal prism; and 
     FIG. 12 is a 3-D schematic perspective exploded view of two silicon dioxide coated wafers etched to expose void rectangular regions in the silicon dioxide, the two etched wafers being stacked under a single solid silicon or germanium wafer before assembly of the strongly refractive one-dimensional photonic crystal prism. 
    
    
     DETAILED DESCRIPTION 
     The invention strongly refractive one-dimensional photonic crystal prism will now be discussed using the drawings of FIGS. 1-12. In FIG. 1, the photonic crystal  10  is shown receiving a first ray of light  12  from a first light source (not shown). The crystal superprism has a first vertically stacked parallel array of layers,  14   a - 14   f , formed from a dielectric optical material, such as silicon or GaAs, having a first index of refraction, 1. In the embodiment of FIG. 1, the layers are spaced apart at uniform predetermined distances, such as distance “a” from each other. We identify “a” as the period of the one-dimensional photonic-crystal prism. 
     A second vertically stacked parallel array of layers  16   a - 16   e  are formed from a dielectric optical material or a void space and have a second index of refraction, 2. The second vertically stacked parallel array of layers  16   a - 16   e  are spaced apart at uniform predetermined distances from each other. The second vertically stacked parallel array is interleaved into, as a stack of cards, the first vertically stacked parallel array. Optional sidewalls  17   a ,  17   b  are shown, although they are not necessary if the multilayers are mechanically self-supporting, or supported at the back (not shown). 
     The layer widths of the first and second material within each period are h 1  and h 2 , respectively. We note that 
     
       
           h   i +h 2   =a.    
       
     
     In principle, there could be more than two layers per (repeating) period. The analysis described here also applies to structures having more than two layers per period. However, since one of the principle objectives of the invention is ease of fabrication, the simpler structure with two layers per period is the preferred embodiment. 
     The light ray  12  in FIG. 1 is described to have two wavelength components, λ a  and λ b , each having a common angle of incidence Oinc and a respective angle of refraction θ pca , θ pcb . The rays split at the point of incidence, diverge and pass through the first and second arrays of layers  14   a - 14   f  and  16   a - 16   e  to exit the first and second vertically stacked parallel arrays at the bottom surface  18 . The two rays exit at predetermined locations and are received on respective targets  20 ,  22 . The targets  20 ,  22  are positioned and orientated to select predetermined spectra within the combined light ray  12  after refractive separation. The target array  20 ,  22  could be detectors or ports. 
     The second vertically stacked parallel array of layers  16   a - 16   e , as shown in FIG. 1, is an array of void space layers, but other materials can be used as design choices. The second array of spaces might be filled with a gas such as air or if thermal conductivity is a consideration, xenon might be used. The index of refraction of the gas will be a factor in the selection of any material or gas. 
     ANALYSIS 
     To analyze superprism effects in a strongly refractive one-dimensional photonic crystal  10 , consider the schematic geometry of FIG. 1 with a collimated light ray  12  striking the incident face of the one-dimensional photonic crystal, the ray having a first component of light with a wavelength of λ a  and second component of light with a wavelength λ b . The ray is depicted as having an angle of incidence of θ inc  and is shown as being coupled through a homogeneous medium (e.g., air) into the one-dimensional photonic crystal surface. After entry into the top surface, the light waves split and propagate at separate respective angles of refraction. The component of the ray with a wavelength of λ a  propagates with an angle of refraction of θ pca , and the component of the light ray having wavelength λ b  propagates with an angle of refraction of θ pca . To compute the relationship between OinC and a light ray having a predetermined wavelength λ and an angle of refraction θ pc , we use the following procedure: 
     1. Specify the angular frequency of the ray 
     
       
         ω=2πƒ 
       
     
     (where ƒ is the frequency of light ray) and the incidence angle θ inc  is measured in a homogeneous medium. 
     2. Using the relationships: 
     
       
         ε r ω 2   =k   x   2   +k   y   2    
       
     
     and, 
     find the wave vector in the incident medium. Here ε r  is the relative permittivity of the incident medium, and k x  and k y  are the components of the wave vector perpendicular and parallel, respectively, to the interface between the homogeneous medium and the photonic crystal. (Without lost of generality, we have let k z =0), and 
     3. Compute a photonic crystal dispersion relationship ω(k), using a transfer matrix method, a standard technique commonly found in the literature, such as that described in F. Abeles,  Annales de Physique,  5, 706, 1950. Here the angular frequency ω and the parallel component of the wave vector k y  are the same as those in the incident homogeneous medium. The transfer matrix technique allows us to find the perpendicular component of the wave vector k x  in the photonic crystal. 
     4. From the photonic crystal dispersion relationship, compute the group velocity V g (k) in the photonic crystal using. 
     
       
           V   g ( k )=∇ k ω( k )=(∂ω( k )/∂ k   x , ∂ω( k )/∂ k   z ).  
       
     
     5. The components of the group velocity gives us the angle of refraction, θ pc  in the one-dimensional photonic crystal where: 
     
       
         θ pc=tan   −1 ( v   g,y   /v   g,x ).  
       
     
     The proceeding procedure computes the angle of light propagation or angle of refraction θ pc  in the photonic crystal as a function of wavelength and the angle of incident θ inc . 
     FIG. 2 illustrates how a slab of one-dimensional photonic crystal is used to separate a polychromatic beam into different wavelength components. The incident and exit faces  24 ,  26  are parallel, and both surfaces are perpendicular to the principal axis  28  of the photonic crystal, which is perpendicular to its constituent layers. The principal axis  28  of the photonic crystal (as shown) is along the x-direction. The wavelength components λ a , λ b , λ c  in the incident beam  12  are predetermined to be within an ultra-refractive range. The components of light of different wavelengths are shown to be dispersed into a wide range of propagation angles inside the photonic crystal. The figure illustrates that wavelength component θ c  is directed towards a different exit surface  30  of the photonic crystal, and is separated from θ a  and θ b  which are shown exiting exit surface  26 . FIG. 2 also illustrates that wavelength components θ a  and θ b  are separated having different lateral (y direction) displacements D a  and D b  along exit surface  26 . The wavelength rays for ka and kb are directed to targets  27   a ,  27   b  respectively, such as detectors or ports placed at suitable locations on or in the y direction close to the back surface. FIG. 2 shows that the lateral displacement of a ray is given by: 
     
       
           D=T tan(θ pc ),  
       
     
     where T is the total thickness of the photonic crystal slab. 
     FIGS. 2 and 5 show a photonic crystal in respective alternative embodiments responsive to the collimated light ray  12  from a light source (not shown). As above, the light source has at least two wavelengths and might be a broadband fiber source. The dark straight parallel lines represent a parallel array of dielectric plates. Each dielectric plate has parallel sides. The dielectric plates are periodically spaced at a distance such as distance “a” as shown in FIG.  1 . The plates are made of a dielectric material such as silicon or GaAs. The plates extend normally and homogeneously from the substrate. As depicted, the array has at least an incident face  24  and an exit surface  26  normal to the substrate. The light source is shown coupled to the incident face in both figures. 
     In the embodiments of FIGS. 2,  5 ,  9  and  10 , the light ray passes from the incident face  24  through the a parallel array of dielectric plates to exit the exit surface  26  and provide a spectrally spread image on target surfaces such as the surface of the detectors  27   a ,  27   b , and  27   c  shown. Embodiments, such as those in FIGS. 2,  9  and  10  use dielectric plates and substrate material that is homogenous, or made from the same substance and selected from the group of silicon or GaAs. Alternative embodiments of arrangements are formed on a layer of silicon dioxide or Al x O y . 
     FIG. 3 shows a sample of the results of the analysis discussed above. The calculation was performed for a simple one-dimensional photonic crystal structure, consisting of alternating layers of two materials with different layer thickness (h 1  and h 2 ) and relative permittivities ε i  and ε 2 . FIG. 3 illustrate that in wavelength ranges determined by dimensions h 1 , h 2 ; indices of refraction 
     
       
           n   1 =ε 1   1/2    
       
     
     
       
         and  
       
     
     
       
           n   2 =ε 2   1/2    
       
     
     and angle of incidence θ inc , and the angle of refraction θ pc  can vary widely as a function of wavelength outside the photonic band gaps. In the remainder of this work, angles are understood to be measured in the x-y plane of FIG.  2  and measured with respect to the x-axis. All calculations are performed for TE-mode radiation (electric field along the z-axis). Calculations for TM-modes are performed in a similar fashion yielding qualitatively similar results, but are not shown here. 
     The independent variable, the horizontal axis represents the wavelength in the incident medium. The range extends from 1 to 6, in units of “a,” the period or pitch of the one-dimensional photonic crystal. The dependent variable, the vertical axis, represents the angle of refraction in photonic crystal, θ pc , extends from 0 to 90 degrees. A value on the vertical axis is a measure of the angle of refraction, θ pc , or the angle that the light ray makes with respect to the principal axis  28 , a normal, as it propagates in the photonic crystal  10 . In FIG. 3 we have taken the specific example of 
     
       
         ε 1 =11.56  
       
     
     
       
         and  
       
     
     
       
         ε 2 =1  
       
     
     (appropriate for silicon and air, respectively), and 
     
       
         h 1 =0.2 a    
       
     
     
       
         and  
       
     
     
       
           h   2 =0.8 a    
       
     
     (i.e., 20% of each periodic is occupied by the first material, which is silicon in this case). 
     FIG. 3 shows that the refraction angle θ pc  varies rapidly with wavelength in certain wavelength ranges. The variation shown is much greater than in conventional optical material. For instance, for 
     
       
         θ inc =10°,  
       
     
     θ pc  varies monotonically from 70° to 20° as the wavelength λ changes monotonically from 4.6565 a  to 4.6798 a . Some of the other wavelength ranges for which rapid variations in θ pc  occur are listed in Table 1 below. 
     Table 1 below shows five ranges in which the respective refraction angle varies very rapidly and monotonically with wavelength. The wavelengths are given in units of the photonic crystal period “a,” and angles in degrees. The incident angle for each is 10°. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
             
             
               
                   
                   
               
               
                   
                 Wavelength 
                   
                 Refraction Angle 
                   
               
               
                   
                 Range 
                   
                 Range 
               
             
          
           
               
                   
                 Starting 
                 Ending 
                 Starting 
                 Ending 
               
               
                   
                 λ (α) 
                 λ (α) 
                 θ pc  (deg.) 
                 θ pc  (deg.) 
               
               
                   
                   
               
             
          
           
               
                   
                 Range 1 
                 4.6565 
                 4.6798 
                 70 
                 20 
               
               
                   
                 Range 2 
                 2.0257 
                 2.1463 
                 20 
                 70 
               
               
                   
                 Range 3 
                 1.5267 
                 1.5463 
                 70 
                 20 
               
               
                   
                 Range 4 
                 1.4048 
                 1.4075 
                 20 
                 70 
               
               
                   
                 Range 5 
                 1.1078 
                 1.1156 
                 70 
                 20 
               
               
                   
                   
               
             
          
         
       
     
     For each of the above wavelength ranges, two rays of light enter the photonic crystal at the same angle of incidence θ inc . As shown, each ray has a slightly different wavelength producing different angles of refraction inside the photonic crystal (θ pc ), the “Starting θ pc ” and the “Ending θ pc ”. It can be seen that the relatively small shift in wavelength characterized by the starting and ending column values produce changes in the refraction angle that are substantially different. This is called the superprism ffect or ultra-refraction. Note that in the present configuration ultra-refraction occurs ust outside of the gaps in the spectrum shown in FIG.  3 . Electromagnetic waves with wavelengths within the gaps cannot propagate inside the photonic crystal. Rays with wavelengths within the gaps are totally reflected back into the incident medium. The gaps correspond to the gaps in frequency bands (photonic band gaps) where propagation of electromagnetic radiation is forbidden inside the photonic crystal. The photonic band gaps separate the photonic bands, which represent frequency bands where propagation of electromagnetic radiation is allowed in the photonic crystal. In Table 1, Range 1 and Range 2 respectively correspond to electromagnetic radiation with frequency ranges just below and just above the GAP  1  photonic band gap. Ranges 3 and 4 straddle the GAP  2  photonic band gap. Not all of the ultra-refraction ranges are shown because FIG. 3 extends only over the wavelength from 1 a to 6a. In principle, there are an infinite number of photonic band gaps with frequency ranges higher than (or wavelength ranges shorter than) the ones shown in FIG.  3 . In other words, there are an infinite number of ultra-refraction ranges with wavelengths shorter than 1a. However, these ultra-refraction wavelength ranges are very closely spaced. For practical applications, use will be restricted to the ultra-refraction ranges surrounding the lowest few photonic band gaps. 
     In the model computations leading to Table 1 and FIG. 3, the wavelength and the layer widths (h 1  and h 2 ) were expressed in units of the one-dimensional photonic crystal period “a ” to show that the ultra-refractive wavelength range of interest is adjusted by scaling the layer widths. By way of example, if the range of the wavelengths of interest resides between 1.527 μm and 1.546 μm, as characterized by Range 3, we set 
     
       
           a= 1 μm  
       
     
     
       
         (or  h   1 =0.2 μm and  h   2 =0.8 μm).  
       
     
     If, however, we are interested in dispersion light with wavelengths between 3.053 μm and 3.093 μm, we set 
     
       
           a= 1 μm  
       
     
     
       
         (or  h   1 =0.4 μm and  h   2 =1.6 μm)  
       
     
     instead. If we are interested in dispersion light in a range of wavelengths beyond 1.5 μm, we have the option of using any of the ultra-refractive wavelength ranges listed in Table 1 by selecting an appropriate value for the photonic crystal period a. 
     Table 2 lists the values of a for the five wavelength ranges of Table 1, as well of wavelength range in microns for the given the choices of “a” in micrometers. Note that the higher numbered ranges (corresponding to higher photonic band gaps) are associated with larger values of photonic crystal period a, which make them easier to fabricate. However, in general the higher wavelength ranges also tend to be narrower. 
     Table 2 below tabulates wavelength ranges in (a) and the choice of photonic crystal period a for application to wavelengths extending from 1.53 μm. 
     
       
         
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
             
             
               
                   
                   
               
               
                   
                 Wavelength 
                   
                 Wavelength 
               
               
                   
                 Range in α 
                   
                 Range in μm 
               
             
          
           
               
                   
                 Starting 
                 Ending 
                 Period α 
                 Starting 
                 Ending 
               
               
                   
                 λ (α) 
                 λ (α) 
                 (μm) 
                 λ (μm) 
                 λ (μm) 
               
               
                   
                   
               
             
          
           
               
                   
                 Range 1 
                 4.6565 
                 4.6798 
                 0.3286 
                 1.53 
                 1.5377 
               
               
                   
                 Range 2 
                 2.0257 
                 2.1463 
                 0.7553 
                 1.53 
                 1.6210 
               
               
                   
                 Range 3 
                 1.5267 
                 1.5463 
                 1.0022 
                 1.53 
                 1.5496 
               
               
                   
                 Range 4 
                 1.4048 
                 1.4075 
                 1.0891 
                 1.53 
                 1.5329 
               
               
                   
                 Range 5 
                 1.1078 
                 1.1156 
                 1.3811 
                 1.53 
                 1.5408 
               
               
                   
                   
               
             
          
         
       
     
     FIG. 4 is a graph of the lateral displacement D in units of photonic crystal slab thickness T, i.e., D/T or tan(θ pc ), as a function of incident wavelength for an incident angle of θ inc =10°. FIG. 2 shows values of D extending in the y-axis direction with T extending in the x-axis direction. We find that the lateral displacement also varies rapidly over narrow wavelength ranges associated with the band edges Oust outside the reflection gaps), in the same way that θ pc  does in FIG.  3 . The plot of displacement versus wavelength underscores another feature of using ultra-refraction in this way. As wavelength approaches a gap, the displacerment increases rapidly in a highly non-linear fashion. While this hypersensitivity of displacement to wavelength is precisely the effect we wish to exploit, the use of this effect would also require a high degree of precision in the location of targets such as  27   a - 27   c  (e.g., detectors). In addition, we would expect diminished transmission into the photonic crystal as wavelength approaches the gaps where transmission is not allowed. The use anti-reflection coating might be necessary to ensure that we can couple enough light into the photonic crystal to take advantage of ultra-refraction. 
     For some applications (e.g., spectroscopy), band-edge ultra-refraction characteristics (narrow wavelength range, high non-linearity, and diminished transmission) might not be desirable. In the discussions on the following figures, we will show an implementation that deals effectively with these issues. 
     FIG. 5 shows a preferred embodiment of a strongly refractive one-dimensional photonic crystal prism  29 , made from a photonic crystal  10 . The strongly refractive one-dimensional photonic crystal prism  29  of FIG. 5 has a cross section that is illustrated schematically in perspective in the configuration of FIG.  10 . As shown in the schematic plan view of FIG. 5, the strongly refractive one-dimensional photonic crystal prism  29  is responsive to a light ray  12  from a light source (not shown), which also has at least two wavelengths. The strongly refractive one-dimensional photonic crystal prism  29  of FIG. 5 also has a one-dimensional periodic layered dielectric structure formed as an array of two or more parallel layers of homogenous optical material. 
     FIGS. 9 and 10 show that the parallel layers  25   a ,  25   b ,  25   c  . . . etc, of a segment of a strongly refractive one-dimensional photonic crystal prism  29  have a predetermined thickness “a ”. The structures of FIGS. 9 and 10 schematically show an embodiment in which a light ray will pass through the parallel layers  25   a ,  25   b ,  25   c , of optical crystal and void spaces  34   a ,  34   b ,  34   c . Each respective contiguous alternating layer has a different dielectric constant from the next successive layer as in the case of FIG. 9 where the dielectric constant of silicon is different from that of the next void space. FIG. 10 shows the use of GaAs in an alternative embodiment. The one-dimensional periodic layered dielectric structure or strongly refractive one-dimensional photonic crystal prism  29  has an incident surface  24  and an exit surface  26 . The incident surface  24  is shown as parallel to the parallel layers  25   a ,  25   b ,  25   c  however, the incident surface may or may not be parallel to the parallel layers as a function of the design. The same is true for the exit surface  26 . Referring to FIG. 5, by adjusting the angle θ xs  to a predetermined value, the exit angle θ out  can be arranged to change very rapidly and monotonically with wavelength, except for the normal band gap regions as appear on FIGS. 3 and 4. The exit surface  30  on FIG. 2 is also an example of an exit surface that is not parallel with the parallel layers. 
     With the exit surface  26  positioned to be non-parallel to the layers  25   a ,  25   b ,  25   c  of the one-dimensional periodic layered dielectric structure, as shown in FIGS. 5,  9  and  10 , the light ray  12  enters the incident surface  24 , passes through the one-dimensional periodic layered dielectric structure formed by layers  25   a ,  25   b ,  25   c  and void spaces  34   a ,  34   b , and  34   c  and exits the external exit surface  26  providing a spectrally spread image on a target surface, such as the three rectangular targets  27   a ,  27   b ,  27   c  depicted. 
     FIG. 9 shows a one-dimensional periodic layered dielectric structure  29  that further comprises a base  38 , such as the layer of SiO 2    40  formed on the substrate of silicon  42 . The SiO 2  operates as an optically confining cladding material. The base layer of SiO 2    40  reduces the amount of evanescent energy lost from the light ray  12  as it passes through the one-dimensional periodic layered dielectric structure  29 . In FIG. 10, the base  38  is performed from a layer of Aluminum Oxide which performs the same function as the SiO2 layer  42  shown on FIG.  9 . 
     The homogenous array of FIG.  5  and FIGS. 9 and 10 are formed to have two or more parallel layers  25   a ,  25   b  and  25   c  that repeat as an array. Each layer is formed from an optical material. The first layer  25   a  has a first dielectric constant that is different from the successive material. The intermediate layer or layers are formed from material having a second dielectric constant or even a third dielectric constant. It might be possible to form the strongly refractive one-dimensional photonic crystal prism  29 , as the one-dimensional periodic layered dielectric structure of FIGS. 9 and 10 on a silicon substrate that would be of sufficient size, to permit the formation of additional optical components thereon as discrete components, or additional optical components linked by optical paths, such as waveguides to form integrated optical circuits using the one-dimensional periodic layered dielectric structure. 
     The one-dimensional periodic layered dielectric structure of FIGS. 5,  9  and  10  can be sized and dimensioned to form a strongly refractive one-dimensional photonic crystal prism  29  that has a number of operating wavelength ranges separated by gaps, such as the gaps shown on FIGS. 3 and 4 for which strong reflection from the incident surface  24  occurs. 
     FIGS. 5,  9  and  10  shows a photonic crystal  10  having a prism shape. The principal axis  28  of the one-dimensional photonic crystal  10  is along the x-axis. For the purpose of the present discussion, we assume that the normal vector for the front or the incident surface  24  is also along the x-axis, and that the normal vector of the back or angled exit surface  26  is at an angle θ xs  with respect to the x-axis as depicted in FIG.  5 . The shape of the prism  29  we have drawn here is triangular. In general the prism  29  could be of other shapes, such as a trapezoid. A ray  12  of polychromatic electromagnetic wave entering from the incident surface at an angle θ inc  would be dispersed in the photonic crystal prism  29 , and different wavelength components would exit the angled exit surface at different exit angles (θ out ) as depicted in FIG. 5 for wavelengths λ a , λ b , and λ c . 
     FIG. 6 shows the exit beam propagation angle θ out (deg.) as a function of incident wavelength for a set of prisms with four different exit surface orientations, characterized by surface normal angles of: 
     
       
         θ xs =0°, 15°, 30°, and  45 °l    
       
     
     The incidence angle: 
     
       
         θ inc =10° 
       
     
     is used for all four cases. On the top side of the graph, we have divided the wavelengths into a number of regions, named Band  1 , Band  2 , Gap  1  and Gap  2 , etc. Band  1  corresponds to the lowest transmission band, i.e., the lowest in frequency or longest in wavelength. Band  2  is the next transmission band in ascending frequency, etc. The transmission bands are separated by gaps, labeled as Gap  1 , Gap  2 , etc. with the lowest gap (in frequency) being Gap  1 . Incident waves with wavelengths in the gaps are reflected at the front surface, and do not propagate inside the photonic crystal. 
     For a surface normal angle of: 
     
       
         θ xs =0°,  
       
     
     the back and front surfaces are parallel, and, as expected, the exit beam propagation angle θ out  is the same as the incident angle for all transmitted wavelengths such that: 
     
       
         θ out =θ inc =10° 
       
     
     For other values of θ xs , the exit angle Lout exhibit large variations as functions of transmitted wavelength, as we have seen earlier with the angle of propagation in photonic crystal θ pc  and in the lateral displacement D. However, there are some fundamental differences. While the rapid variations in Opc and D occur over narrow wavelength ranges near the band edges, just outside the reflection gaps, the variation in θ out  occur over the full range of allowed wavelength bands. For example, as listed in Table 1, the dispersion in the angle of refraction θ pc  for wavelengths in Range 2, covers 
     
       
         λ=2.0257 a  to λ=2.1463 a,    
       
     
     and the dispersion in the angle of refraction θ pc  for wavelengths in Range 3, covers 
     
       
         λ=1.5267 a  to λ=1.5463 a.    
       
     
     However, using values of surface normal angles of: 
     
       
         θ xs =15°, 30°, and 45°,  
       
     
     we obtain a range in dispersion for θ our  which covers both Range 2 and Range 3, plus all the wavelengths in between, giving total coverage from 
     
       
         θ=1.5267 a  to θ=2.1463 a    
       
     
     for each of the respective θ xs  values used. 
     FIG. 6 shows that an exit surface normal angle of 30° or 45° allows θ out  to cover the entire second transmission band labeled Band  2  in FIG. 6, while the use of θ pc , cover only the edges of the same band. The dispersion of θ out  in Band  2  is closer to being linear in comparison to that of Band  1  in wavelength, making it more useful than the highly non-linear variation of θ pc . Since the dispersion of θ out  occurs with a transmission band, rather than at the band edges near reflection gaps where transmission amplitudes diminish, we expect that embodiments scheme to be much more efficient. 
     Note that the strong dispersion in the exit angle θ out  is evident in Band  2  and Band  3  as well as at the edge of Band  1  (which corresponds to longer wavelengths). As shown in Table 2, the use of higher numbered bands permits the use of a larger period (a) to cover the same wavelength range. A larger value of period (a) reduces the demand on fabrication, as larger feature sizes are in general easier to make. 
     FIG. 7 shows the exit angle θ out  as a function of wavelength for a set of three structures with different layer widths: 
     
       
         h 1 =0.2 a, h   2 =0.8 a,   (1)  
       
     
     in dashed lines, 
     
       
         h 1 =0.5 a, h   2 =0.5 a,   (2)  
       
     
     in solid lines, and 
     
       
           h =0.8 a, h   2 =0.2 a,   (3)  
       
     
     in dash-dot lines. The same angle of incidence of 
     
       
         θ inc =10° 
       
     
     and exit surface normal angle of 
     
       
         θ xs =45° 
       
     
     are used for all 3 cases. FIG. 7 therefore provides a method of tuning the ultra-refractive properties of the one-dimensional photonic crystal prismlo by adjusting the ratio of h 1  and h 2  to a required range of exit angle θ out  for a predetermined range of wavelength (a). 
     FIG. 8 shows the exit angle θ out  as a function of wavelength for a structure with: 
     
       
           h   1 =0.5 a, h   2 =0.5 a,    
       
     
     and exit surface angle 
     
       
         θ xs =45°.  
       
     
     Three different incidence angles of: 
     
       
         θ inc =10°, 20°, and 30° 
       
     
     are used. FIG. 8 therefore provides another method of tuning the ultra-refractive properties of the strongly refractive one-dimensional photonic crystal prism  29  the θ out  range for a predetermined wavelength and for a family of incidence angles. 
     The one-dimensional photonic crystal prism  29  might be made in a number of ways. One possibility would be to define a set of equally spaced, vertical, parallel plates using lithographical techniques. FIG. 9 shows how such a structure would appear using a SOI (silicon on insulator) wafer. An article entitled “Two-dimensional Si photonic crystals on oxide using SOI substrate,” by A. Shinya et al., published in  Optical and Quantum Electronics,  34:113-121, in 2002, shows a structure that consists of a silicon dioxide layer sandwiched between silicon layers. 
     Referring now to FIG. 11, the strongly refractive one-dimensional photonic crystal prisms are schematically shown formed in a photonic crystal such as that shown as defined in the top silicon layer  44 , while the oxide layer  46 , having a lower index than silicon, serves as a cladding layer to confine the light to paths in the photonic crystal  10 . The one-dimensional photonic crystal structure could also be implemented in GaAs on Al x O y , in a procedure similar to that described in an article entitled “Three-dimensional control of light in a two dimensional photonic crystal slab,” by E. Chow, S. Y. Lin, S. G. Johnson, et al. that appeared in, Nature, 407, 983-986 in year 2000. The parallel plates  25   a - 25   c  of the one-dimensional photonic crystal  10  can be lithographically defined in a GaAs layer on top of Al 0.9 Ga 0.1 As layer. The Al 0.9 Ga 0.1 As layer can then be wet oxidize to make an Al x O y  layer which has a lower index of refraction than GaAs and acts as a lower cladding layer to confine light in the GaAs photonic crystal. Since all the surfaces in the one-dimensional photonic crystal  10  are parallel, simple anisotropic wet etching can be used in the fabrication process. For instance, KOH (potassium hydroxide) can be used to etch [110]-oriented silicon to produce the parallel-plate one-dimensional photonic crystal structure inexpensively. 
     FIG.  11  and FIG. 12 allow for the possibility of monolithic integration with other micro optical components on the same wafer, or applications requiring longer wavelengths (such as millimeter waves). One-dimensional photonic crystal prisms could be made by bonding pre-formed wafers  44 ,  46 , together. FIG.  11  and FIG. 12 suggest that a large number of strongly refractive one-dimensional photonic crystal prisms  29  could be could be formed on silicon wafers. One-dimensional photonic crystals, as shown in FIG. 5, could be etched in the wafers in large numbers using a suitable mask (not shown). The structures of FIGS. 11 and 12 are schematic in that they suggest that the channels of alternating index of refraction could be formed in horizontal arrays on a single wafer or possibly in vertical arrays since the stack of wafers might be formed and registered with many layers positioned over each other vertically. If the layers are formed in the plane of a wafer, the incident and exit faces are formed by slicing the wafer as required at appropriate angles. 
     FIG. 11 shows two round wafer layers  44 ,  48  of material, possibly silicon, separated by insulator layer  50  and covered by insulator layers  46  and  52 , that have been prepared by masking and etching an array of rectangular void spaces  49 ,  51 ,  53  and  55  respectively in and through the wafers. It might be possible to punch or form the wafers with the subject void spaces. Ion milling or chemical etching using masks are also possible alternative steps in the preparation of silicon wafers  44 ,  48  typically having a diameter of three to four inches and which could contain hundreds of void spaces  49 ,  51 ,  53  and  55 . Once the silicon wafers layers  44 ,  48  are aligned and stacked they are bonded using a pre deposited gold eutectic between layers  46 ,  44 ;  50 ,  48 ,  52  or by bonding layers  44 ,  50 ,  48  on their edges. Optical cement and other adhesives are possible alternative methods of attachment. Wafer bonding using intermediate SiO 2  layers is another possibility. 
     A second alternative for fabrication of large numbers of the one-dimensional photonic crystal structure is pictured in FIG. 12, which shows a stack of SOI (silicon on insulator) wafers  60 ,  62  that have been masked and pre-processed to remove the silicon in regions to form rectangular void spaces  53 ,  55 . Cover layer  64  is typically an insulator layer of material such as silicon dioxide. The etch or mill operations stop before the material removed includes the base material of insulator  66 ,  68 , typically silicon dioxide. Once the wafers  60 ,  62  are aligned and stacked, they are bonded using a pre deposited gold eutectic between layers or on the edges. Optical cement and other adhesives are possible methods of attachment. 
     After a suitable number of wafers are stacked they are bonded again using the method described above in connection with FIG.  11 . The wafers are aligned, or registered and stacked and then bonded using a pre deposited gold eutectic between layers or on the edges as in the case of the assembly of FIG.  11 . Optical cement and other adhesives are possible methods of attachment. In the preferred embodiment, silicon is used for the plates and air is used for the gaps between the plates. 
     Those skilled in the art will appreciate that various adaptations and modifications of the preferred embodiments can be configured without departing from the scope and spirit of the invention. Therefore, it is to be understood that the invention may be practiced other than as specifically described herein, within the scope of the claims.