Abstract:
A phase shifter includes at least one photonic crystal structure having alternating high and low index dielectric layers. At least two defect structures are positioned between said photonic crystal structures. The defect structure includes one or more nonlinear materials used to produce an index change, whose effect is amplified to produce a specified phase shift in the output signal of said phase shifter.

Description:
This invention was made with government support awarded by the National Science Foundation (NSF) under Grant No. DMR-0213282. The government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     The invention relates to the field of phase shifters, and in particular a phase shifter comprising an arrangement of photonic crystal microcavities, which each include a defect region containing nonlinear materials. 
     Phased arrays are playing an increasingly significant role in space-based and national defense applications. However, a practical implementation of arrays with thousands of elements is limited by the complexity of the antenna and feed structures as well as the active phase-shifting elements. The use of integrated photonics for the realization of phased array beam forming is of much interest due to benefits like low cost, low weight, and low power consumption. One of the key components of such an integrated approach is a photonic radio frequency (RF) phase shifter that can provide an accurate and easily controllable phase shift. 
     SUMMARY OF THE INVENTION 
     According to one aspect of the invention, there is provided a phase shifter. The phase shifter includes at least one photonic crystal structure having alternating high and low index dielectric layers. At least two defect structures are positioned between said photonic crystal structures. The defect structure includes one or more nonlinear materials used to produce an index change, whose effect is amplified to produce a specified phase shift in the output signal of said phase shifter. 
     According to another aspect of the invention, there is provided a method of forming a phase shifter. The method includes forming at least one photonic crystal structure having alternating high and low index dielectric layers. Also, the method includes positioning at least two defect structures between said photonic crystal structures. The defect structure includes one or more nonlinear materials used to produce an index change, whose effect is amplified to produce a specified phase shift in the output signal of said phase shifter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of an exemplary 1-D photonic crystal in accordance with the invention; 
         FIG. 2  is a graph demonstrating the transmission as a function of frequency for two values of the index of the nonlinear material in the microcavities, n c =1.178 and n c =1.6324; and 
         FIG. 3  is a graph demonstrating the electric fields as a function of time at a point opposite the source for two values of the index of the nonlinear material in the microcavities, n c =1.178 and n c =1.6324. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Consider the problem of changing the phase of a beam of light. The most direct approach is to modulate the index of the material through which it passes. The phase change for a plane wave with frequency ω passing through a material of thickness d with index modulation Δn is Δφ=Δnωd/c (where c is the speed of light). Physically, index modulation is realized by applying an electric field to a nonlinear material. Effects causing this index modulation include the Pockels effect (first order in field strength) and the Kerr effect (second order in field strength). There are limits to how much of an index change can be induced by an applied voltage before electrical breakdown occurs. 
     When the level of index modulation of a particular material for a given thickness is found to be insufficient to achieve a desired phase shift directly, there are two alternative approaches that can be used. First, a different material can be chosen. However, typically there is a limit to the performance of all materials in a given frequency range due to physical reasons, and some of the materials with the best performance in terms of nonlinearity may also have drawbacks such as high absorption. Second, a structural approach can be employed. Introducing a structure which slows down light can enhance the phase change associated with a given thickness of nonlinear material. Physically, this can be pictured as light bouncing back and forth multiple times, picking up a fixed phase shift on each pass. As a result of this picture, the maximum phase shift enhancement is proportional to the number of bounces, and therefore the quality factor Q. More formally, one can write the phase φ associated with a collection of resonances with central frequencies ω i  and widths Γ i  as: 
     
       
         
           
             
               
                 
                   
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     The linearity of the arccotangent function near resonance yields a phase derivative dφ/dn=2/Γ i =2Q/ω i , which proves the maximum enhancement is proportional to Q. Going completely across one resonance by integrating over all frequencies yields a π phase shift. Combining multiple resonances can allow for arbitrarily large phase shifts. 
     An embodiment of the inventive phase shifter  2  includes three photonic crystals  4 ,  6 , and  16 , and two resonant cavities  8  and  9 , as shown in  FIG. 1 . All of these photonic crystal regions  4 ,  6 , and  16  can be 1D photonic crystals comprising of high and low dielectric indices; in this embodiment, region  16  is reduced to the minimum possible size of one layer of high dielectric material. Note that in other embodiments, the photonic crystal regions  4 ,  6 , and  16  can comprise a high index photonic crystal slab in 2D or a photonic crystal having a complete photonic bandgap in 3D; furthermore, in higher dimensions, regions  4 ,  6 , and  16  could be combined to enclose resonant cavities  8  and  9 . The defect structure  8  is placed between the two photonic crystals  4  and  16 , and comprises a multi-layered arrangement that includes a transparent electrode  10 , an insulator layer  12 , and a nonlinear layer  14 . The defect structure  9  is placed between the two photonic crystals  16  and  6 , and comprises a multi-layered arrangement the same as in defect structure  8  but reversed in order, so that the transparent electrodes  10  and  11  can simultaneously shift the index of both nonlinear layers  14  and  15  upon the application of an electric field. 
     This structure will give rise to low transmission within the bandgap except close to the two resonant frequencies. For two well-separated peaks, the adjacent peak phase difference will be given by π. One can then exploit this property by taking the following approach. First, choose the nonlinear material index and thickness such that the lower cavity resonant frequency coincides with the desired operating frequency. Then apply a voltage sufficient to shift the higher frequency peak down to the operating frequency. 
     Now, the phase of the output light signal will be π out of phase with what was observed previously. The thickness of the device proposed in  FIG. 1  is about 8.2a, where a is the period of a bilayer structure, when using high and low indices of n hi =2.4 and n low =1.6 for the microcavities, respectively. Converting to physical distances yields device thicknesses of 12.3 cm at 5 GHz, and 1.23 m at 500 MHz. The thicknesses could be reduced by at least 32% through the use of very high index contrast materials. Furthermore, note that the fractional bandwidth of the phase shifting effect will be inversely proportional to the quality factor of the cavity. Therefore, if a bandwidth of about 3% of the central frequency is required, this could be achieved using a relatively low quality factor Q≦33. 
     Using a high and low dielectric of indices n 1 =2.4 and n 2 =1.6 and period a with 2.5 exterior bilayers and only a single interior layer yields two resonant peaks within the bandgap at normal incidence, centered around ω=0.25(2πc/a), with a quality factor Q≈40, which corresponds to a bandwidth of approximately 2.5% of the central frequency. Choosing the microcavities to have equal thicknesses of 1.5a and indices of n c =1.178 and n c =1.6324 yields the result shown in  FIG. 2 : two different resonances peaking at the same frequency, also displaying very similar bandwidths. According to equation (1), the peaks of the two resonances should differ in phase by π. This prediction is checked in  FIG. 3 , which shows that the fields as a function of time for the two microcavity index values are almost exactly π out of phase with one another. 
     By comparison, the phase change associated with a layer of nonlinear material with thickness 1.5a and equal index change is only 0.341π, about a third of the phase change seen for this device. 
     The invention can be applied both in the optical and microwave regime. The material used will be determined by whether the optical or microwave regime is of interest. In the optical regime, the high index layers can be silicon or silicon nitride, the low index layers can be silica, and the nonlinear material can be tellurium, gallium arsenide or aluminum oxide. In the microwave regime, the high index layers can be aluminum oxide or silicon nitride, low index layers can be quartz or Teflon®, and the nonlinear material can be lithium niobate. 
     Note that the parameters used in this discussion are just an example, and one can use this design with any frequency where dielectric media can be treated macroscopically, ranging from radio frequencies to ultraviolet light. The range of materials that can be used in this design is almost unlimited and only restricted by practical considerations such as device size and loss tolerance. Furthermore, any bandwidth that is not extremely broad, for example less than 10% of the mid-range frequency, could conceivably be used in this device with proper choice of dielectric materials. There is, however, a tradeoff between bandwidth and index shift: the smaller the bandwidth needed, the lower the index shift needed, and vice-versa. As a consequence, one can achieve a π phase shift for monochromatic light with an arbitrarily small index shift given a sufficiently high quality factor cavity. 
     Alternatively, one can forgo the maximum bandwidth in order to maximize transmission. When the bandwidth of the signal is comparable to that of the full width at half maximum for the cavity modes used, transmission should be substantial but not 100%. However, reflection losses can be decreased to arbitrarily low amounts by decreasing the ratio of the signal bandwidth to the utilized cavity mode FHWM. 
     Although the present invention has been shown and described with respect to several preferred embodiments thereof, various changes, omissions and additions to the form and detail thereof, may be made therein, without departing from the spirit and scope of the invention.