Abstract:
An electromagnetic reflector for reflecting an electromagnetic signal is provided based on meta-surface phase control using photo-capacitive materials, varactors or other tuning means. The shape of the metamaterial unit cell enhances the resonance and phase shift. The reflector includes first and second cells having respective first and second phase states, along with a switch for selecting between the first and second cells.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention described was made in the performance of official duties by one or more employees of the Department of the Navy, and thus, the invention herein may be manufactured, used or licensed by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor. 
    
    
     BACKGROUND 
     The invention relates generally to electromagnetic radiation reflectors. In particular, the invention relates to signal reflectors to redirect and/or reshape electromagnetic radiation. 
     Radiation reflectors include reflect-arrays, which are known to those skilled in the art of antenna designs as useful for reflecting an electromagnetic wave at various angles by controlling the phase of the elements that compose the array. 
     A phased array can be used to control electromagnetic radiation. By controlling the phase of each element within the array, a narrow electromagnetic beam can be formed. By dynamically changing the phase in a way known to those skilled in the art of antenna design, the beam can be steered, as reported by A. J. Fenn et al., “The Development of Phased-Array Radar Technology”,  LINCOLN Laboratory Journal,  12 321-340 (2000), available at https://www.ll.mitedu/publications/journal/pdf/vol12_no2/12_2devphasedarray.pdf. 
     Reflect-arrays are similar to phased arrays but the elements in the array produce no radiation of their own. Instead, each element is a reflector that reflects a small portion of incident radiation. Often, the elements are designed to be resonant at a given frequency or over a range of frequencies. By controlling the resonance, the phase of the reflected signal can be dynamically controlled into different directions as reported by D. G. Berry et al., “The Reflectarray Antenna”,  IEEE Transactions on Antennas and Propagation,  11 645-651 (1963). 
     The transition between two phases in a reflect-array often occurs over a very narrow range of control parameters. Precise control of the phase of each element can be difficult in relation to the others in order to achieve precise beam steering. Further, due to material losses and resonant component losses, the amplitude of the reflected signal can be dramatically reduced at resonance, which is often an undesirable effect. 
     SUMMARY 
     Conventional electromagnetic reflectors yield disadvantages addressed by various exemplary embodiments of the present invention. Various exemplary embodiments provide a method and system for controlling the phase (and amplitude) of a reflect-array at any angle while maintaining high reflected amplitude of the signal. In particular, the proposed two-stage elements provide a simple solution and are easy to implement. Other various embodiments alternatively or additionally provide for a broader range of phase control. Unlike conventional reflector array where each element is separated by about half wavelength, various reflector array embodiments contain a set of panels, each panel has several super-cells and each super-cell has several unit cells. This high resolution also enhances control of the beam in a more precise way than traditional array reflectors. 
     Various exemplary embodiments provide optical control without the electromagnetic interference effect. These can be performed in conjunction with other methods for control. These and other objects are achieved by the invention, embodiments of which comprise a system and method for controlling the phase shift of a reflected electromagnetic signal in a reflect-array by employing a unit cell comprising an element having multiple phase states. Additional aspects and/or advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and various other features and aspects of various exemplary embodiments will be readily understood with reference to the following detailed description taken in conjunction with the accompanying drawings, in which like or similar numbers are used throughout, and in which: 
         FIGS. 1A and 1B  are plot views of idealized step function phase response; 
         FIG. 2  is a tabular view of phase responses for various states; 
         FIG. 3  is a tabular view of amplitude and phase responses; 
         FIGS. 4A and 4B  are plot views of phase responses over a range of direction angle values; 
         FIGS. 5A and 5B  are plot views of power responses to reflection angle; 
         FIGS. 6A and 6B  are plot views of phase responses to polar and azimuthal angles; 
         FIG. 7  is a grid view of wavelength-scale cells; 
         FIGS. 8A and 8B  are phase amplitude responses to frequency; 
         FIG. 9  is a plot view of phase response to frequency; and 
         FIG. 10  is an isometric view of a unit cell disposable to form a planar reflective array. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description of exemplary embodiments of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific exemplary embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized, and logical, mechanical, and other changes may be made without departing from the spirit or scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims. 
     In accordance with a presently preferred embodiment of the present invention, the components, process steps, and/or data structures may be implemented using various types of operating systems, computing platforms, computer programs, and/or general purpose machines. In addition, those of ordinary skill in the art will readily recognize that devices of a less general purpose nature, such as hardwired devices, or the like, may also be used without departing from the scope and spirit of the inventive concepts disclosed herewith. General purpose machines include devices that execute instruction code. A hardwired device may constitute an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA) or other related component. 
     Reference will now be made in detail to the present embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. The embodiments are described below in order to explain the present invention by referring to the figures. The embodiments are predicated on the discovery that, in reflect-arrays, the phase shift of the reflected wave may be controlled at any particular angle by employing elements having multiple phase states. 
     More particularly, the phase of the reflected wave has discrete values depending on the number of elements in the array that can be controlled in a more stable way. Various embodiments provide a method and a system for reflecting an electromagnetic wave with a phase change from that of normal metallic or dielectric materials. 
     The phase of the reflected wave can be any number of discrete steps in phase dependent on the number of elements in the reflect-array. A principal advantage of exemplary embodiments is that the phase change can be accomplished using any unit-cell structure that has two states. Another advantage is that phase resolution and dynamic range can be independently controlled. For example, in a simple linear array, a ten-element array can reflect the electromagnetic wave with any one of eleven phase values in one particular direction (normal to the array for example). For elements that have two states of phase shift, given by phases φ 1  and φ 2 , then the eleven phase values will lie between φ 1  and φ 2 . 
     Exemplary embodiments enable the control of the phase (and amplitude) of a reflect-array at any angle. For clarity, the angle can be assumed to be normal to the array in the following description. Each unit-cell in the array can be assumed to have two phases. For example, each unit-cell can be phase φ 1  or phase φ 2 . The continuous phase change between φ 1  and φ 2  can be assumed to be infinitely sharp effectively for clarity. 
       FIG. 1A  shows a diagram view  100  of the step function phase response of a two-phase unit-cell. A control parameter represents the abscissa  110  and phase denotes the ordinate  120 . Values for the first phase  130  and the second phase  140  are plotted as different constants, with the phase transition at a specified value of the control variable assumed to be infinitely sharp for clarity.  FIG. 1B  shows a diagram view  150  of the step function phase response with transition points for a group of unit-cells and the same abscissa  110  and ordinate  120 . Values for the first phase  160  and the second phase  170  are plotted as different constants, with the transitions  180  being responsive to different elements. 
     For unique transition points for each element, either by design or caused by general manufacturing tolerances, then each element can change states at a different setting of the control parameter. The phase shift ψ n  for each element n represents one of two states for any of the N elements. Depending on how many of the N elements are in state φ 1  or in state φ 2  then the final wave will have any phase between φ 1  and φ 2  with N+1 discrete steps. For example, one can assume that a simple two-element system has a total of three phase states. 
     A plurality of elements can reflect many discrete phases. With N elements, one can achieve N+1 discrete phases. Depending on the configuration of phase distribution among the elements, either linear or random phase patterns of the total field can be generated. For example, for six elements with ±90° of two phase states, a linear phase chirp can be generated if the distribution pattern of each step is given by the array:
         +90+90+90+90+90+90   −90+90+90+90+90+90   −90−90+90+90+90+90   −90−90−90+90+90+90   −90−90−90−90+90+90   −90−90−90−90−90+90   −90−90−90−90−90−90       

     Possible control elements include, but are not limited to, photo-capacitance chips with different capacitance and conductivity controlled by infrared (IR) light intensity, as well as piezoelectric materials and carbon nanotubes (CNT). Other control elements exist and this invention should not be restricted by any particular control method. For example, some control methods might use electric control, or thermal control, piezo control, liquid crystal control, etc. instead of optical control. If a wavelet is reflected from each of n elements, then the final wave will have a net phase Φ of approximately:
 
Φ=Σ n=1   N  sin(ψ n   +ωt ),  (1)
 
where n denotes an element, N is the total number of elements, ψ n  is the phase shift of the element n, ω is angular frequency and t is time.
 
     For a wavelet reflected from each of n elements, the final wave has a net phase of approximately eqn. (1) where ψ n  represents one of two states for any of the N elements. Depending on how many of the N elements are in state φ 1  or in state φ 2 , the final wave has any phase between φ 1  and φ 2  with N+1 discrete steps. For example, a simple two-element system has a total of three phase states. Table  1  in  FIG. 2  shows a tabular listing  200  with particular states and resulting values, together with their resulting phase shift. Table  2  in  FIG. 3  shows a tabular listing  300  with amplitudes and phase states that yield resulting phase shifts. In particular, the tabular listing  300  in Table  2  summarizes an example with two elements, two phase states (0° and 90°) and two amplitude states (0.5 and 1). 
     The exemplary process can be applied to military fields as well as in civilian; e.g., transmission of radiation with controlled direction, such as beam steering, for nonmilitary use from radio frequency (RF) to infrared (IR), and thus would be of great interest for maritime and aerial navigation, and for weather radars. An advantage of various exemplary embodiments is that the phase can be controlled with simple two-stage elements and that the control can be accomplished without loss of amplitude of the reflected wave. 
     Phase resolution depends on the number of elements while dynamic range depends on the phase difference of the two states. Therefore, the resolution and the dynamic range can be independently controlled. A side lobe will exist because the system represents a two-element reflect-array where each element has different phases and amplitudes that can be controlled through, but not limited to, photocapacitors with different light intensities. 
     Various phase pattern can also be generated if each element is controlled to acquire a phase of either ±90° (or ±π/2 radians). Upon implementation, above phase should be added into propagation phase of electromagnetic wave through Huygens-Fresnel Principle: 
                     E   ⁡     (   r   )       =       1   ⅈλ     ⁢       ∫   ∫     Σ     ⁢     E   ⁡     (     r   ′     )       ⁢       exp   ⁡     (     ⅈ   ⁢           ⁢   k   ⁢           ⁢          r   -     r   ′              )              r   -     r   ′              ⁢   cos   ⁢           ⁢   θ   ⁢     ⅆ     s   ′                 (   2   )               
where E is the electric field, Σ denotes the surface of the reflector array, λ is the wavelength of free space, k=2π/λ is the wave-number of free space, θ is the polar angle between the surface normal and the observation vector r connecting the observation point to the integration vector r′ on the surface Σ, and | . . . | represents the absolute value of an argument. The surface integration includes the areas of two-state elements and the spacing in between where a π phase shift is assumed due to perfect electric conductor backplane.
 
       FIGS. 4A and 4B  shows plot views  400  of phases of the total electromagnetic field in far field reflected from a one-dimensional (1-D) reflector array of twelve two-state elements, assume the input electromagnetic field has a linear chirp of 5° at each step.  FIG. 4A  identifies the 1-D plot  410  absent phase modulation.  FIG. 4B  identifies the plot  420  with phase modulation. Direction angle denotes the abscissa  430  and phase indicates the ordinate  440  for both plots  410  and  420 . 
     Far field power corresponding to views  400  are respectively shown in  FIGS. 5A and 5B  in plot views  500 . Power, whether reference or panel, is shown as a function of reflection angle in degrees. Without phase modulation, plots  510  and  520  provide reference power under add-in-power and add-in-field, respectively. Note that add-in-power refers to the total power in the far field is obtained by adding radiation power of the individual element, and the add-in-field denotes the total power in the far field is obtained by adding radiation field of the individual element and then squaring it. 
     Plots  530  and  540  show provide panel power respectively under add-in-power and add-in-field, the peaks being off-set from null reflection angle. For phase modulation, plots  550  and  560  provide reference power under add-in-power and add-in-field, respectively; while plots  570  and  580  show panel power under add-in-power and add-in-field, respectively. As a comparison, reflection from the same size panel without phase modulation is shown in the panels. Total power decreases about 50% due to phase modulation. 
       FIGS. 6A and 6B  show plot views  600 , depicting the phase of S-band electromagnetic waves (3±1 GHz) having wavelengths of 7.5 cm to 15 cm in far field reflected from a two-dimensional (2-D) reflector array of 12×24 two-state (±90° or ±π/2) elements.  FIG. 6A  provides plot view  610  for phase at zero azimuth angle. The different lines correspond to different sets of initial phases.  FIG. 6B  provides plot view  620  for phase at 10° polar angle. 
     The phase variation is caused by interference among different radiation elements. For view  610 , the polar angle denotes the abscissa  630  and phase identifies the ordinate  640 . For view  620 , the azimuth angle denotes the abscissa  650  and phase indicates the ordinate  660 . Without loss of generality, the size of each element is assumed to be 20×10 mm and spacing 12 mm and 6 mm in x and y direction, respectively. 
       FIG. 7  shows a grid view  700  of cell arrays. Super-cells  710  have sides that measure a half-wavelength, whereas unit cells  720  are subdivided into side lengths much less than a half-wavelength. For view  700 , a phased-array reflector where the elements are called “super-cells”  710 . The periodicity of each super-cell is λ/2, which is typical of a phased-array system (but not limiting). In the configuration illustrated, each super-cell  710  as a cell array  730  is formed of a matrix of unit-cells  720  denoting a unit area  740 . Each unit-cell  720  is a two-state phase system that can have phase state φ 1  or φ 2 . 
     As described, the number of cells in either state can be adjusted, and the net reflected wave from the super-cell  710  will be of some intermediate phase between φ 1  and φ 2 . For example, for all unit-cells  720  being in first state φ 1 , then the super-cell  710  reflects an electromagnetic wave with phase φ 1 . Also, for half the unit-cells being in state φ 1  and half in state φ 2 , the super-cell  710  reflects an electromagnetic wave with a phase of (φ 1 +φ 2 )/2 assuming they both have the same amplitude. 
     Although the wavelength of 10 cm is used in the described simulations, applications are not limited to the S-band (3±1 GHz) in the spectrum. The methodology of exemplary embodiments can be applied to any spectrum range of electromagnetic wave. The phase Φ can be adjusted by:
 
Φ=Σ n=1   N   A   n  sin(ψ n   +ωt ),  (3)
 
where N is the number of elements, A n  is amplitude of element n, ψ n  is the phase shift of element n. Thus, if each element can also control its amplitude among two or more states, then eqn. (1) transitions to eqn. (3). An example of this is shown in view  300  (Table 3) with amplitude states [0.5, 1] and [1, 0.5] and their resulting phase shifts of the total field in the far field.
 
     Super Cells can be Used to Overcome Loss at Resonance: 
     Conventional reflect-array schemes suffer from amplitude loss at the resonant frequency for which they were designed as shown in views  600 . The worst case amplitude loss is at resonance where the phase shift is approximately half way between φ 1  and φ 2 . Thus, to get a strong reflectance between either φ 1  or φ 2  is generally thought difficult to achieve. 
       FIGS. 8A and 8B  show plot views  800  for amplitude loss at specified frequencies.  FIG. 8A  provides reflected phase shift and amplitude in view  810  with loss at the operating frequency f 0    830 .  FIG. 8B  illustrates such phase shift and reflected amplitude loss in view  820  at frequencies adjacent to but not at the operating frequency f 0    835 . The response shows a high amplitude plateau  840 , and a minimal cusp  845  at the operating frequency f 0 . 
     The phase transition  855  at frequency f 0  marks the interface between the first phase φ 1    850  and the second phase φ 2    860 . Reflections between phases denote amplitude loss, as noted by the cusp  845  and corresponding phase transition  855 . In view  820 , the amplitudes show substantial decrease at cusps  870  and  875  for the first and second phases, respectively, showing phase tuning without amplitude loss  880  across a wide frequency band. The transitions correspond to the cusps for the first phase  890  and the second phase  895 , respectively. This improves noise margin at intermediate states. 
     A reflected wave from a super-cell  710  of a phased-array reflector can incorporate any phase between φ 1  and φ 2  by adjusting the number of unit-cells  720  in either state. Because each unit-cell  720  operates at a resonance from the desired operational frequency, there is no loss in amplitude. One can imagine a super-cell  710  made from two unit-cells  720 . To reflect an electromagnetic wave with an intermediate phase shift, the first unit-cell  720  would operate at a frequency lower than operating frequency f 0  and the second unit-cell  720  would operate at a frequency higher than f 0 . 
     The phase from the electromagnetic wave reflected from the super-cell  710  would have a net phase of (φ 1 +φ 2 )/2 at f 0 . Similarly, if both unit-cells  720  were in state φ 1 , then the super-cell  710  would reflect a phase of φ 1  (and similarly for φ 2 ) at f 0 . A higher number of unit-cells  720  within a super-cell  710  produces a higher number of net reflected phases without amplitude loss at f 0 . 
     For example, the 16 unit-cells  720  within each super-cell  710  in the configuration of view  700  can produce up to seventeen discrete phase values. In fact, for n unit-cells  720  within a super-cell  710 , one can derive n+1 unique phase values from the electromagnetic wave reflected from a super-cell  710 . Because each super-cell  710  can then have its own phase value, a phased-array reflector is then possible using the exemplary method. Thus, a phased-array reflector could not be possible by using the reflect-array concept. 
     The phased-array reflector requires each emitter in the array to be capable of a continuum of phase shift values across the array in order to produce a well-defined beam at a desired angle of reflectance. As an example in practice, a two-unit cell system could have states {0,0}, {0,1}, {1,0} and {1,1}. States {0,1} and {1,0} are assumed to be degenerate and to produce the same phase shift. In practice, there might be small variations due to the physical displacement of the two unit cells that would be considered in actual design. 
       FIG. 9  shows a plot view  900  of phase shifts as a function of frequency between phases φ 1    850  and φ 2    860  for four different tuning states. The abscissa  910  denotes frequency in giga-hertz (GHz) and the ordinate  920  identifies phase response. The first and second phases φ 1  and φ 2  are respectively indicated for frequency domains at the lower portion  930  and the higher portion  940 . For exemplary unit cell designs, tuning can be accomplished by any number of means including photo-capacitance, photo-dielectric effect, photo-capacitive ink, semiconductor junction effects (such as varactor, or photo-varactor diodes), piezoelectric materials include aluminum nitride (AlN), quartz (silicon oxide, SiO 2 ), gallium phosphate (GaPO 4 ), etc. or any other method. The lines  950 ,  960 ,  970 , and  980  corresponds to the different capacities (c v =0.5, 0.8, 1.1, and 1.4 pF) of the switching element in the unit cell. 
       FIG. 10  shows an isometric view  1000  showing structural detail of an exemplary unit cell  1010  analogous to unit-cell  720  illustrated schematically. The unit cell  1010  repeats itself in the x (horizontal) and y (vertical) directions to form a planar reflector array. Alternatively, two or more unit-cells  720  of different sizes layout side-by-side in the x-y plane to form a super cell  710 , which repeats itself in the x and y directions to form a planar reflector array. The coordinates x (horizontal to right), y (diagonal to upper right) denote directions in the planes associated with the cell  1010 . The structure includes a substrate that denotes a conductive backplane  1020  comprising for example copper (Cu), gold (Au), silver (Ag), aluminum (Al). 
     A dielectric layer  1030  can be formed by various materials, a FR-4 being a glass-reinforced laminate epoxy, which is low cost but lossy at high frequencies. For optical tuning, a light-guide film  1040  is disposed above the dielectric layer  1030 . The film  1040  includes disposed thereon first and second (i.e., right-and-left) patch elements  1050  and  1060  joined together by a left switch element  1070 . 
     That switch element  1070  can be formed from photo-capacitive ink. Alternatively, the switch element  1070  can be based on any of electric, optical, thermal, piezo, liquid crystal, phase transition material and micro-electromagnetic system (MEMS) configurations The switch element  1070  controls the state of the unit cell  1010 , each of which has a pair of phase states. The design of the unit cell  1010  represents only one of many types that can be implemented. Other designs include but are not limited to cross structures, pad structures, mushroom structures in which a via ties some points of the pad to the ground plane, or inverses of the structures in which the non-metallic regions and metallic regions are reversed. 
     An advantage of exemplary embodiments is that the phase can be controlled with simple two-stage elements. Phase resolution depends on the number of elements while dynamic range in phase depends on the phase difference of the two states. Therefore, the resolution and the dynamic range can be independently controlled. A side lobe will exist since the system basically represents a two-element reflect-array where each element has different phases and amplitudes which can be controlled through, but not limited to, photocapacitors with different light intensities. Alternatively, one could use a microstrip semiconductor p-i-n diode phase shifter (with the high-level injection diode denoting positive-region, intrinsic-charge-carrying-type, negative-region). Side lobes can be minimized by controlling amplitude of the reflector elements in the same way to those skilled in the art with phased arrays. 
     While certain features of the embodiments of the invention have been illustrated as described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the embodiments.