Patent Publication Number: US-7898464-B1

Title: System and method for transmitting signals via photonic excitation of a transmitter array

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     The present application claims the benefit of priority under 35 U.S.C. §119 from U.S. Provisional Patent Application Ser. No. 60/790,820, entitled “Transmitting Signals via Photonic Excitation of an Active Sampler Array,” filed on Apr. 11, 2006, which is hereby incorporated by reference in its entirety for all purposes. 
    
    
     FIELD OF THE INVENTION 
     The present invention generally relates to transmitters and, in particular, relates to systems and methods for transmitting signals via photonic excitation of a transmitter array. 
     BACKGROUND OF THE INVENTION 
     Phased array antennas, both transmit and receive, typically consist of closely spaced individual antenna elements. The close spacing of these elements introduces cross coupling effects which dominate antenna performance characteristics. In addition, the antenna elements are designed for maximum power conversion efficiency between a radiation mode and a transmission line or circuit mode at the operating frequency of the antenna. This latter requirement consists of conjugate impedance matching of the impedance presented by the antenna terminal or port to the source impedance of a transmitter or the load impedance of a receiver. 
     The performance issues facing active phased array transmitters are radio frequency (RF) bandwidth, true time delay steering for wide bandwidth, electromagnetic interference (EMI) and beam steering control. Realizable active array transmitters providing this performance are limited in weight, size and generally costly. 
     SUMMARY OF THE INVENTION 
     According to one embodiment of the present invention, a radio frequency (RF) phased array transmitter system for radar, communication and/or electronic warfare provides the following features: broadband (multi octave), thin and conformal, optically addressed, optically beam controlled, and multi beam. An array of closely spaced conductive pattern elements is fabricated according to one embodiment such that the impedance at the gaps between the conductive areas is, to first order, real and frequency independent. The gaps are supplied by a photogenerated RF current from an optical modulator. The RF power radiated from a single gap is proportional to the square of the RF component of the photocurrent supplied to the gap by the relation P RF =I(photocurrent) 2 ×377/2. 
     According to one embodiment of the present invention, a radio frequency (RF) phased array transmitter system comprises a phased array for generating an RF signal. The phased array includes a plurality of conductive patches formed in an array, a plurality of separation gaps, and a plurality of active sources. Each of the plurality of separation gaps is formed between two adjacent ones of the plurality of conductive patches, and each of the plurality of active sources is formed across its associated one of the plurality of separation gaps. The RF phased array transmitter system further comprises an optical source having an optical output. The optical source is for generating an optical signal. The transmitter system also comprises an RF source having an RF output. The RF source is for generating an RF signal. In addition, the transmitter system comprises an optical modulator coupled to the optical source and the RF source. The optical modulator has a first modulator input, a second modulator input and a modulator output. The first modulator input is for receiving an optical signal, the second modulator input is for receiving an RF signal, and the modulator output is for providing an RF modulated optical signal based on the received optical signal and the received RF signal. 
     According to one embodiment of the present invention, a radio frequency (RF) transmitter system comprises a plurality of pattern elements comprising conductive areas, a plurality of separation gaps, and a plurality of active sources. Each of the plurality of separation gaps is formed between each set of adjacent ones of the plurality of pattern elements. Each of the plurality of active sources is formed across its associated one of the plurality of separation gaps. Each of the plurality of active sources is for receiving electrical power, each of the plurality of active sources is for receiving an optical signal, and the plurality of active sources is for generating RF current. 
     According to one aspect of the present invention, a method is provided for transmitting a radio frequency (RF) signal via photonic excitation of a transmitter. The method comprises the steps of: receiving an optical signal; receiving an RF signal; modulating the optical signal using the RF signal by an optical modulator; receiving electrical power by a plurality of active sources of a transmitter; receiving a modulated optical signal by the plurality of active sources of the transmitter; generating RF current by the plurality of active sources; and radiating RF power. 
     Additional features and advantages of the invention will be set forth in the description below, and in part will be apparent from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are included to provide further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. 
         FIG. 1  illustrates a phased array transmitter in accordance with one embodiment of the present invention. 
         FIG. 2  illustrates a segment of the phased array transmitter in  FIG. 1  in a 3-D view in accordance with one embodiment of the present invention. 
         FIG. 3  illustrates a current sheet distribution and its realization as a transmitter in accordance with one embodiment of the present invention. 
         FIG. 4  illustrates a phased array transmitter having multiple current control sources in accordance with one embodiment of the present invention. 
         FIG. 5  illustrates a receiver array and a transmitter array in accordance with one embodiment of the present invention. 
         FIG. 6  illustrates circuits for a transmitter array having multiple bias supplies in accordance with one embodiment of the present invention. 
         FIG. 7  illustrates circuits for a transmitter array having a single bias supply in accordance with one embodiment of the present invention. 
         FIG. 8  illustrates a modulated optical source for a phased array transmitter system in accordance with one embodiment of the present invention. 
         FIG. 9  is an exemplary block diagram of a phased array transmitter system in accordance with one embodiment of the present invention. 
         FIG. 10  illustrates that the radiated power at each harmonic is proportional to the Bessel function squared in accordance with one aspect of the present invention. 
         FIG. 11  illustrates the maximum power that could be radiated from a gap at the fundamental and first three overtones according to one aspect of the present invention. 
         FIG. 12  illustrates graphs of raw power efficiency as a function of optical power per gap in accordance with one aspect of the present invention. 
         FIG. 13  illustrates the power flows during a transmit mode operation of an active source in a phased array transmitter in accordance with one embodiment of the present invention. 
         FIG. 14  illustrates various power flows as a function of optical power in accordance with one aspect of the present invention. 
         FIG. 15  illustrates various curves for electrical efficiency as a function of optical power per gap in accordance with one aspect of the present invention. 
         FIG. 16  illustrates the drive voltage and drive power requirements for a typical lithium niobate Mach Zehnder optical modulator in accordance with one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following detailed description, numerous specific details are set forth to provide a full understanding of the present invention. It will be obvious, however, to one ordinarily skilled in the art that the present invention may be practiced without some of these specific details. In other instances, well-known structures and techniques have not been shown in detail not to obscure the present invention. 
     One approach to exciting phased array antennas is to use an electronic radio frequency (“RF”) generator. Either a single electronic RF generator is remotely located such that the RF signals are distributed to the elements of the phased array, or individual electronic RF generators are located at the individual element or sub-array sites. 
     Drawbacks to using electronic RF generators to excite phased array antennas include the large amount of circuitry required, the loss of RF power in transmission lines between RF sources and the antenna elements, and the difficulty of making the required structure conformal to non-planar surfaces. 
     According to one embodiment of the present invention, a wideband radio frequency (RF) phased array transmitter includes an array of isolated metallic patches interconnected by photocurrent generators. The isolated metallic patches are preferably squares or rectangles separated by narrow gaps. The invention, however, is not limited to square or rectangular patches. When all gaps are excited by coherently phased currents, the transmitted beam angle and polarization are prescribed by the inter-gap current generator phases. By alternating the phase of excitation of adjacent gaps in a linear array or a checker-board 2-dimensional array, all photodiode current generators may be interconnected to a single power/bias source. Use of a balanced output Mach Zehnder optical modulator (MZM) may be used to provide the alternating phase of excitation of adjacent gaps from a single RF voltage source. By over-driving a MZM, efficient harmonic generation/transmission is obtained at the photocurrent generators. Because the structure uses thin conducting patches on an insulating support, photodiodes bridge the gaps between patches, and inductors connect the patches to a power/bias source, the array is inherently low mass and may be made conformal to the surface of various objects such as the curvature of a fuselage, airplane, satellite or vehicle. Excitation of the individual photocurrent generators is preferably by a fiber optic connection between individual photodiodes and an RF modulated optical source through optical power dividers and/or selected optical delay lines. 
       FIG. 1  illustrates a phased array transmitter in accordance with one embodiment of the present invention. A phased array transmitter  110  includes a plurality of pattern elements such as an N×M array of isolated conductive patches  120   a . N can be any natural number (e.g., 1, 2, 3, 4, . . . 50, . . . 100, . . . etc.), and M can be any natural number (e.g., 1, 2, 3, 4, . . . 50, . . . 100, . . . etc.). N and M can be the same or different numbers. Each of the plurality of pattern elements includes a conductive area that covers the entire surface of the pattern element, as shown in  FIG. 1 . In an alternative embodiment, a pattern element may include a conductive area that occupies only a portion of the surface of the pattern element. The conductive material may be on an insulating support. In an alternate embodiment, the conductive material may occupy the entire thickness of the pattern element. A conductive area can be formed of a metal (e.g., copper) or other types of conductive materials. 
     The phased array transmitter  110  further includes separation gaps  120   b . Each gap is formed between its associated ones of the plurality of pattern elements so that adjacent pattern elements have a gap. Each gap is a fixed gap according to one embodiment. The phased array transmitter  110  also includes active sources such as current generators. According to one embodiment, current generators are an array of photodiodes  120   c  across the gaps  120   b . Each of the active sources interconnects its associated ones of the plurality of pattern elements. According to one embodiment, reverse biased PN or PIN photodiodes are utilized as active sources of gap current generators between adjacent pattern elements. According to one embodiment, the present invention may utilize hundreds of discrete photodiodes, but the invention is not limited to these. Photodiodes are sometimes referred to as photodetectors. The transmitter  110  further includes an array of inductors  120   d . According to one embodiment, the inductors are conical copper-wired inductors and can be less than 1 inch in size. The phased array transmitter  110  is thin (e.g., about ¼ inch or less) according to one embodiment. 
     According to one embodiment, each pattern element has at least a first connection (e.g.,  130   a ) to an inductor and a second connection (e.g.,  140   a ) to a photodiode, if the pattern elements form a linear array. If the pattern elements form a 2-dimensional array as shown in  FIG. 1 , then the pattern elements may have three, four or five connections. An inductor has a first end (e.g.,  130   d ) and a second end (e.g.,  140   d ), and an active source has a first end (e.g.,  130   c ) and a second end (e.g.,  140   c ). One end (e.g.,  130   d ) of each of the inductors is coupled to the first connection (e.g.,  130   a ) of the associated one of the plurality of pattern elements. One end (e.g.,  130   c ) of each of the active sources is coupled to the second connection (e.g.,  140   a ) of the associated one of the plurality of pattern elements. The second end (e.g.,  140   d ) of each of the inductors is coupled to a bias voltage source, V RB . The second end (e.g.,  140   c ) of each of the active sources is coupled to the associated one of the plurality of pattern elements. The two ends of an active source are coupled to adjacent pattern elements. Adjacent active sources are reversed in polarity. 
       FIG. 2  illustrates a segment of a phased array transmitter as shown in  FIG. 1  in a 3-D view according to one embodiment of the present invention. A phased array transmitter  210  includes conductive patches  220   a , separation gaps  220   b  between adjacent conductive patches, photodiodes  220   c  bridging the gaps between the adjacent patches, and conical inductors  220   d  having one end attached to a conductive patch and the other end attached to the voltage source, V RB . Optical signals (e.g., optical power) are supplied to the photodiodes  220   c  via fiber optic bundles  220   e.    
       FIG. 3  illustrates a current sheet distribution and a transmitter according to one embodiment of the present invention. A drawing  310  illustrates a current sheet distribution over a plane, and the present invention utilizes the concept that a current sheet on a surface may couple energy to or from a free space electromagnetic wave. A drawing  320  illustrates that a current sheet may be approximated by an array of photocurrent generators (e.g.,  320   c ) when the size of each individual cell (e.g., each of Dx and Dy) is much less than the shortest wavelength of the RF signals produced by a phased array transmitter (e.g., much less than ¼ or ½ of the shortest wavelength of the RF signals radiated or transmitted by the transmitter). Each of Dx and Dy can be viewed as a distance between the centers of the adjacent conductive patches along the x-axis or y-axis, or a distance between the adjacent active sources along the x-axis or y-axis. 
     The required current sheet is developed by an array of photocurrent generators (e.g.,  330   c ) connected across the gaps (e.g.,  330   b ) of an array of rectangular metal patches (e.g.,  330   a ), as shown by a drawing  330  in  FIG. 3 . When the conductive patches are square and all of the gaps are supplied by in-phase current sources, each individual gap presents an impedance of Z 0 /2=188.5Ω to the photocurrent generators. Z 0 , which is the characteristic impedance of free space, is 377Ω. The division by 2 arises since a signal propagating away from the current sheet is generated on both sides of the sheet. The individual current generators may be phased to generate either an E-plane (TM polarized) wave or an H-plane (TE polarized) wave propagating at an angle, θ, to the plane of the current sheet as indicated in Table 1 below. An arbitrary azimuth angle may be obtained by appropriate combination of i x  and i y  for either an E-plane of H-plane excitation. Circular polarized waves may also be generated by adding an appropriately phased E-plane wave to a corresponding H-plane wave. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Current distribution 
                 surface 
                 current 
                 polarization 
                   
               
               
                 A/m in xy-plane 
                 current 
                 phase 
                 of 
                 plane of 
               
               
                 (z = 0 plane) 
                 direction 
                 variation 
                 emittance 
                 emittance 
               
               
                   
               
             
            
               
                 â x I 0x   TM e j(ωt+φ     1     -kx sin θ)   
                 x-directed 
                 along  
                 E-plane or 
                 xz- plane 
               
               
                   
                   
                 x-direction 
                 TM wave 
                   
               
               
                 â y I 0y   TM e j(ωt+φ     4     -kx sin θ)   
                 y-directed 
                 along  
                 E-plane or 
                 yz-plane 
               
               
                   
                   
                 y-direction 
                 TM wave 
                   
               
               
                 â x I 0x   TE e j(ωt+φ     2     -kx sin θ)   
                 x-directed 
                 along  
                 H-plane or 
                 yz-plane 
               
               
                   
                   
                 y-direction 
                 TE wave 
                   
               
               
                 â y I 0y   TE e j(ωt+φ     3     -kx sin θ)   
                 y-directed 
                 along  
                 H-plane or 
                 xz- plane 
               
               
                   
                   
                 x-direction 
                 TE wave 
               
               
                   
               
            
           
         
       
     
     The photocurrent generators may be high optical power handling (20-40 mW), high frequency (10-50 GHz) photodiodes currently available as discrete elements, according to one embodiment. The present invention provides broadband (multi octave) coverage. For example, the frequencies can be 100 MHz to 20 or 30 GHz, 1 GHz to 4 GHz (2 octaves), or 1 GHz to 8 GHz (3 octaves). These are exemplary, and the invention is not limited to these frequency ranges. The RF modulation of an optical carrier may be generated by a balanced MZM which enables a simple, single source direct current (DC) bias supply for an array of photodiode-connected patches. In addition, the use of overdriven MZMs provides potential power efficiencies of RF power radiated to total electrical and optical power into the photodiodes of 58% for fundamental generation, 48% for second harmonic generation, 43% for third harmonic generation, and 40% for forth harmonic generation. 
     The required phasing of the photo-excitation signals for the individual photocurrent generators may be accomplished in the photonic domain by any of a number of photonic controlled active array systems. Various photonic controlled beam forming methods are known to those skilled in the art. 
       FIG. 4  illustrates a phased array transmitter having two control sources in accordance with one embodiment of the present invention. A phased array transmitter  400  includes conductive patches  410  and separation gaps  420 . The transmitter  400  further includes x-axis current generators  430  controlled by x-axis current control optical fibers  440 , and y-axis current generators  450  controlled by y-axis current control optical fibers  460 . While  FIG. 4  shows two current control sources, the present invention is not limited to two current control sources, and in an alternate embodiment, it may utilize any number of control sources. 
       FIG. 5  illustrates a receiver and a transmitter according to one embodiment. A receiver  510  includes an array of conductive patches capacitively coupled across gaps. The passive gap load impedances (e.g., capacitive impedances  530 ) include the electro-optically active arms of a Mach Zehnder modulator to sense the voltage induced across the gaps by an incident electro-magnetic field. The receiver configurations are described in U.S. Pat. Nos. 6,252,557 and 7,062,115. A transmitter  520  includes active sources (e.g.,  540 ). Active sources may be current generators such as reverse biased PN or PIN photodiodes. The transmitter  520  also includes conductive pattern elements and gaps. 
     A basic circuit concept is illustrated in  FIG. 6 , according to one embodiment of the present invention. The reverse bias connections (V RB ) to the photodiodes  620   a ,  620   b ,  620   c  and  620   d  are RF isolated from the circulating RF currents, i RF , by inductors, L. The gap impedance (neglecting fringing capacitance across the gaps) is Z 0 /2 since the gap can radiate both to the front and to the back. The circulating RF currents, i RF , produce photovoltages, v RF , across the gaps. For each gap, v RF =i RF Z 0 /2. 
     While  FIG. 6  shows a linear array with a separate bias supply to each gap (or to each photodiode), the alternating reverse polarity of photodiodes can be accommodated with a single reverse biased DC power supply (V RB ), as shown in  FIG. 7 . The alternating polarity photodiodes are addressed by alternating ±sinusoidal photon intensities superimposed on the DC photon intensity so that the RF photovoltages generated across all gaps are in-phase. 
     For an N element array of active sources, the two required anti-phase optical signals may be obtained from a single balanced MZM modulator as illustrated in  FIG. 8 . N can be any number, but in this particular example, N is 4. According to one embodiment of the present invention, a transmitter system  800  in  FIG. 8  includes an RF source  810 , an optical source such as a laser  820 , an optical modulator  830 , and an optical power divider  840 . The optical modulator  830  receives an optical signal (e.g., optical power) from the laser  820  and an RF voltage signal (e.g., V Ω  sin Ωt) from the RF source  810  and optically modulates the optical signal at the RF frequency, Ω, of the RF signal. The optical power divider  840  receives the modulated optical signal and divides it into N number of optical signals, each being supplied to its associated active source of a phased array transmitter via an optical fiber. For example, the optical signal  850   a  is supplied to the photodiode  620   a  in  FIG. 6 , the optical signal  850   b  is supplied to the photodiode  620   b , the optical signal  850   c  is supplied to the photodiode  620   c , and the optical signal  850   d  is supplied to the photodiode  620   d.    
       FIG. 9  illustrates an exemplary block diagram of a transmitter system according to one embodiment of the present invention. A transmitter system  900  includes an RF source such as an RF voltage generator  910 , an optical source such as a laser optical source  920 , an optical modulator  930 , an optical power divider  940 , active sources such photodiodes  950   a ,  950   b ,  950   c , . . .  950   d , and  950   e , conductive patches  960  and separation gaps between the patches. The blocks shown in  FIG. 9  provide the functions described in the foregoing paragraphs. While  FIG. 9  shows one RF source, one optical source, one optical modulator, and one optical power divider block, in an alternate embodiment, a transmitter system may include multiple RF sources, multiple optical sources, multiple optical modulators and/or multiple optical power dividers. 
     According to one aspect of the present invention, the phase modulation is given by:
 
φ( t )=φ 0   +πV   Ω  sin Ω t/V   π   (1)
 
where φ 0  is the phase bias (a constant phase which can be any number), V Ω  is the amplitude of the RF source  810  expressed in voltage, and V π  is the sensitivity of the optical modulator  830  expressed as a voltage.
 
     Following Equation (1), the modulated optical signal is given by: 
                         P   0     2     ⁢     (     1   ±     sin   ⁢           ⁢     ϕ   ⁡     (   t   )           )       =       ⁢         P   0     2     ⁢     (     1   ±     sin   ⁡     (       ϕ   0     +         π   ⁢           ⁢     V   Ω         V   π       ⁢   sin   ⁢           ⁢   Ω   ⁢           ⁢   t       )         )                   =       ⁢         P   0     2     ⁢     (           1   ±     sin   ⁢           ⁢     ϕ   0     ⁢       J   0     ⁡     (       π   ⁢           ⁢     V   Ω         V   π       )                       ±   2     ⁢   sin   ⁢           ⁢     ϕ   0     ⁢       ∑     n   =   1     ∞     ⁢         J     2   ⁢   n       ⁡     (       π   ⁢           ⁢     V   Ω         V   π       )       ⁢     cos   ⁡     (     2   ⁢   n   ⁢           ⁢   Ω   ⁢           ⁢   t     )                         ±   2     ⁢   cos   ⁢           ⁢     ϕ   0     ⁢       ∑     n   =   0     ∞     ⁢         J       2   ⁢   n     +   1       ⁡     (       π   ⁢           ⁢     V   Ω         V   π       )       ⁢     cos   ⁡     (       {       2   ⁢   n     +   1     }     ⁢           ⁢   Ω   ⁢           ⁢   t     )                   )     ⁢           dc   ⁢           ⁢   term                               even   ⁢           ⁢   harmonics                               odd   ⁢           ⁢   harmonics                         
where P 0  is a constant optical power indicating how much optical power an optical source such as the laser  820  produces, and J 0 , J 2n , and J 2n+1  are Bessel functions of the first kind. The phase bias, φ 0 , will be set either to sin φ 0 =±1 (with cos φ 0 =0) or to cos φ 0 =±1 (with sin φ 0 =0).
 
     Note that the dc term for the even harmonics is increased by sin φ 0 J 0 (πV Ω /V π ) for the “+” signed terms and decreased by an equal amount for the “−” signed terms. Therefore, when the phase bias is set at sin φ 0 =1 to maximize even harmonic terms, one channel results in a P dc =A R P 0 [1+J o (πV Ω /V π )]V RB /2, where A R  is the responsivity of a photodiode (expressed in Amps/Watt), and the anti-phase channel results in a P dc =A R P 0 [1−J o (πV Ω /V π )]V RB /2, but the total dc power supplied by the V RB  source for two channels is P dc =A R P 0 V RB . When the phase bias is set at cos φ 0 =1 to maximize odd harmonic terms, the dc power supplied by the V RB  source for each channel is P dc =A R P 0 V RB /2. 
     According to one aspect of the present invention, the current flowing in a dc mesh in  FIG. 6  is: 
                     I   DC     =             A   R     ⁢     P   0       2     +       I   0     ⁡     (     1   -     ⅇ     -       V   RB     kT           )         ≈         A   R     ⁢     P   0       2               (   2   )               
where the approximation is valid as long as the photodiodes remain in reverse bias. The power supplied by the reverse bias source V RB  is then simply:
 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       DC 
                     
                     ≡ 
                     
                       
                         I 
                         DC 
                       
                       ⁢ 
                       
                         V 
                         RB 
                       
                     
                   
                   = 
                   
                     
                       V 
                       RB 
                     
                     ⁢ 
                     
                       
                         
                           A 
                           R 
                         
                         ⁢ 
                         
                           P 
                           0 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The RF current and voltage at the p th  harmonic generated at the gap impedance are: 
                           I   RF     =       ⁢       A   R     ⁢     P   0     ⁢       J   p     ⁡     (       π   ⁢           ⁢     V   Ω         V   π       )       ⁢     cos   ⁡     (     p   ⁢           ⁢   Ω   ⁢           ⁢   t     )                       V   RF     =       ⁢       A   R     ⁢     P   0     ⁢       J   p     ⁡     (       π   ⁢           ⁢     V   Ω         V   π       )       ⁢       Z   0     2     ⁢     cos   ⁡     (     p   ⁢           ⁢   Ω   ⁢           ⁢   t     )                       (   4   )               
so that the average radiated power contribution from a single gap in an infinite array is:
 
     
       
         
           
             
               
                 
                   
                     P 
                     RF 
                   
                   = 
                     
                   ⁢ 
                   
                     
                       
                         ( 
                         
                           
                             A 
                             R 
                           
                           ⁢ 
                           
                             P 
                             0 
                           
                         
                         ) 
                       
                       2 
                     
                     ⁢ 
                     
                       
                         J 
                         p 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               Ω 
                             
                           
                           
                             V 
                             π 
                           
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         Z 
                         0 
                       
                       4 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     According to one aspect of the present invention, to the extent that fringing field capacitance at the gap can be neglected compared to Z 0 /2, the radiated power at each harmonic is proportional to the Bessel function squared as shown in  FIG. 10  (assuming sin φ 0  or cos φ 0  set to 0 as appropriate). The maximum values of the Bessel function squares are shown on  FIG. 10 . By over modulating, the maximum value of the 5 th  harmonic can reach 40% of the maximum power available from the fundamental. 
       FIG. 11  shows the maximum power that could be radiated from a gap at the fundamental and first three overtones according to one aspect of the present invention. In Equation (5) above, responsivity, A R , is assumed to be 0.8 Amps/Watt, which is a typical value for photonic systems operating at an optical wavelength of 1.55 μm. The optical power per gap in all of the equations is taken to be P 0 /2 since there is a division of in-phase and anti-phase modulations in the balanced output of the modulator as shown in  FIG. 8 . Note that as in the case of a receiver, the RF power is a quadratic function of the optical power. In  FIG. 11 , the diamonds on the RF power curves are the points at which the radiated RF power equals the optical power into the photodiodes. 
     According to one embodiment, the photodiodes need to be retained in reverse bias. If any one harmonic is to be the desired RF signal, the voltage amplitude is dominated by that term with optimized RF drive of πV Ω /V π . The amplitude of the RF voltage across the gap should not exceed the bias supply reverse bias, V RB , which imposes the requirement on V RB  of: 
                     V   RB     ≥       A   R     ⁢     P   0     ⁢       J   p     ⁡     (       π   ⁢           ⁢     V   Ω         V   π       )       ⁢         Z   0     2     .               (   6   )               
which, in turn, places a lower limit on the bias supply electrical power requirement:
 
                     P   DC     ≥       ⁢         (       A   R     ⁢     P   0       )     2     ⁢       J   p     ⁡     (       π   ⁢           ⁢     V   Ω         V   π       )       ⁢       Z   0     4               (   7   )               
per gap. The “raw power” supplied to each photodiode is then given by:
 
                     P   raw     ≡       P   DC     +       P   0     2               (   8   )               
and the elemental gap conversion efficiency is:
 
     
       
         
           
             
               
                 
                   
                     η 
                     gap 
                   
                   ≡ 
                   
                     
                       P 
                       RF 
                     
                     
                       
                         P 
                         DC 
                       
                       + 
                       
                         
                           P 
                           0 
                         
                         / 
                         2 
                       
                     
                   
                   ≤ 
                   
                     
                       
                         J 
                         p 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               Ω 
                             
                           
                           
                             V 
                             π 
                           
                         
                         ) 
                       
                     
                     
                       1 
                       + 
                       
                         2 
                         
                           
                             P 
                             0 
                           
                           ⁢ 
                           
                             A 
                             R 
                             2 
                           
                           ⁢ 
                           
                             
                               J 
                               p 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     Ω 
                                   
                                 
                                 
                                   V 
                                   π 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             Z 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     The maximum gap conversion efficiency from Equation (9) is plotted in  FIG. 12 . The diamond points on the “raw power” efficiency curves are the points at which the bias source electrical power equals the optical power to each gap of the phased array transmitter. Note that the asymptotic value of each efficiency curve is J p (x max ) where x max  is the argument at which the pth order Bessel function takes on its maximum value. 
       FIG. 13  illustrates the power flows during a transmit mode operation of an active source (e.g., a photodiode) in a phased array transmitter in accordance with one aspect of the present invention. A photodiode  1310  receives bias supply electrical power from a bias source and optical power from an optical source and produces RF power being radiated from the transmitter and power being dissipated in the transmitter. 
       FIG. 14  illustrates various power flows as a function of optical power to the photodiode for the two drive cases maximizing either the fundamental or the 4 th  harmonic in accordance with one aspect of the present invention.  FIG. 14  shows the operation of a transmit system as the control of RF radiated power by the RF modulated optical signal incident on the photodiode. The powers shown in  FIG. 13  and the powers plotted in  FIG. 14  are: 
     P 0 /2, the controlling optical power into the photodiode, Eqn. (3) 
     P DC =I DC V RB =V RB A R P 0 /2, the DC electrical power with 
     V RB =A R P 0 J p (πV Ω /V π )Z 0 /2 from the peak value of V RF  in Eqn. (4). 
     Eqn. (5), P RF =(A R P 0 ) 2 J p   2 (πV Ω /V π )Z 0 /4, the average radiated RF power 
     P PD =P DC +P 0 /2−P RF , the power dissipated in the photodiode. 
     The analyses provided in the foregoing paragraphs only considered the power delivered to or from the photodiode. According to one aspect of the present invention, if the optical power is obtained from a Yb fiber laser, the electro optic (EO) conversion efficiency may be up to 25% so that the electrical power required to generate P 0 /2 is 2P 0 . In this case, the wall plug electrical efficiency is: 
     
       
         
           
             
               η 
               
                 elect 
                 . 
               
             
             ≡ 
             
               
                 P 
                 RF 
               
               
                 
                   P 
                   DC 
                 
                 + 
                 
                   
                     
                       P 
                       0 
                     
                     / 
                     2 
                   
                   
                     η 
                     EO 
                   
                 
               
             
             ≤ 
             
               
                 
                   
                     A 
                     R 
                     2 
                   
                   ⁢ 
                   
                     
                       J 
                       p 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             Ω 
                           
                         
                         
                           V 
                           π 
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     Z 
                     0 
                   
                   ⁢ 
                   
                     
                       P 
                       0 
                     
                     2 
                   
                 
                 
                   
                     
                       A 
                       R 
                       2 
                     
                     ⁢ 
                     
                       
                         J 
                         p 
                         
                             
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               Ω 
                             
                           
                           
                             V 
                             π 
                           
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       Z 
                       0 
                     
                     ⁢ 
                     
                       
                         P 
                         0 
                       
                       2 
                     
                   
                   + 
                   
                     1 
                     
                       η 
                       EO 
                     
                   
                 
               
               . 
             
           
         
       
     
     If the reverse bias voltage is taken as a fixed value, e.g., V RB =9 volts, bias source power from Equation (3) becomes simply: 
     
       
         
           
             
               P 
               DC 
             
             = 
             
               9 
               ⁢ 
               
                 
                   
                     A 
                     R 
                   
                   ⁢ 
                   
                     P 
                     0 
                   
                 
                 2 
               
             
           
         
       
     
     and the electrical efficiency is given by: 
     
       
         
           
             
               η 
               
                 elect 
                 . 
               
             
             ≡ 
             
               
                 P 
                 RF 
               
               
                 
                   P 
                   DC 
                 
                 + 
                 
                   
                     
                       P 
                       0 
                     
                     / 
                     2 
                   
                   
                     η 
                     EO 
                   
                 
               
             
             ≤ 
             
               
                 
                   
                     A 
                     R 
                     2 
                   
                   ⁢ 
                   
                     
                       J 
                       p 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             Ω 
                           
                         
                         
                           V 
                           π 
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     Z 
                     0 
                   
                   ⁢ 
                   
                     
                       P 
                       0 
                     
                     2 
                   
                 
                 
                   
                     
                       V 
                       RB 
                     
                     ⁢ 
                     
                       A 
                       R 
                     
                   
                   + 
                   
                     1 
                     
                       η 
                       EO 
                     
                   
                 
               
               . 
             
           
         
       
     
       FIG. 15  illustrates various curves for electrical efficiency as a function of optical power per gap when the optimum bias voltage is used (where p=1, 2, 3 or 4) and when the bias voltage is fixed at 9 volts (where p=1, 2, 3 or 4) according to one aspect of the invention. 
     The RF power required to modulate the optical carrier is not considered in  FIGS. 10-15 . If the MZM is unterminated, it presents a purely capacitive load to the RF current generator, and no RF power is supplied to the MZM. In  FIG. 16 , the drive voltage and drive power requirements are shown for a typical lithium niobate MZM in accordance with one aspect of the present invention, assuming a typical RF generator with 50Ω source impedance. 
     Many benefits accrue to an array of conductive pattern elements according to the present invention. An array of square (or rectangular) conductive pattern elements (e.g., metallic patches) with photodiodes interconnecting the patches has a broadband, purely resistive radiation impedance loading the photodiode current sources. The required structure is easily made conformal to non-planar surfaces. Because the RF signal is already on an optical carrier, various photonic approaches to beam control may be utilized. In addition, because the RF current is photogenerated, rather than provided by an electronic RF generator, there is a minimum of circuitry associated with each element. 
     According to one embodiment, the present invention does not require a highly integrated structure but rather uses conventional components to construct a versatile emitting array. In particular, the present invention utilizes direct conversion of DC power from a voltage source into a radiated RF power. In addition, the present invention provides methods to provide negligible electronic circuitry immediately behind the antenna terminal or port to minimize the losses associated with metallic connections between antenna terminals or ports and transmit or receive electronics at microwave frequencies and above. 
     The description of the invention is provided to enable any person skilled in the art to practice the various embodiments described herein. While the present invention has been particularly described with reference to the various figures and embodiments, it should be understood that these are for illustration purposes only and should not be taken as limiting the scope of the invention. 
     There may be many other ways to implement the invention. Various functions and elements described herein may be partitioned differently from those shown without departing from the sprit and scope of the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and generic principles defined herein may be applied to other embodiments. Thus, many changes and modifications may be made to the invention, by one having ordinary skill in the art, without departing from the spirit and scope of the invention. 
     A reference to an element in the singular is not intended to mean “one and only one” unless specifically stated, but rather “one or more.” The term “some” refers to one or more. All structural and functional equivalents to the elements of the various embodiments described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and intended to be encompassed by the invention. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the above description.