Abstract

We present an approach to receive-mode broadband beam forming and jammer nulling for large adaptive antenna arrays as well as its efficient and compact optical implementation. This broadband efficient adaptive method for true-time-delay array processing (BEAMTAP) algorithm decreases the number of tapped delay lines required for processing an N-element phased-array antenna from N to only 2, producing an enormous savings in delay-line hardware (especially for large broadband arrays) while still providing the full NM degrees of freedom of a conventional N-element time-delay-and-sum beam former that requires N tapped delay lines with M taps each. This allows the system to adapt fully and optimally to an arbitrarily complex spatiotemporal signal environment that can contain broadband signals of interest, as well as interference sources and narrow-band and broadband jammers—all of which can arrive from arbitrary angles onto an arbitrarily shaped array—thus enabling a variety of applications in radar, sonar, and communication. This algorithm is an excellent match with the capabilities of radio frequency (rf) photonic systems, as it uses a coherent optically modulated fiber-optic feed network, gratings in a photorefractive crystal as adaptive weights, a traveling-wave detector for generating time delay, and an acousto-optic device to control weight adaptation. Because the number of available adaptive coefficients in a photorefractive crystal is as large as 109, these photonic systems can adaptively control arbitrarily large one- or two-dimensional antenna arrays that are well beyond the capabilities of conventional rf and real-time digital signal processing techniques or alternative photonic techniques.

© 2000 Optical Society of America

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  1. D. Psaltis, J. Hong, “Adaptive acoustooptic filter,” Appl. Opt. 23, 3475–3481 (1984).
    [CrossRef] [PubMed]
  2. W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
    [CrossRef]
  3. R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
    [CrossRef]
  4. P. J. Matthews, M. Y. Frankel, R. D. Esman, “A wide-band fiber-optic true-time-steered array receiver capable of multiple independent simultaneous beams,” IEEE Photonics Technol. Lett. 10, 722–724 (1998).
    [CrossRef]
  5. D. Casasent, “Optical processing for adaptive phased-array radar,” IEE Proc. F. 127, 278–284 (1980).
  6. D. Voskresenskii, A. Grinev, E. Voronin, Electrooptical Arrays (Springer-Verlag, Berlin, 1989).
    [CrossRef]
  7. D. Psaltis, J. Hong, “Adaptive acoustooptic processor,” in Analog Optical Processing and Computing, H. J. Caulfield, ed., Proc. SPIE519, 62–68 (1984).
    [CrossRef]
  8. S.-C. Lin, J. Hong, R. Boughton, D. Psaltis, “Broadband beamforming via acousto-optics,” in Advances in Optical Information Processing III, D. R. Pape, ed., Proc. SPIE936, 152–162 (1988).
    [CrossRef]
  9. J. H. Hong, “Broadband phased array beamforming,” in Optical Technology for Microwave Applications IV, S.-K. Yao, ed., Proc. SPIE1102, 134–141 (1989).
    [CrossRef]
  10. W. A. Penn, R. Wasiewicz, R. Iodice, “Optical adaptive multipath canceller for surveillance radar,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 151–160 (1990).
    [CrossRef]
  11. R. M. Montgomery, “Acousto-optic/photorefractive processor for adaptive antenna arrays,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 207–217 (1990).
    [CrossRef]
  12. D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
    [CrossRef]
  13. J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
    [CrossRef]
  14. A. P. Goutzoulis, D. K. Davies, J. M. Zomp, “Hybrid electronic fiber optic wavelength-multiplexed system for true time-delay steering of phased array antennas,” Opt. Eng. 31, 2312–2322 (1992).
    [CrossRef]
  15. R. Soref, “Optical dispersion technique for time-delay beam steering,” Appl. Opt. 31, 7395–7397 (1992).
    [CrossRef] [PubMed]
  16. L. J. Lembo, T. Holcomb, M. Wickham, P. Wisseman, J. C. Brock, “Low-loss fiber optic time-delay element for phased-array antennas,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 13–23 (1994).
    [CrossRef]
  17. R. T. Weverka, K. Wagner, A. Sarto, “Photorefractive processing for large adaptive phased arrays,” Appl. Opt. 35, 1344–1366 (1996).
    [CrossRef] [PubMed]
  18. K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
    [CrossRef]
  19. M. A. Copeland, D. Roy, J. D. E. Beynon, F. Y. K. Dea, “An optical CCD convlover,” IEEE Trans. Electron Devices ED-23, 152–155 (1976).
    [CrossRef]
  20. K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
    [CrossRef]
  21. T. Merlet, D. Dolfi, J.-P. Huignard, “A traveling fringes photodetector for microwave signals,” IEEE J. Quantum Electron. 32, 778–783 (1996).
    [CrossRef]
  22. D. Dolfi, T. Merlet, A. Mestreau, J.-P. Huignard, “Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern,” Appl. Phys. Lett. 65, 2931–2933 (1994).
    [CrossRef]
  23. B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1985).
  24. B. Widrow, P. E. Mantey, L. J. Griffiths, B. B. Goode, “Adaptive antenna systems,” Proc. IEEE 55, 2143–2161 (1967).
    [CrossRef]
  25. A. W. Sarto, R. T. Weverka, K. Wagner, “Beam-steering and jammer nulling photorefractive phased-array radar processor,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 378–388 (1994).
    [CrossRef]
  26. A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Blair, S. Weaver, “Photorefractive phased-array antenna beam-forming processor,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 307–318 (1996).
    [CrossRef]
  27. R. T. Compton, Adaptive Antennas (Prentice-Hall, Englewood Cliffs, N.J., 1988).
  28. M. A. G. Abushagur, H. J. Caulfield, “Speed and convergence of bimodal optical computers,” Opt. Eng. 26, 22–27 (1987).
    [CrossRef]
  29. A. W. Sarto, “Adaptive phased-array radar signal processing array using photoreactive crystals,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 1996).
  30. R. T. Compton, “The effect of differential time delays in the LMS feedback loop,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 222–228 (1981).
    [CrossRef]
  31. A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Weaver, E. K. Walge, “Wide angular aperture holograms in photorefractive crystals by the use of orthogonally polarized write and read beams,” Appl. Opt. 35, 5765–5775 (1996).
    [CrossRef] [PubMed]
  32. A. Kiruluta, G. Kriehn, P. E. X. Silveira, S. Weaver, K. H. Wagner, “Operator notational analysis of a photorefractive phased array processor,” in Digest of Topical Meeting on Optics in Computing, Y. Fainman, ed. (Optical Society of America, Washington, D.C., 1999), 170–172.
  33. D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
    [CrossRef]
  34. A. A. Zozulya, D. Z. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).
    [CrossRef] [PubMed]
  35. Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
    [CrossRef]
  36. M. Y. Frankel, R. D. Esman, “Optical single-side-band suppressed-carrier modulator for wide-band signal-processing,” J. Lightwave Technol. 16, 859–863 (1998).
    [CrossRef]
  37. M. H. Garrett, J. Y. Chang, H. P. Jenssen, C. Warde, “High photorefractive sensitivity in an n-type 45°-cut BaTiO3 crystal,” Opt. Lett. 17, 103–105 (1992).
    [CrossRef] [PubMed]
  38. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

1998

P. J. Matthews, M. Y. Frankel, R. D. Esman, “A wide-band fiber-optic true-time-steered array receiver capable of multiple independent simultaneous beams,” IEEE Photonics Technol. Lett. 10, 722–724 (1998).
[CrossRef]

M. Y. Frankel, R. D. Esman, “Optical single-side-band suppressed-carrier modulator for wide-band signal-processing,” J. Lightwave Technol. 16, 859–863 (1998).
[CrossRef]

1996

1995

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).
[CrossRef] [PubMed]

1994

D. Dolfi, T. Merlet, A. Mestreau, J.-P. Huignard, “Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern,” Appl. Phys. Lett. 65, 2931–2933 (1994).
[CrossRef]

1993

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

1992

D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
[CrossRef]

A. P. Goutzoulis, D. K. Davies, J. M. Zomp, “Hybrid electronic fiber optic wavelength-multiplexed system for true time-delay steering of phased array antennas,” Opt. Eng. 31, 2312–2322 (1992).
[CrossRef]

R. Soref, “Optical dispersion technique for time-delay beam steering,” Appl. Opt. 31, 7395–7397 (1992).
[CrossRef] [PubMed]

M. H. Garrett, J. Y. Chang, H. P. Jenssen, C. Warde, “High photorefractive sensitivity in an n-type 45°-cut BaTiO3 crystal,” Opt. Lett. 17, 103–105 (1992).
[CrossRef] [PubMed]

1991

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

1989

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

1987

M. A. G. Abushagur, H. J. Caulfield, “Speed and convergence of bimodal optical computers,” Opt. Eng. 26, 22–27 (1987).
[CrossRef]

1986

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

1984

1981

R. T. Compton, “The effect of differential time delays in the LMS feedback loop,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 222–228 (1981).
[CrossRef]

1980

D. Casasent, “Optical processing for adaptive phased-array radar,” IEE Proc. F. 127, 278–284 (1980).

1976

M. A. Copeland, D. Roy, J. D. E. Beynon, F. Y. K. Dea, “An optical CCD convlover,” IEEE Trans. Electron Devices ED-23, 152–155 (1976).
[CrossRef]

1967

B. Widrow, P. E. Mantey, L. J. Griffiths, B. B. Goode, “Adaptive antenna systems,” Proc. IEEE 55, 2143–2161 (1967).
[CrossRef]

Abushagur, M. A. G.

M. A. G. Abushagur, H. J. Caulfield, “Speed and convergence of bimodal optical computers,” Opt. Eng. 26, 22–27 (1987).
[CrossRef]

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).
[CrossRef] [PubMed]

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

Bernstein, N.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

Beynon, J. D. E.

M. A. Copeland, D. Roy, J. D. E. Beynon, F. Y. K. Dea, “An optical CCD convlover,” IEEE Trans. Electron Devices ED-23, 152–155 (1976).
[CrossRef]

Blair, S.

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Blair, S. Weaver, “Photorefractive phased-array antenna beam-forming processor,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 307–318 (1996).
[CrossRef]

Boughton, R.

S.-C. Lin, J. Hong, R. Boughton, D. Psaltis, “Broadband beamforming via acousto-optics,” in Advances in Optical Information Processing III, D. R. Pape, ed., Proc. SPIE936, 152–162 (1988).
[CrossRef]

Brock, J. C.

L. J. Lembo, T. Holcomb, M. Wickham, P. Wisseman, J. C. Brock, “Low-loss fiber optic time-delay element for phased-array antennas,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 13–23 (1994).
[CrossRef]

Bromley, K.

K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
[CrossRef]

Casasent, D.

D. Casasent, “Optical processing for adaptive phased-array radar,” IEE Proc. F. 127, 278–284 (1980).

Caulfield, H. J.

M. A. G. Abushagur, H. J. Caulfield, “Speed and convergence of bimodal optical computers,” Opt. Eng. 26, 22–27 (1987).
[CrossRef]

Chang, J. Y.

Compton, R. T.

R. T. Compton, “The effect of differential time delays in the LMS feedback loop,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 222–228 (1981).
[CrossRef]

R. T. Compton, Adaptive Antennas (Prentice-Hall, Englewood Cliffs, N.J., 1988).

Cooper, D. G.

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

Copeland, M. A.

M. A. Copeland, D. Roy, J. D. E. Beynon, F. Y. K. Dea, “An optical CCD convlover,” IEEE Trans. Electron Devices ED-23, 152–155 (1976).
[CrossRef]

Davies, D. K.

A. P. Goutzoulis, D. K. Davies, J. M. Zomp, “Hybrid electronic fiber optic wavelength-multiplexed system for true time-delay steering of phased array antennas,” Opt. Eng. 31, 2312–2322 (1992).
[CrossRef]

Dea, F. Y. K.

M. A. Copeland, D. Roy, J. D. E. Beynon, F. Y. K. Dea, “An optical CCD convlover,” IEEE Trans. Electron Devices ED-23, 152–155 (1976).
[CrossRef]

Dexter, J. L.

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

Dolfi, D.

T. Merlet, D. Dolfi, J.-P. Huignard, “A traveling fringes photodetector for microwave signals,” IEEE J. Quantum Electron. 32, 778–783 (1996).
[CrossRef]

D. Dolfi, T. Merlet, A. Mestreau, J.-P. Huignard, “Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern,” Appl. Phys. Lett. 65, 2931–2933 (1994).
[CrossRef]

Esman, R. D.

M. Y. Frankel, R. D. Esman, “Optical single-side-band suppressed-carrier modulator for wide-band signal-processing,” J. Lightwave Technol. 16, 859–863 (1998).
[CrossRef]

P. J. Matthews, M. Y. Frankel, R. D. Esman, “A wide-band fiber-optic true-time-steered array receiver capable of multiple independent simultaneous beams,” IEEE Photonics Technol. Lett. 10, 722–724 (1998).
[CrossRef]

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

Fainman, Y.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Feinberg, J.

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

Frankel, M. Y.

M. Y. Frankel, R. D. Esman, “Optical single-side-band suppressed-carrier modulator for wide-band signal-processing,” J. Lightwave Technol. 16, 859–863 (1998).
[CrossRef]

P. J. Matthews, M. Y. Frankel, R. D. Esman, “A wide-band fiber-optic true-time-steered array receiver capable of multiple independent simultaneous beams,” IEEE Photonics Technol. Lett. 10, 722–724 (1998).
[CrossRef]

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

Garrett, M. H.

Goldberg, L.

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

Goode, B. B.

B. Widrow, P. E. Mantey, L. J. Griffiths, B. B. Goode, “Adaptive antenna systems,” Proc. IEEE 55, 2143–2161 (1967).
[CrossRef]

Goutzoulis, A. P.

A. P. Goutzoulis, D. K. Davies, J. M. Zomp, “Hybrid electronic fiber optic wavelength-multiplexed system for true time-delay steering of phased array antennas,” Opt. Eng. 31, 2312–2322 (1992).
[CrossRef]

Griffiths, L.

K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
[CrossRef]

Griffiths, L. J.

B. Widrow, P. E. Mantey, L. J. Griffiths, B. B. Goode, “Adaptive antenna systems,” Proc. IEEE 55, 2143–2161 (1967).
[CrossRef]

Grinev, A.

D. Voskresenskii, A. Grinev, E. Voronin, Electrooptical Arrays (Springer-Verlag, Berlin, 1989).
[CrossRef]

Holcomb, T.

L. J. Lembo, T. Holcomb, M. Wickham, P. Wisseman, J. C. Brock, “Low-loss fiber optic time-delay element for phased-array antennas,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 13–23 (1994).
[CrossRef]

Hong, J.

D. Psaltis, J. Hong, “Adaptive acoustooptic filter,” Appl. Opt. 23, 3475–3481 (1984).
[CrossRef] [PubMed]

D. Psaltis, J. Hong, “Adaptive acoustooptic processor,” in Analog Optical Processing and Computing, H. J. Caulfield, ed., Proc. SPIE519, 62–68 (1984).
[CrossRef]

S.-C. Lin, J. Hong, R. Boughton, D. Psaltis, “Broadband beamforming via acousto-optics,” in Advances in Optical Information Processing III, D. R. Pape, ed., Proc. SPIE936, 152–162 (1988).
[CrossRef]

Hong, J. H.

J. H. Hong, “Broadband phased array beamforming,” in Optical Technology for Microwave Applications IV, S.-K. Yao, ed., Proc. SPIE1102, 134–141 (1989).
[CrossRef]

Huignard, J.-P.

T. Merlet, D. Dolfi, J.-P. Huignard, “A traveling fringes photodetector for microwave signals,” IEEE J. Quantum Electron. 32, 778–783 (1996).
[CrossRef]

D. Dolfi, T. Merlet, A. Mestreau, J.-P. Huignard, “Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern,” Appl. Phys. Lett. 65, 2931–2933 (1994).
[CrossRef]

Iodice, R.

W. A. Penn, R. Wasiewicz, R. Iodice, “Optical adaptive multipath canceller for surveillance radar,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 151–160 (1990).
[CrossRef]

Jenssen, H. P.

Jones, V. I.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

Keenan, T. E.

K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
[CrossRef]

Kiruluta, A.

A. Kiruluta, G. Kriehn, P. E. X. Silveira, S. Weaver, K. H. Wagner, “Operator notational analysis of a photorefractive phased array processor,” in Digest of Topical Meeting on Optics in Computing, Y. Fainman, ed. (Optical Society of America, Washington, D.C., 1999), 170–172.

Klancnik, E.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Kraut, S.

K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
[CrossRef]

Kriehn, G.

A. Kiruluta, G. Kriehn, P. E. X. Silveira, S. Weaver, K. H. Wagner, “Operator notational analysis of a photorefractive phased array processor,” in Digest of Topical Meeting on Optics in Computing, Y. Fainman, ed. (Optical Society of America, Washington, D.C., 1999), 170–172.

Lee, J. J.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

Lee, S. H.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Lembo, L. J.

L. J. Lembo, T. Holcomb, M. Wickham, P. Wisseman, J. C. Brock, “Low-loss fiber optic time-delay element for phased-array antennas,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 13–23 (1994).
[CrossRef]

Lewis, J. B.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

Lin, S.-C.

S.-C. Lin, J. Hong, R. Boughton, D. Psaltis, “Broadband beamforming via acousto-optics,” in Advances in Optical Information Processing III, D. R. Pape, ed., Proc. SPIE936, 152–162 (1988).
[CrossRef]

Livingston, S.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

Loo, R. Y.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

Louie, A. C. H.

K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
[CrossRef]

Mantey, P. E.

B. Widrow, P. E. Mantey, L. J. Griffiths, B. B. Goode, “Adaptive antenna systems,” Proc. IEEE 55, 2143–2161 (1967).
[CrossRef]

Martin, R. D.

K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
[CrossRef]

Matthews, P. J.

P. J. Matthews, M. Y. Frankel, R. D. Esman, “A wide-band fiber-optic true-time-steered array receiver capable of multiple independent simultaneous beams,” IEEE Photonics Technol. Lett. 10, 722–724 (1998).
[CrossRef]

Merlet, T.

T. Merlet, D. Dolfi, J.-P. Huignard, “A traveling fringes photodetector for microwave signals,” IEEE J. Quantum Electron. 32, 778–783 (1996).
[CrossRef]

D. Dolfi, T. Merlet, A. Mestreau, J.-P. Huignard, “Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern,” Appl. Phys. Lett. 65, 2931–2933 (1994).
[CrossRef]

Mestreau, A.

D. Dolfi, T. Merlet, A. Mestreau, J.-P. Huignard, “Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern,” Appl. Phys. Lett. 65, 2931–2933 (1994).
[CrossRef]

Monahan, M. A.

K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
[CrossRef]

Montgomery, R. M.

R. M. Montgomery, “Acousto-optic/photorefractive processor for adaptive antenna arrays,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 207–217 (1990).
[CrossRef]

Newberg, I. L.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

Ng, W.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

Pape, D. R.

D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
[CrossRef]

Parent, M. G.

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

Penn, W. A.

W. A. Penn, R. Wasiewicz, R. Iodice, “Optical adaptive multipath canceller for surveillance radar,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 151–160 (1990).
[CrossRef]

Psaltis, D.

D. Psaltis, J. Hong, “Adaptive acoustooptic filter,” Appl. Opt. 23, 3475–3481 (1984).
[CrossRef] [PubMed]

S.-C. Lin, J. Hong, R. Boughton, D. Psaltis, “Broadband beamforming via acousto-optics,” in Advances in Optical Information Processing III, D. R. Pape, ed., Proc. SPIE936, 152–162 (1988).
[CrossRef]

D. Psaltis, J. Hong, “Adaptive acoustooptic processor,” in Analog Optical Processing and Computing, H. J. Caulfield, ed., Proc. SPIE519, 62–68 (1984).
[CrossRef]

Roy, D.

M. A. Copeland, D. Roy, J. D. E. Beynon, F. Y. K. Dea, “An optical CCD convlover,” IEEE Trans. Electron Devices ED-23, 152–155 (1976).
[CrossRef]

Sarto, A.

Sarto, A. W.

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Weaver, E. K. Walge, “Wide angular aperture holograms in photorefractive crystals by the use of orthogonally polarized write and read beams,” Appl. Opt. 35, 5765–5775 (1996).
[CrossRef] [PubMed]

A. W. Sarto, “Adaptive phased-array radar signal processing array using photoreactive crystals,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 1996).

A. W. Sarto, R. T. Weverka, K. Wagner, “Beam-steering and jammer nulling photorefractive phased-array radar processor,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 378–388 (1994).
[CrossRef]

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Blair, S. Weaver, “Photorefractive phased-array antenna beam-forming processor,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 307–318 (1996).
[CrossRef]

K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
[CrossRef]

Silveira, P. E. X.

A. Kiruluta, G. Kriehn, P. E. X. Silveira, S. Weaver, K. H. Wagner, “Operator notational analysis of a photorefractive phased array processor,” in Digest of Topical Meeting on Optics in Computing, Y. Fainman, ed. (Optical Society of America, Washington, D.C., 1999), 170–172.

Soref, R.

Stearns, S. D.

B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1985).

Stilwell, D.

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

Symanski, J. J.

K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
[CrossRef]

Tangonan, G. L.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

Voronin, E.

D. Voskresenskii, A. Grinev, E. Voronin, Electrooptical Arrays (Springer-Verlag, Berlin, 1989).
[CrossRef]

Voskresenskii, D.

D. Voskresenskii, A. Grinev, E. Voronin, Electrooptical Arrays (Springer-Verlag, Berlin, 1989).
[CrossRef]

Wagner, K.

R. T. Weverka, K. Wagner, A. Sarto, “Photorefractive processing for large adaptive phased arrays,” Appl. Opt. 35, 1344–1366 (1996).
[CrossRef] [PubMed]

K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
[CrossRef]

A. W. Sarto, R. T. Weverka, K. Wagner, “Beam-steering and jammer nulling photorefractive phased-array radar processor,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 378–388 (1994).
[CrossRef]

Wagner, K. H.

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Weaver, E. K. Walge, “Wide angular aperture holograms in photorefractive crystals by the use of orthogonally polarized write and read beams,” Appl. Opt. 35, 5765–5775 (1996).
[CrossRef] [PubMed]

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Blair, S. Weaver, “Photorefractive phased-array antenna beam-forming processor,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 307–318 (1996).
[CrossRef]

A. Kiruluta, G. Kriehn, P. E. X. Silveira, S. Weaver, K. H. Wagner, “Operator notational analysis of a photorefractive phased array processor,” in Digest of Topical Meeting on Optics in Computing, Y. Fainman, ed. (Optical Society of America, Washington, D.C., 1999), 170–172.

Walge, E. K.

Walston, A. A.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

Warde, C.

Wasiewicz, R.

W. A. Penn, R. Wasiewicz, R. Iodice, “Optical adaptive multipath canceller for surveillance radar,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 151–160 (1990).
[CrossRef]

Weaver, S.

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Weaver, E. K. Walge, “Wide angular aperture holograms in photorefractive crystals by the use of orthogonally polarized write and read beams,” Appl. Opt. 35, 5765–5775 (1996).
[CrossRef] [PubMed]

A. Kiruluta, G. Kriehn, P. E. X. Silveira, S. Weaver, K. H. Wagner, “Operator notational analysis of a photorefractive phased array processor,” in Digest of Topical Meeting on Optics in Computing, Y. Fainman, ed. (Optical Society of America, Washington, D.C., 1999), 170–172.

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Blair, S. Weaver, “Photorefractive phased-array antenna beam-forming processor,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 307–318 (1996).
[CrossRef]

K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
[CrossRef]

Wechsberg, M.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

Weverka, R. T.

R. T. Weverka, K. Wagner, A. Sarto, “Photorefractive processing for large adaptive phased arrays,” Appl. Opt. 35, 1344–1366 (1996).
[CrossRef] [PubMed]

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Weaver, E. K. Walge, “Wide angular aperture holograms in photorefractive crystals by the use of orthogonally polarized write and read beams,” Appl. Opt. 35, 5765–5775 (1996).
[CrossRef] [PubMed]

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Blair, S. Weaver, “Photorefractive phased-array antenna beam-forming processor,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 307–318 (1996).
[CrossRef]

A. W. Sarto, R. T. Weverka, K. Wagner, “Beam-steering and jammer nulling photorefractive phased-array radar processor,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 378–388 (1994).
[CrossRef]

K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
[CrossRef]

Wickham, M.

L. J. Lembo, T. Holcomb, M. Wickham, P. Wisseman, J. C. Brock, “Low-loss fiber optic time-delay element for phased-array antennas,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 13–23 (1994).
[CrossRef]

Widrow, B.

B. Widrow, P. E. Mantey, L. J. Griffiths, B. B. Goode, “Adaptive antenna systems,” Proc. IEEE 55, 2143–2161 (1967).
[CrossRef]

B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1985).

Wisseman, P.

L. J. Lembo, T. Holcomb, M. Wickham, P. Wisseman, J. C. Brock, “Low-loss fiber optic time-delay element for phased-array antennas,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 13–23 (1994).
[CrossRef]

Yen, H.-W.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

Zomp, J. M.

A. P. Goutzoulis, D. K. Davies, J. M. Zomp, “Hybrid electronic fiber optic wavelength-multiplexed system for true time-delay steering of phased array antennas,” Opt. Eng. 31, 2312–2322 (1992).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

D. Dolfi, T. Merlet, A. Mestreau, J.-P. Huignard, “Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern,” Appl. Phys. Lett. 65, 2931–2933 (1994).
[CrossRef]

IEE Proc. F.

D. Casasent, “Optical processing for adaptive phased-array radar,” IEE Proc. F. 127, 278–284 (1980).

IEEE J. Quantum Electron.

T. Merlet, D. Dolfi, J.-P. Huignard, “A traveling fringes photodetector for microwave signals,” IEEE J. Quantum Electron. 32, 778–783 (1996).
[CrossRef]

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

IEEE Photonics Technol. Lett.

R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photonics Technol. Lett. 5, 1347–1349 (1993).
[CrossRef]

P. J. Matthews, M. Y. Frankel, R. D. Esman, “A wide-band fiber-optic true-time-steered array receiver capable of multiple independent simultaneous beams,” IEEE Photonics Technol. Lett. 10, 722–724 (1998).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

R. T. Compton, “The effect of differential time delays in the LMS feedback loop,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 222–228 (1981).
[CrossRef]

IEEE Trans. Antennas Propag.

J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, H.-W. Yen, G. L. Tangonan, M. Wechsberg, “Photonic wideband array antennas,” IEEE Trans. Antennas Propag. 43, 966–982 (1995).
[CrossRef]

IEEE Trans. Electron Devices

M. A. Copeland, D. Roy, J. D. E. Beynon, F. Y. K. Dea, “An optical CCD convlover,” IEEE Trans. Electron Devices ED-23, 152–155 (1976).
[CrossRef]

J. Lightwave Technol.

W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Newberg, N. Bernstein, “The first demonstration of an optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9, 1124–1131 (1991).
[CrossRef]

M. Y. Frankel, R. D. Esman, “Optical single-side-band suppressed-carrier modulator for wide-band signal-processing,” J. Lightwave Technol. 16, 859–863 (1998).
[CrossRef]

Opt. Eng.

A. P. Goutzoulis, D. K. Davies, J. M. Zomp, “Hybrid electronic fiber optic wavelength-multiplexed system for true time-delay steering of phased array antennas,” Opt. Eng. 31, 2312–2322 (1992).
[CrossRef]

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

M. A. G. Abushagur, H. J. Caulfield, “Speed and convergence of bimodal optical computers,” Opt. Eng. 26, 22–27 (1987).
[CrossRef]

D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. A. Zozulya, D. Z. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).
[CrossRef] [PubMed]

Proc. IEEE

B. Widrow, P. E. Mantey, L. J. Griffiths, B. B. Goode, “Adaptive antenna systems,” Proc. IEEE 55, 2143–2161 (1967).
[CrossRef]

Other

A. W. Sarto, R. T. Weverka, K. Wagner, “Beam-steering and jammer nulling photorefractive phased-array radar processor,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 378–388 (1994).
[CrossRef]

A. W. Sarto, K. H. Wagner, R. T. Weverka, S. Blair, S. Weaver, “Photorefractive phased-array antenna beam-forming processor,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 307–318 (1996).
[CrossRef]

R. T. Compton, Adaptive Antennas (Prentice-Hall, Englewood Cliffs, N.J., 1988).

B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1985).

A. W. Sarto, “Adaptive phased-array radar signal processing array using photoreactive crystals,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 1996).

A. Kiruluta, G. Kriehn, P. E. X. Silveira, S. Weaver, K. H. Wagner, “Operator notational analysis of a photorefractive phased array processor,” in Digest of Topical Meeting on Optics in Computing, Y. Fainman, ed. (Optical Society of America, Washington, D.C., 1999), 170–172.

L. J. Lembo, T. Holcomb, M. Wickham, P. Wisseman, J. C. Brock, “Low-loss fiber optic time-delay element for phased-array antennas,” in Optoelectronic Signal Processing for Phased-Array Antennas IV, B. M. Hendrickson, ed., Proc. SPIE2155, 13–23 (1994).
[CrossRef]

K. Bromley, A. C. H. Louie, R. D. Martin, J. J. Symanski, T. E. Keenan, M. A. Monahan, “Electro-optical signal processing module,” in Real-Time Signal Processing II, T. F. Tau, ed., Proc. SPIE180, 107–113 (1979).
[CrossRef]

K. Wagner, S. Kraut, L. Griffiths, S. Weaver, R. T. Weverka, A. W. Sarto, “Efficient true-time-delay adaptive-array processing,” in Radar Processing, Technology, and Applications, W. J. Miceli, ed., Proc. SPIE2845, 287–300 (1996).
[CrossRef]

D. Voskresenskii, A. Grinev, E. Voronin, Electrooptical Arrays (Springer-Verlag, Berlin, 1989).
[CrossRef]

D. Psaltis, J. Hong, “Adaptive acoustooptic processor,” in Analog Optical Processing and Computing, H. J. Caulfield, ed., Proc. SPIE519, 62–68 (1984).
[CrossRef]

S.-C. Lin, J. Hong, R. Boughton, D. Psaltis, “Broadband beamforming via acousto-optics,” in Advances in Optical Information Processing III, D. R. Pape, ed., Proc. SPIE936, 152–162 (1988).
[CrossRef]

J. H. Hong, “Broadband phased array beamforming,” in Optical Technology for Microwave Applications IV, S.-K. Yao, ed., Proc. SPIE1102, 134–141 (1989).
[CrossRef]

W. A. Penn, R. Wasiewicz, R. Iodice, “Optical adaptive multipath canceller for surveillance radar,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 151–160 (1990).
[CrossRef]

R. M. Montgomery, “Acousto-optic/photorefractive processor for adaptive antenna arrays,” in Optoelectronic Signal Processing for Phased-Array Antennas II, B. M. Hendrickson, G. A. Koepf, eds., Proc. SPIE1217, 207–217 (1990).
[CrossRef]

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

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Figures (11)

Fig. 1
Fig. 1

(a) Narrow-band phased array that suffers from frequency-dependent beam squint. (b) Conventional broadband time-delay-and-sum beam-forming algorithm illustrating the requirement for one TDL at each antenna element to eliminate beam squint of the main beam and the nulls.

Fig. 2
Fig. 2

Conventional time-delay-and-sum approach to adaptive array processing for broadband squint-free TTD beam forming with LMS adaptation based on a desired signal and a correlation–cancellation-loop feedback, where the desired signal d(t) is subtracted from the output signal o(t) to produce the feedback signal f(t). Each weight is formed by integration of the multiplication of the feedback with the delayed antenna signals. The delayed antenna signals are then multiplied by the weights and summed to produce the output.

Fig. 3
Fig. 3

BEAMTAP algorithm for broadband squint-free TTD beam forming with a single output tap-in delay line. For adaptive calculation of the weights within the array, the additional input TDL is also required. The desired signal d(t) is again subtracted from the output signal o(t) to produce the feedback signal f(t). Here the variably delayed feedback is multiplied by the antenna signals delayed by T and integrated to produce the weights. The weights are then multiplied by the undelayed antenna signals, column summed, and input into the tap-in delay line.

Fig. 4
Fig. 4

Optical architecture of BEAMTAP. A single coherent laser is divided with two beam splitters with amplitude reflectances a r and ar, and amplitude transmittances a t and at, respectively, to drive both the fiber-feed network and the BEAMTAP processor—the fiber-feed network from the phased array is shown on the left-hand side. The diffracted light from the AOD interferes with signals from the array, which are imaged through lens system L 0 to form gratings in the photorefractive crystal (PR crystal). Diffraction of the phased-array signals off this grating is detected by a synchronous TFD, which has a carrier velocity matched to the magnified acoustic velocity of the AOD by the lens systems L 1 and L 2—producing a resonant charge carrier distribution q(x 2, t). The output signal o(t) is amplified by g 1, passed through a bandpass filter (BPF), subtracted from the desired signal d(t), amplified by g 2, and fed back into the AOD as the feedback signal f(t) to close the adaptive feedback loop necessary for the system to cancel any jamming signals present in the signal environment. A Rochon prism, linear polarizer (LP), and spatial filter (SF) are used for the read–write isolation of the AOD beam from the diffracted phased-array signals off the grating. The illustrated system places the photorefractive crystal in the image plane of the fiber feed and the AOD, and uses orthogonally propagating fields, for illustrative purposes.

Fig. 5
Fig. 5

Frequency offset scheme for the phased-array radar processor that allows for tuning of the processing bandwidth B (determined by the AOD bandwidth and typically limited to 1–2 GHz) anywhere within the rf spectrum spanned by the EOM’s bandwidths. The laser beam ω l is premodulated by ±ω s (in this case only the negative sideband is used), and then the rf signals modulate within a bandwidth of B and are offset by ±ω p such that the desired mix term overlaps the bandwidth B and carrier ω r of the AOD. The photorefractive crystal responds only to the near-dc interferometric products between the phased-array signals and AO diffractions, and all moving gratings wash out.

Fig. 6
Fig. 6

Example of a linear equispaced phased array and a random fiber-optic feed network. A broadband rf signal is incident from one angle and a jammer j from another angle onto a phased-array antenna with element spacing d, creating time delays t p and t j between the elements of the array for the signal and jammer, respectively. Both signals are modulated onto a much-higher-frequency optical carrier and transduced into the optical domain; then these signals are propagated through an optical fiber-feed manifold to a linear array of polished fiber ends. While propagating through the polarization-maintaining fiber, each beam passes through a polarizing beam splitter (PBS) so that the y -polarized writing beam passes through the delay loop and experiences a time delay T with respect to the z -polarized reading beam. Typical fiber cores of 8 µm and spacings of 250 µm are shown being collimated by a lenslet array, which allows us to make the simplifying assumption of propagation without diffraction used in the analysis of this section. These lenslets are not required in the real system, and the simplifying assumption of propagation without diffraction is not required in practice, but is illustrated here for analytic and diagrammatic simplicity.

Fig. 7
Fig. 7

k-space representation of the polarization, angle, and time-multiplexed recording and readout geometry in strontium barium niobate (SBN) used to separate the diffracted phased-array beam k d from the AOD beam k A used to write the grating. The upper left-hand portion of the figure is a 2-D projection of the three-dimensional momentum space on the right-hand side, where the three beams incident on the photorefractive (the write beam from the phased array k P 1 with polarization y , the vertically deflected read beam from the phased array k P 2 z , and the diffracted AOD beam k A y ) refract into the crystal and are projected onto the ordinary and extraordinary momentum surfaces, based on their respective polarizations. The deflected read beam has been tilted vertically in the direction of Bragg degeneracy, allowing for efficient light diffraction off the grating k G produced by the interference between k P 1 and k A . This produces a diffracted beam k d with polarization x (once refracted back into air), which is vertically tilted from the reference signal beam from the AOD k A with polarization y , as can be seen in the bottom portion of the figure. A lens, when in conjunction with a spatial filter, can then be used to block the beam from the AOD while allowing for the diffracted beam to pass through the system. A polarizer can also be used to increase the overall isolation between the two beams.

Fig. 8
Fig. 8

Spatiotemporal Fourier space representation of the input signals used in the computer simulation of the BEAMTAP algorithm, which were selected to test the system’s jammer-nulling capacity over a diversified signal environment. The desired signal is a broadband Gaussian chirp (1.2–1.8 GHz) at 0.25 rad AOA. Jammer 1 is broadband filtered Gaussian noise (0.5–2.5 GHz) at -0.2 rad AOA, and jammer 2 is a single-frequency 0.8 GHz at 0.5 rad AOA sine wave, each of which are 30 dB stronger than the signal of interest.

Fig. 9
Fig. 9

Diagram illustrating the simulation of the BEAMTAP architecture. The input signal is represented by the array of time histories shown on the left-hand side. At every time step an instantaneous slice of the input is detected by the antenna arrays and is propagated through the adaptive weight matrix (center of figure). The product of the input vector with the weight matrix is diffracted vertically and detected and accumulated on the scrolling detector (top of figure). The output o(t) is subtracted from the desired signal d(t), generating the feedback signal f(t), which is fed through the scrolling delay line (bottom of figure). An outer product between the scrolling feedback signal and a delayed version of the input is used to adapt the weights, producing the resulting tilted cross-correlation slice seen in the weight matrix in the center of the figure at steady state.

Fig. 10
Fig. 10

AOA versus frequency receptivity pattern that develops after adaptation when only the desired signal is present at the input. Note that the main lobe at 0.25 rad AOA does not vary its position with frequency (although its width does change) as it spans the entire input signal bandwidth—thereby demonstrating squint-free TTD beam forming.

Fig. 11
Fig. 11

AOA versus frequency receptivity pattern after adaptation when the desired signal and strong jammers are both present at the input—demonstrating squint-free jammer suppression with deep nulls. Note the extremely narrow constant angle squint-free null at the angle of the broadband jammer (-0.2 rad) over its full bandwidth, a narrow-band null at 0.5 rad and 800 MHz with deep sidelobe nulls, and a slight reduction in the bandwidth of the system response to the desired signal in comparison with Fig. 10 (although more than the full 1/e bandwidth of the signal is still uniformly detected).

Equations (32)

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ot=n=1Nm=0M-1 snt-mτWnm*.
Wnm*=-t sn*t1-mτft1dt1.
ot=n=1Nm=0M-1 snt-mτWnm*=n=1Nm=0M-1 snt-mτ-t sn*t1-mτft1dt1=nm snt-mτ-t sn*t1-mτ×dt1-ot1dt1.
Ymt=n=1N sntWnm*.
ot=m=0M-1 Ymt-mτ=m=0M-1n=1N snt-mτWnm*.
Wnm*t=-t sn*t1ft1+m-M-1τdt1.
ot=m Ymt-mτ=mn-t δt-t-mτsntWnm*tdt=n,m snt-mτ-t-mτ sn*t1ft1+m-Mτdt1=n,m snt-mτ-t sn*t2-mτft2-Mτdt2.
ot=nm snt-mτ-t sn*t2-mτ-Mτ×ft2-Mτdt2=nm snt-mτ-t-Mτ sn*t2-mτ×dt2-ot2dt2.
f˜x0, t0=g2d˜t0-td-x0vA-tr1-g1õt0-tf-x0vA-tr1f˜t0-x0vA-tr1,
EAx0, t0=atatEo expikBx0-ωlt0×1-ηAO2|f˜|21/2pˆx+ηAOf˜t0-x0vA-tr1pˆy,
EAx, z, t0=atatE0 expikBx-ωlt0×ηAOf˜t0-xv-tr1expikzpˆy,
s˜nt=r˜t-ntp+j j˜jt-ntj,
EPz0, t0=arN E0n=1Nexp-iωct0-tnaz0-nD0×1-ηP2|s˜n|2+ηPs˜nt0-tn-T+ηP*s˜n*t0-tn-Tpˆy,
EPx, z, t0=arN E0n=1Nexp-iωlt0-tnaz-nD×1-ηP2|s˜n|21/2+ηPs˜nt0-tn-T×exp-ikxpˆy,
Gx, z, t=β -t EAx, z, t0EP*x, z, t0×exp-t-t0τdt0+c.c.,
Gx, z, t=β -texpikz+xexpikBx×aratatN E02ηAOf˜t0-xv-tr1×n=1Nexp-iωltna*z-nD×1-ηP2|s˜n|21/2+ηPs˜n*t0-tn-Tpˆy×exp-t-t0τdt0.
Gx, z, t=expikz+xexpikBx×κ0n=1Nexp-iωltna*z-nD×-t f˜t0-xv-tr1s˜n*t0-tn-Tdt0,
Edx1, t=0L EPx, z, tGx, z, texpikL-zdz=0LarN E0n=1Nexp-iωlt-tnaz-nD1-ηP2|s˜n|21/2+ηPs˜nt-tnexp-ikxpˆz×expikz+xexpikBxκ0n=1Nexp-iωltna*z-nD-t f˜t0-xv-tr1s˜n*t0-tn-Tdt0×expikL-zdz,
Edx1, t=expikBx1-ωltexpikL×Eoκ1n=1N s˜nt-tn-t f˜t0-x1v-tr1×s˜n*t0-tn-Tdt0pˆz,
Edx2, t=E0 expikBx2-ωlt×atar+ηDκ1n=1N s˜nt-tn×-t f˜t0-x2vD-tr1s˜n*t0-tn-Tdt0pˆx,
Ix2, t=atarE02+ηDκ12n=1N s˜nt-tn×-t f˜t0-x2vD-tr1s˜n*t0-tn-Tdt02+κ2n=1N s˜nt-tn-t f˜t0-x2vD-tr1×s˜n*t0-tn-Tdt0+c.c.,
ot=R -TD/2TD/2-t Ix2, tδt-t-x2vD+tr2×dtdx2/vD=R -TD/2TD/2 Ix2, t+τx-tr2dτx,
ot=Rκ2-TD/2TD/2n=1N s˜nt-tn+τx-tr2×-t+τx-tr2 f˜t0-τx-tr1s˜n*t0-tn-Tdt0dτx=Rκ2-TD/2TD/2n=1N s˜nt-tn+τx-tr2×-t f˜t1-tr1+tr2s˜n*t1-tn-T+τx-tr2×dt1dτx.
õt=Rκ2-TD/2TD/2n=1N s˜nt-tn+τx-tr2×-t g2d˜t1-td-g1õt1-T×s˜n*t1-tn-T+τx-tr2dt1dτx=Rκ2-TD/2TD/2n=1N s˜nt-tn+τx-tr2×-t-T g2d˜t2+T-td-g1õt2×s˜n*t2-tn+τx-tr2dt1dτx.
Õf=Rκ2n s˜nfg2D˜fexpi2πfT-td-g1ÕfS˜n*-f * TD sincTDf,
Õf=g2Rκ2n |s˜nf|2D˜fexpi2πfT-td * TD sincTDf1+g1g2Rκ2n |s˜nf|2 * TD sincTDf,
Õf=gg1n S˜nfS˜n*-fD˜fexpi2πfT-td1+g nj |J˜jf|2,
S˜kl, f=R˜fδkl-fcsin θr+j J˜jf×δkl-fcsin θj * Nd sincNdkl.
Õf=kl S˜kl, f×gg1 α|D˜f|2 expi2πfT-tdδkl-fcsin θr * bkl, f1+g klj |J˜jf|2δkl-fcsin θj * bkl, f,
Õf=kl S˜kl, fT˜kl, f,
T˜kl, f=gg1 α|D˜f|2 expi2πfT-tdδkl-fcsin θr * bkl, f1+g klj |J˜jf|2δkl-fcsin θj * bkl, f.
Tθ, f=n=1Nτ=0M-1 Wτn exp-i2πftsτ+n dcsin θ,

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