Abstract

Traditional lens-based photonic Fourier beam-forming systems can be used to steer multiple beams for narrowband radio-frequency (RF) phased-array antennas. For wideband RF phased-array antennas, such Fourier beam-forming systems suffer from frequency-dependent beam steering, known as beam squint. We present a novel squint-free Fourier-based photonic multibeam-forming system for wideband two-dimensional RF phased-array antennas using a lens and frequency-mapped modulation. In this new beam-forming system, we modulate the receiving wideband RF signals onto a broadband light source in a frequency-mapped manner by a traveling-wave tunable filter at each antenna element. These modulated signals are launched in a miniaturized topology of the RF antenna array, and the wavelength-scaling factor in the lens Fourier transform exactly compensates the frequency dependence of beam steering. Heterodyne detection at the Fourier plane between the focused modulated multicolor spots and the broadband laser reference beams from the same light source recovers the received RF signals. An analysis with numerical simulations and then demonstrated with preliminary experimental results of this beam-forming system is presented.

© 2009 Optical Society of America

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  1. J. L. Allen, “A theoretical limitation on the formation of lossless multiple beams in linear arrays,” IRE Trans. Antennas Propag. AP-9, 350-352 (1961).
    [CrossRef]
  2. L. Stark, “Theory of phased arrays,” Proc. IEEE 62, 1661(1974).
    [CrossRef]
  3. A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased-array radar technology,” Lincoln Lab. J. 12, 321-340 (2000).
  4. H. Zmuda and E. N. Toughlian, Photonic Aspects of Modern Radar (Artech House, 1994).
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    [CrossRef] [PubMed]
  8. K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
    [CrossRef]
  9. R. A. Sparks, N. Slawsby, J. Prince, and J. Munro, “Experimental demonstration of a fiber optic Rotman beamformer,” in International Topical Meeting on Microwave Photonics, 1998 (IEEE, 1998), pp. 127-130.
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    [CrossRef] [PubMed]
  11. H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, “Photonic beamformer for phased array antennas using a fiber grating prism,” Photon.Technol. Lett. 9, 241-243 (1997).
    [CrossRef]
  12. D. T. K. Tong and M. C. Wu, “Programmable dispersion matrix using Bragg fibre grating for optically controlled phased array antennas,” Electron. Lett. 32, 1532-1533 (1996).
    [CrossRef]
  13. R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G. Parent, D. Stilwell, and D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” Photon. Technol. Lett. 5, 1347-1349 (1993).
    [CrossRef]
  14. L. H. Gesell and T. M. Turpin, “True time delay beam forming using acousto-optics,” Proc. SPIE 1703, 592-602 (1992).
    [CrossRef]
  15. M. Kondo, K. Komatsu, Y. Ohta, S. Suzuki, K. Nagashima, and H. Goto, “High-speed optical time switch with integrated optical 1×4 switches and single-polarization fiber delay lines,” in 4th International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communications Engineers, 1983), p. 04967.
  16. M. Arm, L. Lambert, I. Weissman, and L. Slobodin, “Optical correlation technique for radar pulse compression,” Proc. IEEE 52, 842-842 (1964).
    [CrossRef]
  17. L. Gao, S. Herriot, and K. H. Wagner, “A novel approach to rf photonic signal processing using an ultrafast laser comb modulated by traveling-wave tunable filters,” IEEE J. Sel. Top. Quantum Electron. 12, 315-329 (2006).
    [CrossRef]
  18. B. Braker and K. Wagner, “Self calibrated optical imaging of sparse rf arrays,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), paper CTuB7.
    [PubMed]
  19. S. Kim, L. Gao, K. Wagner, R. T. Weverka, and R. McLeod, “Acousto-optic tunable filter using phased-array transducer with linearized rf to optical frequency mapping,” Proc. SPIE 5953, 59530M (2005).
    [CrossRef]
  20. K. H. Wagner, B. Braker, M. Colice, F. Schlottau, and R. T. Weverka, “Spectrally-compensated, squint-free, multiple-beam forming system for broadband rf antenna arrays,” in Proceedings International Commission for Optics, Optics in Computing (European Optical Society, 2004).
  21. L. Gao, S. Herriot, and K. H. Wagner, “Sluggish light for radio-frequency true-time-delay applications with a large time-bandwidth product,” Opt. Lett. 31, 3360-3362 (2006).
    [CrossRef] [PubMed]
  22. I. C. Chang, “Noncollinear acousto-optical filter with large angular aperture,” Appl. Phys. Lett. 25, 370-372 (1974).
    [CrossRef]
  23. C. N. Pannell, H. J. Gnewuch, and J. Ward, “Some new developments in acousto-optic and electro-optic devices,” Proc. SPIE 97-108 (2004).
    [CrossRef]
  24. P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
    [CrossRef]
  25. Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165-170 (1985).
    [CrossRef]

2006 (2)

L. Gao, S. Herriot, and K. H. Wagner, “A novel approach to rf photonic signal processing using an ultrafast laser comb modulated by traveling-wave tunable filters,” IEEE J. Sel. Top. Quantum Electron. 12, 315-329 (2006).
[CrossRef]

L. Gao, S. Herriot, and K. H. Wagner, “Sluggish light for radio-frequency true-time-delay applications with a large time-bandwidth product,” Opt. Lett. 31, 3360-3362 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Kim, L. Gao, K. Wagner, R. T. Weverka, and R. McLeod, “Acousto-optic tunable filter using phased-array transducer with linearized rf to optical frequency mapping,” Proc. SPIE 5953, 59530M (2005).
[CrossRef]

2004 (1)

C. N. Pannell, H. J. Gnewuch, and J. Ward, “Some new developments in acousto-optic and electro-optic devices,” Proc. SPIE 97-108 (2004).
[CrossRef]

2000 (1)

A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased-array radar technology,” Lincoln Lab. J. 12, 321-340 (2000).

1999 (1)

1997 (2)

H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, “Photonic beamformer for phased array antennas using a fiber grating prism,” Photon.Technol. Lett. 9, 241-243 (1997).
[CrossRef]

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
[CrossRef]

1996 (1)

D. T. K. Tong and M. C. Wu, “Programmable dispersion matrix using Bragg fibre grating for optically controlled phased array antennas,” Electron. Lett. 32, 1532-1533 (1996).
[CrossRef]

1993 (1)

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

1992 (2)

L. H. Gesell and T. M. Turpin, “True time delay beam forming using acousto-optics,” Proc. SPIE 1703, 592-602 (1992).
[CrossRef]

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

1985 (2)

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165-170 (1985).
[CrossRef]

1981 (1)

1980 (1)

1974 (2)

L. Stark, “Theory of phased arrays,” Proc. IEEE 62, 1661(1974).
[CrossRef]

I. C. Chang, “Noncollinear acousto-optical filter with large angular aperture,” Appl. Phys. Lett. 25, 370-372 (1974).
[CrossRef]

1964 (1)

M. Arm, L. Lambert, I. Weissman, and L. Slobodin, “Optical correlation technique for radar pulse compression,” Proc. IEEE 52, 842-842 (1964).
[CrossRef]

1961 (1)

J. L. Allen, “A theoretical limitation on the formation of lossless multiple beams in linear arrays,” IRE Trans. Antennas Propag. AP-9, 350-352 (1961).
[CrossRef]

Allen, J. L.

J. L. Allen, “A theoretical limitation on the formation of lossless multiple beams in linear arrays,” IRE Trans. Antennas Propag. AP-9, 350-352 (1961).
[CrossRef]

Arm, M.

M. Arm, L. Lambert, I. Weissman, and L. Slobodin, “Optical correlation technique for radar pulse compression,” Proc. IEEE 52, 842-842 (1964).
[CrossRef]

Blanchard, P. M.

Bor, Z.

Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165-170 (1985).
[CrossRef]

Braker, B.

B. Braker and K. Wagner, “Self calibrated optical imaging of sparse rf arrays,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), paper CTuB7.
[PubMed]

K. H. Wagner, B. Braker, M. Colice, F. Schlottau, and R. T. Weverka, “Spectrally-compensated, squint-free, multiple-beam forming system for broadband rf antenna arrays,” in Proceedings International Commission for Optics, Optics in Computing (European Optical Society, 2004).

Chang, I. C.

I. C. Chang, “Noncollinear acousto-optical filter with large angular aperture,” Appl. Phys. Lett. 25, 370-372 (1974).
[CrossRef]

Colice, M.

K. H. Wagner, B. Braker, M. Colice, F. Schlottau, and R. T. Weverka, “Spectrally-compensated, squint-free, multiple-beam forming system for broadband rf antenna arrays,” in Proceedings International Commission for Optics, Optics in Computing (European Optical Society, 2004).

Cooper, D. G.

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

Courtney, W. E.

A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased-array radar technology,” Lincoln Lab. J. 12, 321-340 (2000).

Cutler, C. C.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Delaney, W. P.

A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased-array radar technology,” Lincoln Lab. J. 12, 321-340 (2000).

Dexter, J. L.

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

Esman, R. D.

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

Fenn, A. J.

A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased-array radar technology,” Lincoln Lab. J. 12, 321-340 (2000).

Frankel, M. Y.

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

Gao, L.

L. Gao, S. Herriot, and K. H. Wagner, “Sluggish light for radio-frequency true-time-delay applications with a large time-bandwidth product,” Opt. Lett. 31, 3360-3362 (2006).
[CrossRef] [PubMed]

L. Gao, S. Herriot, and K. H. Wagner, “A novel approach to rf photonic signal processing using an ultrafast laser comb modulated by traveling-wave tunable filters,” IEEE J. Sel. Top. Quantum Electron. 12, 315-329 (2006).
[CrossRef]

S. Kim, L. Gao, K. Wagner, R. T. Weverka, and R. McLeod, “Acousto-optic tunable filter using phased-array transducer with linearized rf to optical frequency mapping,” Proc. SPIE 5953, 59530M (2005).
[CrossRef]

George, N.

Gesell, L. H.

L. H. Gesell and T. M. Turpin, “True time delay beam forming using acousto-optics,” Proc. SPIE 1703, 592-602 (1992).
[CrossRef]

Gnewuch, H. J.

C. N. Pannell, H. J. Gnewuch, and J. Ward, “Some new developments in acousto-optic and electro-optic devices,” Proc. SPIE 97-108 (2004).
[CrossRef]

Goldberg, L.

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

Goodman, J. W.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Goto, H.

M. Kondo, K. Komatsu, Y. Ohta, S. Suzuki, K. Nagashima, and H. Goto, “High-speed optical time switch with integrated optical 1×4 switches and single-polarization fiber delay lines,” in 4th International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communications Engineers, 1983), p. 04967.

Greenaway, A. H.

Harvey, A. R.

Herriot, S.

L. Gao, S. Herriot, and K. H. Wagner, “A novel approach to rf photonic signal processing using an ultrafast laser comb modulated by traveling-wave tunable filters,” IEEE J. Sel. Top. Quantum Electron. 12, 315-329 (2006).
[CrossRef]

L. Gao, S. Herriot, and K. H. Wagner, “Sluggish light for radio-frequency true-time-delay applications with a large time-bandwidth product,” Opt. Lett. 31, 3360-3362 (2006).
[CrossRef] [PubMed]

Jackson, K. P.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Johns, S.

H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, “Photonic beamformer for phased array antennas using a fiber grating prism,” Photon.Technol. Lett. 9, 241-243 (1997).
[CrossRef]

Kim, S.

S. Kim, L. Gao, K. Wagner, R. T. Weverka, and R. McLeod, “Acousto-optic tunable filter using phased-array transducer with linearized rf to optical frequency mapping,” Proc. SPIE 5953, 59530M (2005).
[CrossRef]

Komatsu, K.

M. Kondo, K. Komatsu, Y. Ohta, S. Suzuki, K. Nagashima, and H. Goto, “High-speed optical time switch with integrated optical 1×4 switches and single-polarization fiber delay lines,” in 4th International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communications Engineers, 1983), p. 04967.

Kondo, M.

M. Kondo, K. Komatsu, Y. Ohta, S. Suzuki, K. Nagashima, and H. Goto, “High-speed optical time switch with integrated optical 1×4 switches and single-polarization fiber delay lines,” in 4th International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communications Engineers, 1983), p. 04967.

Lambert, L.

M. Arm, L. Lambert, I. Weissman, and L. Slobodin, “Optical correlation technique for radar pulse compression,” Proc. IEEE 52, 842-842 (1964).
[CrossRef]

McLeod, R.

S. Kim, L. Gao, K. Wagner, R. T. Weverka, and R. McLeod, “Acousto-optic tunable filter using phased-array transducer with linearized rf to optical frequency mapping,” Proc. SPIE 5953, 59530M (2005).
[CrossRef]

Morris, G. M.

Moslehi, B.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Munro, J.

R. A. Sparks, N. Slawsby, J. Prince, and J. Munro, “Experimental demonstration of a fiber optic Rotman beamformer,” in International Topical Meeting on Microwave Photonics, 1998 (IEEE, 1998), pp. 127-130.

Nagashima, K.

M. Kondo, K. Komatsu, Y. Ohta, S. Suzuki, K. Nagashima, and H. Goto, “High-speed optical time switch with integrated optical 1×4 switches and single-polarization fiber delay lines,” in 4th International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communications Engineers, 1983), p. 04967.

Newton, S. A.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Ohta, Y.

M. Kondo, K. Komatsu, Y. Ohta, S. Suzuki, K. Nagashima, and H. Goto, “High-speed optical time switch with integrated optical 1×4 switches and single-polarization fiber delay lines,” in 4th International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communications Engineers, 1983), p. 04967.

Pannell, C. N.

C. N. Pannell, H. J. Gnewuch, and J. Ward, “Some new developments in acousto-optic and electro-optic devices,” Proc. SPIE 97-108 (2004).
[CrossRef]

Parent, M. G.

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

Payson, P.

H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, “Photonic beamformer for phased array antennas using a fiber grating prism,” Photon.Technol. Lett. 9, 241-243 (1997).
[CrossRef]

Prince, J.

R. A. Sparks, N. Slawsby, J. Prince, and J. Munro, “Experimental demonstration of a fiber optic Rotman beamformer,” in International Topical Meeting on Microwave Photonics, 1998 (IEEE, 1998), pp. 127-130.

Rácz, B.

Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165-170 (1985).
[CrossRef]

Schlottau, F.

K. H. Wagner, B. Braker, M. Colice, F. Schlottau, and R. T. Weverka, “Spectrally-compensated, squint-free, multiple-beam forming system for broadband rf antenna arrays,” in Proceedings International Commission for Optics, Optics in Computing (European Optical Society, 2004).

Shaw, H.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Slawsby, N.

R. A. Sparks, N. Slawsby, J. Prince, and J. Munro, “Experimental demonstration of a fiber optic Rotman beamformer,” in International Topical Meeting on Microwave Photonics, 1998 (IEEE, 1998), pp. 127-130.

Slobodin, L.

M. Arm, L. Lambert, I. Weissman, and L. Slobodin, “Optical correlation technique for radar pulse compression,” Proc. IEEE 52, 842-842 (1964).
[CrossRef]

Soref, R.

Soref, R. A.

H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, “Photonic beamformer for phased array antennas using a fiber grating prism,” Photon.Technol. Lett. 9, 241-243 (1997).
[CrossRef]

Sparks, R. A.

R. A. Sparks, N. Slawsby, J. Prince, and J. Munro, “Experimental demonstration of a fiber optic Rotman beamformer,” in International Topical Meeting on Microwave Photonics, 1998 (IEEE, 1998), pp. 127-130.

Stark, L.

L. Stark, “Theory of phased arrays,” Proc. IEEE 62, 1661(1974).
[CrossRef]

Stilwell, D.

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

Suzuki, S.

M. Kondo, K. Komatsu, Y. Ohta, S. Suzuki, K. Nagashima, and H. Goto, “High-speed optical time switch with integrated optical 1×4 switches and single-polarization fiber delay lines,” in 4th International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communications Engineers, 1983), p. 04967.

Temme, D. H.

A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased-array radar technology,” Lincoln Lab. J. 12, 321-340 (2000).

Tong, D. T. K.

D. T. K. Tong and M. C. Wu, “Programmable dispersion matrix using Bragg fibre grating for optically controlled phased array antennas,” Electron. Lett. 32, 1532-1533 (1996).
[CrossRef]

Toughlian, E. N.

H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, “Photonic beamformer for phased array antennas using a fiber grating prism,” Photon.Technol. Lett. 9, 241-243 (1997).
[CrossRef]

H. Zmuda and E. N. Toughlian, Photonic Aspects of Modern Radar (Artech House, 1994).

Tournois, P.

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
[CrossRef]

Tur, M.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. Shaw, “Optical fiber delay-line signal-processing,” IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Turpin, T. M.

L. H. Gesell and T. M. Turpin, “True time delay beam forming using acousto-optics,” Proc. SPIE 1703, 592-602 (1992).
[CrossRef]

Wagner, K.

S. Kim, L. Gao, K. Wagner, R. T. Weverka, and R. McLeod, “Acousto-optic tunable filter using phased-array transducer with linearized rf to optical frequency mapping,” Proc. SPIE 5953, 59530M (2005).
[CrossRef]

B. Braker and K. Wagner, “Self calibrated optical imaging of sparse rf arrays,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), paper CTuB7.
[PubMed]

Wagner, K. H.

L. Gao, S. Herriot, and K. H. Wagner, “A novel approach to rf photonic signal processing using an ultrafast laser comb modulated by traveling-wave tunable filters,” IEEE J. Sel. Top. Quantum Electron. 12, 315-329 (2006).
[CrossRef]

L. Gao, S. Herriot, and K. H. Wagner, “Sluggish light for radio-frequency true-time-delay applications with a large time-bandwidth product,” Opt. Lett. 31, 3360-3362 (2006).
[CrossRef] [PubMed]

K. H. Wagner, B. Braker, M. Colice, F. Schlottau, and R. T. Weverka, “Spectrally-compensated, squint-free, multiple-beam forming system for broadband rf antenna arrays,” in Proceedings International Commission for Optics, Optics in Computing (European Optical Society, 2004).

Ward, J.

C. N. Pannell, H. J. Gnewuch, and J. Ward, “Some new developments in acousto-optic and electro-optic devices,” Proc. SPIE 97-108 (2004).
[CrossRef]

Webster, K.

Weissman, I.

M. Arm, L. Lambert, I. Weissman, and L. Slobodin, “Optical correlation technique for radar pulse compression,” Proc. IEEE 52, 842-842 (1964).
[CrossRef]

Weverka, R. T.

S. Kim, L. Gao, K. Wagner, R. T. Weverka, and R. McLeod, “Acousto-optic tunable filter using phased-array transducer with linearized rf to optical frequency mapping,” Proc. SPIE 5953, 59530M (2005).
[CrossRef]

K. H. Wagner, B. Braker, M. Colice, F. Schlottau, and R. T. Weverka, “Spectrally-compensated, squint-free, multiple-beam forming system for broadband rf antenna arrays,” in Proceedings International Commission for Optics, Optics in Computing (European Optical Society, 2004).

Wu, M. C.

D. T. K. Tong and M. C. Wu, “Programmable dispersion matrix using Bragg fibre grating for optically controlled phased array antennas,” Electron. Lett. 32, 1532-1533 (1996).
[CrossRef]

Zmuda, H.

H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, “Photonic beamformer for phased array antennas using a fiber grating prism,” Photon.Technol. Lett. 9, 241-243 (1997).
[CrossRef]

H. Zmuda and E. N. Toughlian, Photonic Aspects of Modern Radar (Artech House, 1994).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Conventional Fourier lens based photonic beamformer for narrowband RF phased-array antennas. Eight wideband RF point sources are shown on the left, and through the narrowband Fourier beamformer squinted images are formed on the Fourier plane of the lens shown on the right.

Fig. 2
Fig. 2

Numerical simulation of multiple beam forming using conventional Fourier-lens beamformers. Fourier images of nine RF sources formed at the back focal plane of the lens. (a) Point images of narrowband RF sources emitting a monochromatic RF tone of 100 MHz . (b) Squinted images of the nine sources emitting wideband RF signals covering a bandwidth from 41 to 164 MHz , where color (online) codes for the RF frequency shift of the modulated laser.

Fig. 3
Fig. 3

Squint-free image of the nine RF sources emitting wideband RF signals covering a bandwidth from 41 to 164 MHz using wavelength-compensated lens beam-forming systems.

Fig. 4
Fig. 4

Femtosecond pulse readout of three RF tones input to the AOTF. Three RF tones at 90, 100, and 110 MHz are applied to the AOTF, and three narrow spectral bands near 360, 400, and 440 THz are diffracted and Doppler shifted by the associated frequencies assuming a frequency mapping factor of κ = 4 × 10 6 (which is also the scaling ratio between plots a and b).

Fig. 5
Fig. 5

Illustration of AOTF pulse shaping. Three frames are shown for the phase-matched acousto-optic interaction at three different locations for a single incident femtosecond pulse as it propagates through the crystal. The diffracted optical spectral components are orthogonally polarized to the input femtosecond pulses and propagate at a different speed of c / n e . The diffracted optical pulse is a temporal image of the input RF pulse compressed by the frequency mapping factor.

Fig. 6
Fig. 6

AOTF modulation and heterodyne detection setup for the slow light experiment. Modulated pulse train is the time replica of the input RF signal scaled by κ. For both time and space aligned heterodyne beams, the RF signal is recreated without optically induced time delay. However, when the reference pulse train is delayed with respect to the modulated pulse train by L, an RF time delay of T d between the heterodyne detected RF signal and the input RF signal is induced through the sluggish-light effect.

Fig. 7
Fig. 7

Sluggish light induced TTD in the wavelength-compensated Fourier beamformer. The receiving wideband RF signals are modulated onto a broadband optical carrier using AOTFs. Due to the sluggish-light effect, the much smaller extra path length l d between the modulated optical beams from the first and the mth AOTF exactly compensates the time delay induced by the extra path length L d of the receiving RF signals between the first and the mth antenna elements.

Fig. 8
Fig. 8

Wavelength-compensated 2D beamformer using AOTFs and a broadband femtosecond laser. A fiber array feed is self-calibrated using a cohering spectral hologram to eliminate phase fluctuation in the fiber array. Heterodyne detection between the modulated and the reference femtosecond pulses recreates the RF signals.

Fig. 9
Fig. 9

Acoustically induced time delay in an AOTF.

Fig. 10
Fig. 10

Prism-induced pulse front tilt for TTD compensation.

Fig. 11
Fig. 11

Experimental setup for array beam forming using prism-induced pulse front tilt. A prism pair is used to introduce pulse front tilt of the modulated beams. Upon heterodyne detection, different heterodyne pairs experience different optical delays induced by the pulse front tilt and the sluggish-light effect magnifies the optical delay to compensate the acoustically induced delay by the AOTF.

Fig. 12
Fig. 12

Experimental results of TTD beam forming for an emulated 12-element antenna array. (a) Emulated RF receiving signals from a 12-element antenna array. (b) Prism-induced pulse front tilt for TTD beam forming through the sluggish-light effect.

Equations (14)

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S ( X , Y , Z , t ) = A e j ( K · r + Ω t ) s ( t ) = A e j ( K cos α · X + K cos β · Y ) e j K cos γ Z e j Ω t s ( t ) ,
S m , l ( t ) = δ ( x m D , y l D ) S ( X , Y , 0 , t ) .
E ( x , y , t ) = g ( x , y ) m l δ ( x m d , y l d ) s ( t ) e j [ K cos α · m D + K cos β · l D + ( ω 0 + Ω 0 ) t + ϕ m l ] W m l ,
U ( x , y ) t t + T g ( x , y ) m l δ ( x m d , y l d ) e j [ K cos α · m D + K cos β · l D + ϕ m l ] s ( t ) W m l exp [ j 2 π λ f ( x x + y y ) ] e j ( ω 0 + Ω 0 ) t d x d y d t .
| U ( x , y ) | 2 | [ δ ( x f Ω ω D d cos α , y f Ω ω D d cos β ) W ( x , y ) ] G ( x , y ) | 2 ,
| U ( x , y ) | 2 | δ ( x f κ D d cos α , y f κ D d cos β ) W ( x , y ) G ( x , y ) S ( Ω ) d Ω | 2 .
τ = L c ( n o n e ) = T 0 V a c ( n o n e ) = Ω ω T 0 T 0 κ .
T d = L d c = ( N 1 ) D sin θ c ,
Φ ( Ω ) = Ω c D sin θ .
sin β = Ω ω D d sin θ .
ϕ ( ω ) = ω c l d = ω c ( N 1 ) d sin β .
t d = d [ ϕ ( ω ) ] d Ω = d [ ω l d / c ] d Ω = d [ κ Ω ( N 1 ) d sin β / c ] d Ω = κ ( N 1 ) d sin β c = κ Ω ω ( N 1 ) D sin θ c = ( N 1 ) D sin θ c = L d c = T d .
T a = d V a sin α ,
sin θ = c V a sin α d D .

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