Abstract

Analog optical signal processing of complex radio-frequency signals for range-Doppler radar information is theoretically described and experimentally demonstrated using crystalline optical memory materials and off-the-shelf photonic components. A model of the range-Doppler processing capability of the memory material for the case of single-target detection is presented. Radarlike signals were emulated and processed by the memory material; they consisted of broadband (>1GHz), spread-spectrum, pseudorandom noise sequences of 512bits in length, which were binary phase-shift keyed on a 1.9GHz carrier and repeated at 100kHz over 7.5ms. Delay (range) resolution of 8ns and Doppler resolution of 130Hz over 100kHz were demonstrated.

© 2006 Optical Society of America

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  1. Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
    [CrossRef]
  2. K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
    [CrossRef]
  3. T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).
  4. K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.
  5. R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.
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    [CrossRef]
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    [CrossRef]
  9. J. C. Toomay, Radar Principles for the Non-Specialist, 2nd ed. (SciTech, 1998).
  10. J. Z. Peebles, Radar Principles (Wiley, 1998).
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    [CrossRef]
  12. R. R. Reibel, Z. W. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high-bandwidth phase-modulated signals at 793 nm," J. Opt. Soc. Am. B 19, 2315-2321 (2002).
    [CrossRef]
  13. N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
    [CrossRef]
  14. T. Chang, M. Tian, R. Krishna Mohan, C. Renner, K. D. Merkel, and W. R. Babbitt, "Recovery of spectral features readout with frequency-chirped laser fields," Opt. Lett. 30, 1129-1131 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2005 (1)

2004 (5)

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

2003 (1)

2002 (3)

R. R. Reibel, Z. W. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high-bandwidth phase-modulated signals at 793 nm," J. Opt. Soc. Am. B 19, 2315-2321 (2002).
[CrossRef]

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002), and references therein.
[CrossRef]

2000 (2)

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
[CrossRef]

X. Wang, M. Afzelius, N. Ohlsson, U. Gustafsson, and S. Kröll, "Coherent transient data-rate conversion and data transform," Opt. Lett. 25, 945-947 (2000).
[CrossRef]

1998 (2)

J. C. Toomay, Radar Principles for the Non-Specialist, 2nd ed. (SciTech, 1998).

J. Z. Peebles, Radar Principles (Wiley, 1998).

1997 (1)

Afzelius, M.

Babbitt, W. R.

T. Chang, M. Tian, R. Krishna Mohan, C. Renner, K. D. Merkel, and W. R. Babbitt, "Recovery of spectral features readout with frequency-chirped laser fields," Opt. Lett. 30, 1129-1131 (2005).
[CrossRef] [PubMed]

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

R. R. Reibel, Z. W. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high-bandwidth phase-modulated signals at 793 nm," J. Opt. Soc. Am. B 19, 2315-2321 (2002).
[CrossRef]

R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002), and references therein.
[CrossRef]

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

Babbitt, Wm. R.

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

Barber, Z.

R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002), and references therein.
[CrossRef]

Barber, Z. W.

Böttger, T.

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

Carlsten, J. L.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
[CrossRef]

Chang, T.

T. Chang, M. Tian, R. Krishna Mohan, C. Renner, K. D. Merkel, and W. R. Babbitt, "Recovery of spectral features readout with frequency-chirped laser fields," Opt. Lett. 30, 1129-1131 (2005).
[CrossRef] [PubMed]

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

Cole, Z.

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

R. R. Reibel, Z. W. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high-bandwidth phase-modulated signals at 793 nm," J. Opt. Soc. Am. B 19, 2315-2321 (2002).
[CrossRef]

Colice, M.

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

Cone, R. L.

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
[CrossRef]

Dolfi, D.

Gustafsson, U.

Harris, T. L.

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

Hobbs, P. C. D.

Kröll, S.

Lavielle, V.

Le Gout, J.-L.

Lorger, I.

Merkel, K. D.

T. Chang, M. Tian, R. Krishna Mohan, C. Renner, K. D. Merkel, and W. R. Babbitt, "Recovery of spectral features readout with frequency-chirped laser fields," Opt. Lett. 30, 1129-1131 (2005).
[CrossRef] [PubMed]

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

R. R. Reibel, Z. W. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high-bandwidth phase-modulated signals at 793 nm," J. Opt. Soc. Am. B 19, 2315-2321 (2002).
[CrossRef]

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

Mohan, R. K.

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

Mohan, R. Krishna

T. Chang, M. Tian, R. Krishna Mohan, C. Renner, K. D. Merkel, and W. R. Babbitt, "Recovery of spectral features readout with frequency-chirped laser fields," Opt. Lett. 30, 1129-1131 (2005).
[CrossRef] [PubMed]

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

Ohlsson, N.

Olson, A.

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

Peebles, J. Z.

J. Z. Peebles, Radar Principles (Wiley, 1998).

Reibel, R.

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002), and references therein.
[CrossRef]

Reibel, R. R.

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

R. R. Reibel, Z. W. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high-bandwidth phase-modulated signals at 793 nm," J. Opt. Soc. Am. B 19, 2315-2321 (2002).
[CrossRef]

Renner, C.

Schlottau, F.

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

Sellin, P. B.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
[CrossRef]

Strickland, N. M.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
[CrossRef]

Sun, Y.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
[CrossRef]

Tian, M.

T. Chang, M. Tian, R. Krishna Mohan, C. Renner, K. D. Merkel, and W. R. Babbitt, "Recovery of spectral features readout with frequency-chirped laser fields," Opt. Lett. 30, 1129-1131 (2005).
[CrossRef] [PubMed]

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

R. R. Reibel, Z. W. Barber, M. Tian, W. R. Babbitt, Z. Cole, and K. D. Merkel, "Amplification of high-bandwidth phase-modulated signals at 793 nm," J. Opt. Soc. Am. B 19, 2315-2321 (2002).
[CrossRef]

R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002), and references therein.
[CrossRef]

Tonda, S.

Toomay, J. C.

J. C. Toomay, Radar Principles for the Non-Specialist, 2nd ed. (SciTech, 1998).

Wagner, K. H.

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

Wang, X.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Z. Cole, T. Böttger, R. Krishna Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, "Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic biphase codes," Appl. Phys. Lett. 81, 3525-3527 (2002).
[CrossRef]

J. Lumin. (2)

K. D. Merkel, R. Krishna Mohan, Z. Cole, T. Chang, A. Olson, and W. R. Babbitt, "Multi-gigahertz radar range processing of baseband and RF carrier modulated signals in Tm:YAG," J. Lumin. 107, 62-74 (2004).
[CrossRef]

R. Reibel, Z. Barber, M. Tian, and W. R. Babbitt, "High bandwidth spectral gratings programmed with linear frequency chirps," J. Lumin. 98, 355-365 (2002), and references therein.
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Phys. Rev. A (1)

T. Chang, R. Krishna Mohan, M. Tian, T. L. Harris, W. R. Babbitt, and K. D. Merkel, "Frequency-chirped readout of spatial-spectral absorption features," Phys. Rev. A 70, 063803 (2004).
[CrossRef]

Phys. Rev. B (1)

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser frequency stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
[CrossRef]

Other (5)

T. L. Harris, Wm. R. Babbitt, K. D. Merkel, R. Krishna Mohan, Z. Cole, and A. Olson, "Multigigahertz range-Doppler correlative processing in crystals," in Advanced Optical and Quantum Memories and Computing, H. J. Coufal and Z. V. Hasan, eds., Proc. SPIE 5362, 31-42 (2004).

K. D. Merkel, R. K. Mohan, Z. Cole, R. R. Reibel, T. L. Harris, T. Chang, and W. R. Babbitt, "Analog optical signal processing of baseband codes in Tm:YAG up to 10 Gb/s," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 138-141.

R. Krishna Mohan, Z. Cole, R. R. Reibel, T. Chang, K. D. Merkel, Wm. R. Babbitt, M. Colice, F. Schlottau, and K. H. Wagner, "Microwave spectral analysis paper using optical spectral hole burning," in Proceedings of the 2004 IEEE International Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 24-27.

J. C. Toomay, Radar Principles for the Non-Specialist, 2nd ed. (SciTech, 1998).

J. Z. Peebles, Radar Principles (Wiley, 1998).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the S2CHIP device used as a range-Doppler radar signal processor. Tx, transmit; Rx, receive; FM, frequency modulator; ADC, analog-to-digital converter; DSP, digital signal processor.

Fig. 2
Fig. 2

Block diagram of the experimental demonstrator for processing range-Doppler radar signals. PPG, pulse pattern generator; LO, local oscillator; AWG, arbitrary waveform generator; AOM, acousto-optic modulator; BS, beam splitter; PD, photodiode; CMR, common-mode rejection.

Fig. 3
Fig. 3

RF spectrum analyzer trace of an intermediate-frequency SS signal used to emulate range-Doppler transmit radar signals. PN SS sequences were generated at 1 Gbit / s , low-pass filtered at 1 GHz , and binary phase-shift keyed onto a 1.9 GHz RF carrier. The dotted line and W denote the 200 MHz window centered at 2.1 GHz where a chirped pulse reads out the spectral grating resulting from coherent integration of the transmit and receive radar signals emulated using this RF signal.

Fig. 4
Fig. 4

Timing diagram illustrating the generation and processing of transmit and receive waveforms. The top two traces illustrate the internal and relative timing of the emulated transmit and receive signals. The third trace illustrates the combined transmit and receive RF signal that was mixed onto an optical carrier for processing by coherent integration of S2 holographic gratings in an optical memory crystal. The bottom trace illustrates the timing of the Doppler compensation tones applied to the optical waveform used to resolve Doppler shifts in the receive signal.

Fig. 5
Fig. 5

Typical range profile from a single Doppler processing bin given conventionally in terms of the delay between transmit and receive signals. The S2 grating containing the processed range-Doppler results was scanned using a chirped optical pulse. The PSD of the resulting modulation on the transmitted chirp was taken and its frequency axis was converted to time using the chirp rate of the pulse. This profile is from the 1 kHz Doppler bin and is for the case of a 1.0 μs return delay and a 1 kHz Doppler shift. The 8 ns , 3 dB full-width resolution is due to the 125 MHz of spectral grating that the PSD algorithm processed.

Fig. 6
Fig. 6

Range-Doppler ambiguity functions for a return delay of 1.0 μs and a Doppler shift of 1.0 kHz : (a)–(c) measured (open circles) and calculated (curves) Doppler profile in the vicinity of 0.1, 1.0, and 10 kHz ; (d)–(f) measured range-Doppler ambiguity functions in the vicinity of 0.1, 1.0, and 10 kHz .

Fig. 7
Fig. 7

Measured range-Doppler ambiguity functions for emulated return Doppler shifts of (a) 0.1 kHz , (b) 1 kHz , and (c) 10 kHz in the vicinity of resolving 0.1 kHz (left), 1.0 kHz (middle), and 10 kHz (right).

Fig. 8
Fig. 8

Measured range-Doppler ambiguity functions showing aliasing due to a PRF of 100 kHz for a (a) calculated Doppler profile showing a 0.1 kHz return and its aliasing to 100.1 kHz , (b) experimental observation of a 0.1 kHz return, resolved at both 0.1 and 100.1 kHz . (c) Experimental observation for a 100 kHz return, resolved at 100 kHz and aliased to 0 kHz .

Fig. 9
Fig. 9

Grating amplitude buildup as a function of shots (a shot occurred every 10 μs ) for four Doppler bins at 0, 100, 200, and 300 Hz . Each panel is labeled to identify the frequency difference between the return Doppler shift and the Doppler bin frequency. Grating amplitudes were both measured experimentally (filled circles) and calculated with Eq. (20) (solid curves).

Equations (20)

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m j ( t ) = n = 1 N a n j c ( t n R B ) ,
V T ( t ) = j = 0 J 1 V j T ( t ) ,
V j T ( t ) = m j ( t j T R ) cos ( ω RF t + φ j ) ,
V R ( t ) = j = 0 J 1 V j R ( t ) ,
V j R ( t ) = α m j [ t 2 ( R 0 + ν t ) c j T R ] cos { ω RF [ t 2 ( R 0 + ν t ) c ] + φ j } ,
V j R ( t ) = α m j ( t - τ j T R ) cos [ ( ω RF + ω D ) t φ τ + φ j ] .
E R ( t ) = E R exp { i [ ω L t + β V R ( t ) ] } + c . c . ,
E T ( t ; ω C ) = E T exp { i [ ( ω L + ω C ) t + φ c + β V T ( t ) ] } + c . c . ,
E T ( t ; ω C ) = E T [ 1 + i β V T ( t ) ] exp [ i ( ω L + ω C ) t + i φ c ] + c . c . ,
E R ( t ) = E R [ 1 + i β V R ( t ) ] exp ( i ω L t ) + c . c .
E T ( t ; ω c , J ) = j = 0 J 1 i β E T m j ( t j T R ) cos ( ω RF t + φ j ) exp [ i ( ω L + ω C ) t + i φ c ] = 1 2 j = 0 J 1 i β E T m j ( t j T R ) ( exp { i [ ( ω L + ω RF + ω C ) t + φ j + φ c ] } + exp { i [ ( ω L ω RF + ω C ) t φ j + φ c ] } ) .
E T ( t ; ω c , J ) = 1 2 j = 0 J 1 i β E T m j ( t j T R ) ( exp { i [ ( ω L + ω RF ) t + j ω C T R + φ j + φ c ] } + exp { i [ ( ω L ω RF ) t + j ω C T R φ j + φ c ] } ) .
E R ( t ; J ) = 1 2 j = 0 J 1 i αβ E R m j ( t τ j T R ) ( exp { i [ ( ω L + ω RF ) t + j ω D T R φ τ + φ j ] } + exp { i [ ( ω L ω RF ) t j ω D T R + φ τ φ j ] } ) .
E ˜ T ( ω ; ω C , J ) = 1 2 j = 0 J 1 i β E T ( m ˜ j ( ω ω L ω RF ) exp { i [ ( ω + ω L + ω RF + ω C ) j T R + φ j + φ c ] } + m ˜ j ( ω ω L + ω RF ) exp { i [ ( - ω + ω L ω RF + ω C ) j T R φ j + φ c ] } ) ,
E ˜ R ( ω ; J ) = 1 2 j = 0 J 1 i αβ E R ( m ˜ j ( ω ω L ω RF ) exp { i [ ( ω + ω L + ω RF ) τ + ( ω + ω L + ω RF + ω D ) j T R φ τ + φ j ] } + m ˜ j ( ω ω L + ω RF ) exp { i [ ( ω + ω L ω RF ) τ + ( ω + ω L ω RF ω D ) j T R + φ τ φ j ] } ) ,
G ( ω ; ω C , J ) = E ˜ T ( ω ; ω C , J ) * E ˜ R ( ω ; J ) exp [ i ( k R k T ) · r ] + c . c . ,
G ( ω ; ω C , J ) = 1 4 j = 0 J 1 αβ 2 E R E T × ( | m ˜ j ( ω ω L ω RF ) | 2 exp { i [ ( ω ω L ω RF ) τ ( ω C ω D ) j T R φ τ φ c ( k R k T ) · r ] } + | m ˜ j ( ω ω L + ω RF ) | 2 exp { i [ ( ω ω L + ω RF ) τ ( ω D + ω C ) j T R + φ τ φ c ( k R k T ) · r ] } ) + c . c .
G ( ω ; ω C , J ) = αβ 2 4 E R E T | m ˜ ( ω ω L ω RF ) | 2 exp { i [ ( ω ω L ω RF ) τ φ τ φ c ( k R k T ) · r ] } j = 0 J 1 exp [ i ( ω C ω D ) j T R ] + c . c . + αβ 2 4 E R E T | m ˜ ( ω ω L + ω RF ) | 2 exp { i [ ( ω ω L + ω RF ) τ + φ τ φ c ( k R k T ) · r ] } j = 0 J 1 exp [ i ( ω C + ω D ) j T R ] + c . c .
k = 0 n 1 exp ( iak ) = exp [ ia ( n 1 ) / 2 ] sin ( an / 2 ) sin ( a / 2 ) ,
G ( ω ; ω C , J ) = αβ 2 2 E R E T | m ˜ ( ω ω L ω RF ) | 2 sin [ J T R 2 ( ω C ω D ) ] sin [ T R 2 ( ω C ω D ) ] cos [ - ( ω ω L ω RF ) τ φ τ φ c ( k R k T ) · r T R ( J 1 ) 2 ( ω C ω D ) ] + αβ 2 2 E R E T | m ˜ ( ω ω L + ω RF ) | 2 sin [ J T R 2 ( ω C + ω D ) ] sin [ T R 2 ( ω C + ω D ) ] cos [ - ( ω ω L + ω RF ) τ + φ τ φ c ( k R k T ) · r T R ( J 1 ) 2 ( ω C + ω D ) ] .

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