Abstract

We demonstrate a 20  GHz spectrum analyzer with 1  MHz resolution and >40  dB dynamic range using spectral-hole-burning (SHB) crystals, which are cryogenically cooled crystal hosts lightly doped with rare-earth ions. We modulate a rf signal onto an optical carrier using an electro-optic intensity modulator to produce a signal beam modulated with upper and lower rf sidebands. Illuminating SHB crystals with modulated beams excites only those ions resonant with corresponding modulation frequencies, leaving holes in the crystal's absorption profile that mimic the modulation power spectrum and persist for up to 10  ms. We determine the spectral hole locations by probing the crystal with a chirped laser and detecting the transmitted intensity. The transmitted intensity is a blurred-out copy of the power spectrum of the original illumination as mapped into a time-varying signal. Scaling the time series associated with the transmitted intensity by the instantaneous chirp rate yields the modulated beam's rf power spectrum. The homogeneous linewidth of the rare-earth ions, which can be <100  kHz at cryogenic temperatures, limits the fundamental spectral resolution, while the medium's inhomogeneous linewidth, which can be >20  GHz, determines the spectral bandwidth.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  30. T. Chang, M. Tian, R. K. 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]
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    [CrossRef]
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  33. J. Huang, J. M. Zhang, A. Lezama, and T. W. Mossberg, "Excess dephasing in photon-echo experiments arising from excitation-induced electronic level shifts," Phys. Rev. Lett. 63, 78-81 (1989).
    [CrossRef]
  34. S. Kröll, E. Y. Xu, M. K. Kim, M. Mitsunaga, and R. Kachru, "Intensity-dependent photon-echo relaxation in rare-earth-doped crystals," Phys. Rev. B 41, 11568-11571 (1990).
    [CrossRef]
  35. M. Mitsunaga, T. Takagahara, R. Yano, and N. Uesegi, "Excitation-induced frequency shift probed by stimulated photon echoes," Phys. Rev. Lett. 68, 3216-3219 (1992).
    [CrossRef]
  36. G. K. Liu and R. L. Cone, "Laser-induced instantaneous spectral diffusion in Tb3+ compounds as observed in photon-echo experiments," Phys. Rev. B 41, 6193-6200 (1990).
    [CrossRef]
  37. G. W. Burr, T. L. Harris, W. R. Babbitt, and C. M. Jefferson, "Incorporating excitation-induced dephasing into the Maxwell-Bloch numerical modeling of photon echoes," J. Lumin. 107, 314-331 (2004).
    [CrossRef]
  38. T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, "Optical decoherence and spectral diffusion at 1.5 μm in Er3+:Y2SiO5 versus magnetic field, temperature, and Er3+ concentration," Phys. Rev. B 73, 075101 (2006).
    [CrossRef]
  39. A. Szaabo and R. Kaarli, "Optical hole burning and spectral diffusion in ruby," Phys. Rev. B 44, 12307-12313 (1991).
    [CrossRef]
  40. G. Armagan, A. M. Buoncristiani, and B. D. Bartolo, "Excited state dynamics of thulium ions in yttrium aluminum garnets," Opt. Mater. 1, 11-20 (1992).
    [CrossRef]
  41. C. J. Karlsson and F. A. A. Olsson, "Linearization of the frequency sweep of a frequency-modulated continuous-wave semiconductor laser radar and the resulting ranging performance," Appl. Opt. 38, 3376-3386 (1999).
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    [CrossRef]
  43. N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, "Laser stabilization using regenerative spectral hole burning," Phys. Rev. B 62, 1473-1476 (2000).
    [CrossRef]
  44. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, "Frequency modulation FM spectroscopy," Appl. Phys. B 32, 145-152 (1983).
    [CrossRef]
  45. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
    [CrossRef]
  46. K. S. Repasky and J. L. Carlsten, "Simple method for measuring frequency chirps with a Fabry-Perot interferometer," Appl. Opt. 39, 5500-5504 (2000).
  47. K. H. Wagner, F. Schlottau, and J. Bregman, "Array imaging using spatial-spectral holography," in Optics in Computing (International Commission on Optics, 2002).
  48. F. Schlottau, K. Wagner, J. Bregman, and J.-L. Le Gouët, "Sparse antenna array multiple beamforming and spectral analysis using spatial-spectral holography," in IEEE International Topical Meeting on Microwave Photonics (IEEE, 2003), pp. 355-358.
    [CrossRef]
  49. F. Schlottau, B. Braker, and K. Wagner, "Squint compensation for a broadband RF array spectral imager using spatial spectral holography," in Imaging Spectrometry X, S. S. Shen and P. E. Lewis, eds., Proc. SPIE 5546, 244-252 (2004).
    [CrossRef]
  50. B. M. Braker, Y. Li, D. Gu, F. Schlottau, and K. H. Wagner, "Broadband microwave imaging with spectral hole burning for squint compensation," in Passive Millimeter-Wave Imaging Technology VIII, R. Appleby and D. A. Wikner, eds., Proc. SPIE 5789, 69-79 (2005).
    [CrossRef]

2006

T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, "Optical decoherence and spectral diffusion at 1.5 μm in Er3+:Y2SiO5 versus magnetic field, temperature, and Er3+ concentration," Phys. Rev. B 73, 075101 (2006).
[CrossRef]

2005

G. Gorju, V. Crozatier, V. Lavielle, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, "Experimental investigation of deterministic and stochastic frequency noises of a rapidly frequency chirped laser," Eur. Phys. J. Appl. Phys. 30, 175-183 (2005).
[CrossRef]

M. Colice, F. Schlottau, and K. Wagner, "Ultrawideband, wide-open rf spectrum analysis using spectral hole burning," in Microwave Photonics, J. Yao, ed., Proc. SPIE 5971, 564-573 (2005).

T. Chang, M. Tian, R. K. 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]

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, "10-GHz bandwidth rf spectral Analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG," IEEE Photon. Technol. Lett. 17, 2385-2387 (2005).
[CrossRef]

F. Schlottau, M. Colice, K. H. Wagner, and W. R. Babbitt, "Spectral hole burning for wideband, high-resolution radio-frequency spectrum analysis," Opt. Lett. 30, 3003-3005 (2005).
[CrossRef]

B. M. Braker, Y. Li, D. Gu, F. Schlottau, and K. H. Wagner, "Broadband microwave imaging with spectral hole burning for squint compensation," in Passive Millimeter-Wave Imaging Technology VIII, R. Appleby and D. A. Wikner, eds., Proc. SPIE 5789, 69-79 (2005).
[CrossRef]

2004

F. Schlottau, B. Braker, and K. Wagner, "Squint compensation for a broadband RF array spectral imager using spatial spectral holography," in Imaging Spectrometry X, S. S. Shen and P. E. Lewis, eds., Proc. SPIE 5546, 244-252 (2004).
[CrossRef]

V. Crozatier, V. Lavielle, F. Bretenaker, J. Le Gouët, and I. Lorgeré, "High-resolution radio frequency spectral analysis with photon echo chirp transform in an Er:YSO crystal," IEEE J. Quantum Electron. 40, 1450-1457 (2004).
[CrossRef]

V. Lavielle, F. D. Seze, I. Lorgeré, and J.-L. Le Gouët, "Wideband radio frequency spectrum analyzer: improved design and experimental results," J. Lumin. 107, 75-89 (2004).
[CrossRef]

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgeré, and J.-L. Le Gouët, "RF Spectrum Analysis in Spectral Hole Burning Media," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

F. Schlottau and K. H. Wagner, "Demonstration of a continuous scanner and time-integrating correlator using spatial-spectral holography," J. Lumin. 107, 90-102 (2004).
[CrossRef]

K. D. Merkel, R. K. 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]

G. W. Burr, T. L. Harris, W. R. Babbitt, and C. M. Jefferson, "Incorporating excitation-induced dephasing into the Maxwell-Bloch numerical modeling of photon echoes," J. Lumin. 107, 314-331 (2004).
[CrossRef]

2002

Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, and R. L. Hutcheson, "Recent progress in developing new rare-earth materials for hole burning and coherent transient applications," J. Lumin. 98, 281-287 (2002).
[CrossRef]

I. Lorgeré, L. Ménager, V. Lavielle, J.-L. Le Gouët, D. Dolfi, S. Tonda, and J.-P. Huignard, "Demonstration of a radio-frequency spectrum analyser based on spectral hole burning," J. Mod. Opt. 49, 2459-2475 (2002).
[CrossRef]

2001

2000

K. D. Merkel, Z. Cole, and W. R. Babbitt, "Signal correlator with programmable variable time delay based on optical coherent transients," J. Lumin. 86, 375-382 (2000).
[CrossRef]

R. M. Macfarlane, "Direct process thermal line broadening in Tm:YAG," J. Lumin. 85, 181-186 (2000).
[CrossRef]

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

K. S. Repasky and J. L. Carlsten, "Simple method for measuring frequency chirps with a Fabry-Perot interferometer," Appl. Opt. 39, 5500-5504 (2000).

1999

1998

K. Noguchi, H. Miyazawa, and O. Mitomi, "Frequency-dependent propagation characteristics of coplanar waveguide electrode on 100 GHz Ti:LiNbO3 optical modulator," Electron. Lett. 34, 661-663 (1998).
[CrossRef]

1997

D. T. Chen, H. R. Fetterman, A. T. Chen, W. H. Steier, L. R. Dalton, W. S. Wang, and Y. Q. Shi, "Demonstration of 110 GHz electro-optic polymer modulators," Appl. Phys. Lett. 70, 3335-3337 (1997).
[CrossRef]

1992

G. Armagan, A. M. Buoncristiani, and B. D. Bartolo, "Excited state dynamics of thulium ions in yttrium aluminum garnets," Opt. Mater. 1, 11-20 (1992).
[CrossRef]

M. Mitsunaga, T. Takagahara, R. Yano, and N. Uesegi, "Excitation-induced frequency shift probed by stimulated photon echoes," Phys. Rev. Lett. 68, 3216-3219 (1992).
[CrossRef]

1991

A. Szaabo and R. Kaarli, "Optical hole burning and spectral diffusion in ruby," Phys. Rev. B 44, 12307-12313 (1991).
[CrossRef]

1990

G. K. Liu and R. L. Cone, "Laser-induced instantaneous spectral diffusion in Tb3+ compounds as observed in photon-echo experiments," Phys. Rev. B 41, 6193-6200 (1990).
[CrossRef]

S. Kröll, E. Y. Xu, M. K. Kim, M. Mitsunaga, and R. Kachru, "Intensity-dependent photon-echo relaxation in rare-earth-doped crystals," Phys. Rev. B 41, 11568-11571 (1990).
[CrossRef]

1989

J. Huang, J. M. Zhang, A. Lezama, and T. W. Mossberg, "Excess dephasing in photon-echo experiments arising from excitation-induced electronic level shifts," Phys. Rev. Lett. 63, 78-81 (1989).
[CrossRef]

1988

M. A. Poletti, "Linearly swept frequency measurements, time-delay spectrometry, and the Wigner distribution," J. Audio Eng. Soc. 36, 457-468 (1988).

1985

M. Mitsunaga and R. G. Brewer, "Generalized perturbation theory of coherent optical emission," Phys. Rev. A 32, 1605-1613 (1985).
[CrossRef]

1984

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, "Real-time optical waveform convolver/cross correlator," Appl. Phys. Lett. 45, 714-716 (1984).
[CrossRef]

1983

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, "Frequency modulation FM spectroscopy," Appl. Phys. B 32, 145-152 (1983).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

1982

1981

T. Turpin, "Spectrum analysis using optical processing," Proc. IEEE 69, 80-92 (1981).

1979

J. L. Anderson, H. B. Brown, and B. V. Markevitch, "Wideband real-time Fourier analyzer using folded spectrum techniques," in Real-Time Signal Processing II, T. F. Tao, ed., Proc. SPIE 180, 146-152 (1979).

1948

G. Hok, "Response of linear resonant systems to excitation of a frequency varying linearly with time," J. Appl. Phys. 19, 242-250 (1948).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Anderson, J. L.

J. L. Anderson, H. B. Brown, and B. V. Markevitch, "Wideband real-time Fourier analyzer using folded spectrum techniques," in Real-Time Signal Processing II, T. F. Tao, ed., Proc. SPIE 180, 146-152 (1979).

Armagan, G.

G. Armagan, A. M. Buoncristiani, and B. D. Bartolo, "Excited state dynamics of thulium ions in yttrium aluminum garnets," Opt. Mater. 1, 11-20 (1992).
[CrossRef]

Babbitt, W. R.

F. Schlottau, M. Colice, K. H. Wagner, and W. R. Babbitt, "Spectral hole burning for wideband, high-resolution radio-frequency spectrum analysis," Opt. Lett. 30, 3003-3005 (2005).
[CrossRef]

T. Chang, M. Tian, R. K. 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]

G. W. Burr, T. L. Harris, W. R. Babbitt, and C. M. Jefferson, "Incorporating excitation-induced dephasing into the Maxwell-Bloch numerical modeling of photon echoes," J. Lumin. 107, 314-331 (2004).
[CrossRef]

K. D. Merkel, R. K. 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]

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgeré, and J.-L. Le Gouët, "RF Spectrum Analysis in Spectral Hole Burning Media," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

M. Tian, R. Reibel, and W. R. Babbitt, "Demonstration of optical coherent transient true-time delay at 4 Gbits/s," Opt. Lett. 26, 1143-1145 (2001).

K. D. Merkel, Z. Cole, and W. R. Babbitt, "Signal correlator with programmable variable time delay based on optical coherent transients," J. Lumin. 86, 375-382 (2000).
[CrossRef]

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, "Real-time optical waveform convolver/cross correlator," Appl. Phys. Lett. 45, 714-716 (1984).
[CrossRef]

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

W. R. Babbitt and R. Krishna Mohan, Spectrum Lab, Department of Physics, Montana State University, Bozeman, Montana 59717 (personal communication, 2005).

Bai, Y. S.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, "Real-time optical waveform convolver/cross correlator," Appl. Phys. Lett. 45, 714-716 (1984).
[CrossRef]

Bartolo, B. D.

G. Armagan, A. M. Buoncristiani, and B. D. Bartolo, "Excited state dynamics of thulium ions in yttrium aluminum garnets," Opt. Mater. 1, 11-20 (1992).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, "Frequency modulation FM spectroscopy," Appl. Phys. B 32, 145-152 (1983).
[CrossRef]

Böttger, T.

T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, "Optical decoherence and spectral diffusion at 1.5 μm in Er3+:Y2SiO5 versus magnetic field, temperature, and Er3+ concentration," Phys. Rev. B 73, 075101 (2006).
[CrossRef]

Braker, B.

F. Schlottau, B. Braker, and K. Wagner, "Squint compensation for a broadband RF array spectral imager using spatial spectral holography," in Imaging Spectrometry X, S. S. Shen and P. E. Lewis, eds., Proc. SPIE 5546, 244-252 (2004).
[CrossRef]

Braker, B. M.

B. M. Braker, Y. Li, D. Gu, F. Schlottau, and K. H. Wagner, "Broadband microwave imaging with spectral hole burning for squint compensation," in Passive Millimeter-Wave Imaging Technology VIII, R. Appleby and D. A. Wikner, eds., Proc. SPIE 5789, 69-79 (2005).
[CrossRef]

Bregman, J.

K. H. Wagner, F. Schlottau, and J. Bregman, "Array imaging using spatial-spectral holography," in Optics in Computing (International Commission on Optics, 2002).

F. Schlottau, K. Wagner, J. Bregman, and J.-L. Le Gouët, "Sparse antenna array multiple beamforming and spectral analysis using spatial-spectral holography," in IEEE International Topical Meeting on Microwave Photonics (IEEE, 2003), pp. 355-358.
[CrossRef]

Bretenaker, F.

G. Gorju, V. Crozatier, V. Lavielle, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, "Experimental investigation of deterministic and stochastic frequency noises of a rapidly frequency chirped laser," Eur. Phys. J. Appl. Phys. 30, 175-183 (2005).
[CrossRef]

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, "10-GHz bandwidth rf spectral Analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG," IEEE Photon. Technol. Lett. 17, 2385-2387 (2005).
[CrossRef]

V. Crozatier, V. Lavielle, F. Bretenaker, J. Le Gouët, and I. Lorgeré, "High-resolution radio frequency spectral analysis with photon echo chirp transform in an Er:YSO crystal," IEEE J. Quantum Electron. 40, 1450-1457 (2004).
[CrossRef]

Brewer, R. G.

M. Mitsunaga and R. G. Brewer, "Generalized perturbation theory of coherent optical emission," Phys. Rev. A 32, 1605-1613 (1985).
[CrossRef]

Brown, H. B.

J. L. Anderson, H. B. Brown, and B. V. Markevitch, "Wideband real-time Fourier analyzer using folded spectrum techniques," in Real-Time Signal Processing II, T. F. Tao, ed., Proc. SPIE 180, 146-152 (1979).

Buoncristiani, A. M.

G. Armagan, A. M. Buoncristiani, and B. D. Bartolo, "Excited state dynamics of thulium ions in yttrium aluminum garnets," Opt. Mater. 1, 11-20 (1992).
[CrossRef]

Burr, G. W.

G. W. Burr, T. L. Harris, W. R. Babbitt, and C. M. Jefferson, "Incorporating excitation-induced dephasing into the Maxwell-Bloch numerical modeling of photon echoes," J. Lumin. 107, 314-331 (2004).
[CrossRef]

Carlson, N. W.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, "Real-time optical waveform convolver/cross correlator," Appl. Phys. Lett. 45, 714-716 (1984).
[CrossRef]

Carlsten, J. L.

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

K. S. Repasky and J. L. Carlsten, "Simple method for measuring frequency chirps with a Fabry-Perot interferometer," Appl. Opt. 39, 5500-5504 (2000).

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

Seze, F. D.

V. Lavielle, F. D. Seze, I. Lorgeré, and J.-L. Le Gouët, "Wideband radio frequency spectrum analyzer: improved design and experimental results," J. Lumin. 107, 75-89 (2004).
[CrossRef]

Shi, Y. Q.

D. T. Chen, H. R. Fetterman, A. T. Chen, W. H. Steier, L. R. Dalton, W. S. Wang, and Y. Q. Shi, "Demonstration of 110 GHz electro-optic polymer modulators," Appl. Phys. Lett. 70, 3335-3337 (1997).
[CrossRef]

Steier, W. H.

D. T. Chen, H. R. Fetterman, A. T. Chen, W. H. Steier, L. R. Dalton, W. S. Wang, and Y. Q. Shi, "Demonstration of 110 GHz electro-optic polymer modulators," Appl. Phys. Lett. 70, 3335-3337 (1997).
[CrossRef]

Strickland, N. M.

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

Sun, Y.

T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, "Optical decoherence and spectral diffusion at 1.5 μm in Er3+:Y2SiO5 versus magnetic field, temperature, and Er3+ concentration," Phys. Rev. B 73, 075101 (2006).
[CrossRef]

Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, and R. L. Hutcheson, "Recent progress in developing new rare-earth materials for hole burning and coherent transient applications," J. Lumin. 98, 281-287 (2002).
[CrossRef]

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

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A. Szaabo and R. Kaarli, "Optical hole burning and spectral diffusion in ruby," Phys. Rev. B 44, 12307-12313 (1991).
[CrossRef]

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M. Mitsunaga, T. Takagahara, R. Yano, and N. Uesegi, "Excitation-induced frequency shift probed by stimulated photon echoes," Phys. Rev. Lett. 68, 3216-3219 (1992).
[CrossRef]

Thiel, C. W.

T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, "Optical decoherence and spectral diffusion at 1.5 μm in Er3+:Y2SiO5 versus magnetic field, temperature, and Er3+ concentration," Phys. Rev. B 73, 075101 (2006).
[CrossRef]

Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, and R. L. Hutcheson, "Recent progress in developing new rare-earth materials for hole burning and coherent transient applications," J. Lumin. 98, 281-287 (2002).
[CrossRef]

Tian, M.

Tonda, S.

I. Lorgeré, L. Ménager, V. Lavielle, J.-L. Le Gouët, D. Dolfi, S. Tonda, and J.-P. Huignard, "Demonstration of a radio-frequency spectrum analyser based on spectral hole burning," J. Mod. Opt. 49, 2459-2475 (2002).
[CrossRef]

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M. Mitsunaga, T. Takagahara, R. Yano, and N. Uesegi, "Excitation-induced frequency shift probed by stimulated photon echoes," Phys. Rev. Lett. 68, 3216-3219 (1992).
[CrossRef]

Wagner, K.

M. Colice, F. Schlottau, and K. Wagner, "Ultrawideband, wide-open rf spectrum analysis using spectral hole burning," in Microwave Photonics, J. Yao, ed., Proc. SPIE 5971, 564-573 (2005).

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgeré, and J.-L. Le Gouët, "RF Spectrum Analysis in Spectral Hole Burning Media," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

F. Schlottau, B. Braker, and K. Wagner, "Squint compensation for a broadband RF array spectral imager using spatial spectral holography," in Imaging Spectrometry X, S. S. Shen and P. E. Lewis, eds., Proc. SPIE 5546, 244-252 (2004).
[CrossRef]

F. Schlottau, K. Wagner, J. Bregman, and J.-L. Le Gouët, "Sparse antenna array multiple beamforming and spectral analysis using spatial-spectral holography," in IEEE International Topical Meeting on Microwave Photonics (IEEE, 2003), pp. 355-358.
[CrossRef]

Wagner, K. H.

B. M. Braker, Y. Li, D. Gu, F. Schlottau, and K. H. Wagner, "Broadband microwave imaging with spectral hole burning for squint compensation," in Passive Millimeter-Wave Imaging Technology VIII, R. Appleby and D. A. Wikner, eds., Proc. SPIE 5789, 69-79 (2005).
[CrossRef]

F. Schlottau, M. Colice, K. H. Wagner, and W. R. Babbitt, "Spectral hole burning for wideband, high-resolution radio-frequency spectrum analysis," Opt. Lett. 30, 3003-3005 (2005).
[CrossRef]

F. Schlottau and K. H. Wagner, "Demonstration of a continuous scanner and time-integrating correlator using spatial-spectral holography," J. Lumin. 107, 90-102 (2004).
[CrossRef]

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

K. H. Wagner, F. Schlottau, and J. Bregman, "Array imaging using spatial-spectral holography," in Optics in Computing (International Commission on Optics, 2002).

Wang, W. S.

D. T. Chen, H. R. Fetterman, A. T. Chen, W. H. Steier, L. R. Dalton, W. S. Wang, and Y. Q. Shi, "Demonstration of 110 GHz electro-optic polymer modulators," Appl. Phys. Lett. 70, 3335-3337 (1997).
[CrossRef]

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R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
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[CrossRef]

Yano, R.

M. Mitsunaga, T. Takagahara, R. Yano, and N. Uesegi, "Excitation-induced frequency shift probed by stimulated photon echoes," Phys. Rev. Lett. 68, 3216-3219 (1992).
[CrossRef]

Zhang, J. M.

J. Huang, J. M. Zhang, A. Lezama, and T. W. Mossberg, "Excess dephasing in photon-echo experiments arising from excitation-induced electronic level shifts," Phys. Rev. Lett. 63, 78-81 (1989).
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D. T. Chen, H. R. Fetterman, A. T. Chen, W. H. Steier, L. R. Dalton, W. S. Wang, and Y. Q. Shi, "Demonstration of 110 GHz electro-optic polymer modulators," Appl. Phys. Lett. 70, 3335-3337 (1997).
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G. Gorju, V. Crozatier, V. Lavielle, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, "Experimental investigation of deterministic and stochastic frequency noises of a rapidly frequency chirped laser," Eur. Phys. J. Appl. Phys. 30, 175-183 (2005).
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IEEE J. Quantum Electron.

V. Crozatier, V. Lavielle, F. Bretenaker, J. Le Gouët, and I. Lorgeré, "High-resolution radio frequency spectral analysis with photon echo chirp transform in an Er:YSO crystal," IEEE J. Quantum Electron. 40, 1450-1457 (2004).
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G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, "10-GHz bandwidth rf spectral Analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG," IEEE Photon. Technol. Lett. 17, 2385-2387 (2005).
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G. W. Burr, T. L. Harris, W. R. Babbitt, and C. M. Jefferson, "Incorporating excitation-induced dephasing into the Maxwell-Bloch numerical modeling of photon echoes," J. Lumin. 107, 314-331 (2004).
[CrossRef]

Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, and R. L. Hutcheson, "Recent progress in developing new rare-earth materials for hole burning and coherent transient applications," J. Lumin. 98, 281-287 (2002).
[CrossRef]

R. M. Macfarlane, "Direct process thermal line broadening in Tm:YAG," J. Lumin. 85, 181-186 (2000).
[CrossRef]

V. Lavielle, F. D. Seze, I. Lorgeré, and J.-L. Le Gouët, "Wideband radio frequency spectrum analyzer: improved design and experimental results," J. Lumin. 107, 75-89 (2004).
[CrossRef]

K. D. Merkel, Z. Cole, and W. R. Babbitt, "Signal correlator with programmable variable time delay based on optical coherent transients," J. Lumin. 86, 375-382 (2000).
[CrossRef]

F. Schlottau and K. H. Wagner, "Demonstration of a continuous scanner and time-integrating correlator using spatial-spectral holography," J. Lumin. 107, 90-102 (2004).
[CrossRef]

K. D. Merkel, R. K. 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]

J. Mod. Opt.

I. Lorgeré, L. Ménager, V. Lavielle, J.-L. Le Gouët, D. Dolfi, S. Tonda, and J.-P. Huignard, "Demonstration of a radio-frequency spectrum analyser based on spectral hole burning," J. Mod. Opt. 49, 2459-2475 (2002).
[CrossRef]

Opt. Lett.

Opt. Mater.

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Phys. Rev. B

G. K. Liu and R. L. Cone, "Laser-induced instantaneous spectral diffusion in Tb3+ compounds as observed in photon-echo experiments," Phys. Rev. B 41, 6193-6200 (1990).
[CrossRef]

T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, "Optical decoherence and spectral diffusion at 1.5 μm in Er3+:Y2SiO5 versus magnetic field, temperature, and Er3+ concentration," Phys. Rev. B 73, 075101 (2006).
[CrossRef]

A. Szaabo and R. Kaarli, "Optical hole burning and spectral diffusion in ruby," Phys. Rev. B 44, 12307-12313 (1991).
[CrossRef]

S. Kröll, E. Y. Xu, M. K. Kim, M. Mitsunaga, and R. Kachru, "Intensity-dependent photon-echo relaxation in rare-earth-doped crystals," Phys. Rev. B 41, 11568-11571 (1990).
[CrossRef]

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

Phys. Rev. Lett.

M. Mitsunaga, T. Takagahara, R. Yano, and N. Uesegi, "Excitation-induced frequency shift probed by stimulated photon echoes," Phys. Rev. Lett. 68, 3216-3219 (1992).
[CrossRef]

J. Huang, J. M. Zhang, A. Lezama, and T. W. Mossberg, "Excess dephasing in photon-echo experiments arising from excitation-induced electronic level shifts," Phys. Rev. Lett. 63, 78-81 (1989).
[CrossRef]

Proc. IEEE

T. Turpin, "Spectrum analysis using optical processing," Proc. IEEE 69, 80-92 (1981).

Proc. SPIE

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M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgeré, and J.-L. Le Gouët, "RF Spectrum Analysis in Spectral Hole Burning Media," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

M. Colice, F. Schlottau, and K. Wagner, "Ultrawideband, wide-open rf spectrum analysis using spectral hole burning," in Microwave Photonics, J. Yao, ed., Proc. SPIE 5971, 564-573 (2005).

F. Schlottau, B. Braker, and K. Wagner, "Squint compensation for a broadband RF array spectral imager using spatial spectral holography," in Imaging Spectrometry X, S. S. Shen and P. E. Lewis, eds., Proc. SPIE 5546, 244-252 (2004).
[CrossRef]

B. M. Braker, Y. Li, D. Gu, F. Schlottau, and K. H. Wagner, "Broadband microwave imaging with spectral hole burning for squint compensation," in Passive Millimeter-Wave Imaging Technology VIII, R. Appleby and D. A. Wikner, eds., Proc. SPIE 5789, 69-79 (2005).
[CrossRef]

Other

K. H. Wagner, F. Schlottau, and J. Bregman, "Array imaging using spatial-spectral holography," in Optics in Computing (International Commission on Optics, 2002).

F. Schlottau, K. Wagner, J. Bregman, and J.-L. Le Gouët, "Sparse antenna array multiple beamforming and spectral analysis using spatial-spectral holography," in IEEE International Topical Meeting on Microwave Photonics (IEEE, 2003), pp. 355-358.
[CrossRef]

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

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Figures (16)

Fig. 1
Fig. 1

Write–read process for spectrum analysis in SHB crystals. The signal beam propagates through an EOM, which is driven by the rf signal of interest, before being focused into the crystal. It burns the rf signal spectrum into the crystal's absorption profile. A chirped read beam probes the altered absorption profile before striking the (+) port of a differential detector. A chirped background beam probes the crystal's background absorption profile before striking the (−) port of the differential detector. The digitizing oscilloscope records changes in transmitted intensity as a map of the signal power spectrum.

Fig. 2
Fig. 2

Absorption variation with frequency detuning for different values of I s ( z = 0 ) . The dark line at z = 2 α 0 L is the absorption integrated over the propagation distance. As intensity increases, the hole begins to saturate and broaden. The saturation point moves from the input to the output of the crystal until the crystal is completely saturated.

Fig. 3
Fig. 3

Spectral hole depth at the signal beam frequency as a function of signal beam intensity.

Fig. 4
Fig. 4

(a) Log–log and (b) log–linear plots of differentially detected current i d as a function of input signal intensity I s ( 0 ) for several values of α 0 L . Differential current is normalized to I r ( 0 ) A . Variation is linear until the crystal begins to saturate, at which point variation becomes exponential for thick crystals until total saturation occurs.

Fig. 5
Fig. 5

Logarithm of the detected spectral hole FWHM normalized to homogeneous linewidth 1 / T 2 as a function of input signal intensity I s ( 0 ) . The hole width remains constant at 1 / T 2 until saturation begins, at which point the hole width starts to grow as the square root of signal beam intensity.

Fig. 6
Fig. 6

Peak volume ( FWHM 2 × i d ) as a function of input signal intensity I s ( 0 ) .

Fig. 7
Fig. 7

Input spectra, aggregate spectral hole depth, and differentially detected current for double-sideband modulation with resonant and tuned optical carriers. The sidebands (inset, top) are three rf tones centered at about 6   GHz and spread over 4   MHz , with power equivalent to I s ( 0 ) / I sat = 10   dB . Close-ups (bottom) of the differentially detected sidebands show resolution.

Fig. 8
Fig. 8

High bandwidth spectrum analyzer based on SHB. A PM fiber coupler splits the signal laser beam into a signal beam and a stabilization beam, which locks the laser to a spectral feature in the crystal. The signal beam writes the signal spectrum into the SHB crystal. A 36 Hz oscillator drives the read laser to produce a chirp beam, which is split into a read beam, a background beam, and a calibration beam by a pair of beam splitters (BSs). The read and background beams probe the crystal to produce a temporal map of the rf signal spectrum. The calibration beam passes through a fiber etalon to produce a measurement of the chirp beam's frequency nonuniformity. Postprocessing oscilloscope data using spectral linearization and recovery techniques yields the signal power spectrum.

Fig. 9
Fig. 9

Spectral linearization. A half-wave plate ( λ / 2 ) used with a polarizing beam splitter (PBS) sends part of the read laser's output through a fiber etalon, which has a free spectral range of about 19   MHz . The oscillator chirps the read laser, causing the etalon output to fluctuate in intensity. The algorithm compares the actual etalon output to the ideal etalon output, generating a map of the chirp distortion for use in linearizing the raw data.

Fig. 10
Fig. 10

Raw spectrum of a 420   MHz square wave and a 10 20   GHz chirp as recorded by the SHB crystal and captured on the oscilloscope. The dc peak associated with the optical carrier triggers the oscilloscope and also acts as the zero frequency reference for the linearization and mapping processes.

Fig. 11
Fig. 11

Spectral linearization algorithm for the experimental data. We show linearized raw etalon output data as the ideal etalon output.

Fig. 12
Fig. 12

Difference between ideal and actual chirp rates.

Fig. 13
Fig. 13

Spectrum of the reference etalon output (a) before and (b) after spectral linearization.

Fig. 14
Fig. 14

Error in the positions of the 420   MHz square wave peaks. The error is the difference between the ideal and the actual peak positions, before and after linearization. The standard deviation of the difference drops from 30   MHz before linearization to 0.3   MHz after linearization.

Fig. 15
Fig. 15

First-order peak of the 420   MHz square wave (a) without and (b) with spectral recovery (Ref. 30). Ringing present in the unrecovered signal is removed by deconvolving (i.e., by Fourier transforming the raw signal, multiplying the conjugate of the chirp, and Fourier transforming the result) the raw signal from the read chirp to produce the recovered peak. Spectral recovery reduces the FWHM from about 2.5   MHz to 1   MHz .

Fig. 16
Fig. 16

Relative power spectrum of a 10 20   GHz chirp and a 420   MHz square wave as measured by our SHB spectrum analyzer after linearization and spectral recovery (Ref. 30). The time–bandwidth product exceeds 20,000. We used a digital frequency synthesizer to produce the 10 20   GHz chirp, hence its discretized structure. Because the sweep and readout times are each 10   ms and the sweep and readout are not synchronized, the spectrum analyzer misses the last portion of the chirp.

Equations (32)

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S ( ω = 2 π κ t ) = [ s ( t ) exp ( - i π κ t 2 ) exp ( i π κ t 2 ) ] × exp ( - i π κ t 2 ) ,
ρ 12 ( t ) = D t d t 3 t 3 d t 2 t 2 d t 1 E 3 ( t 3 ) E 2 ( t 2 ) E 1 * ( t 1 ) × exp [ - ( t - t 3 + t 2 t 1 ) / T 2 ] × exp [ - ( t 3 t 2 ) / T 1 ] × δ ( t 2 t 1 + t 3 t ) ,
ρ 12 ( t ) = D d ω 3 d ω 2 d ω 1 E ˜ 3 ( ω 3 ) E ˜ 2 ( ω 2 ) × E ˜ 1 * ( ω 1 ) exp [ i ( ω 3 + ω 2 ω 1 ) t ] × γ 1 ( ω 2 ω 1 ) γ 2 ( ω 3 + ω 2 2 ω 1 ) ,
γ 1 ( ω 2 ω 1 ) = 1 ( 1 / T 1 ) + i ( ω 2 ω 1 ) ,
γ 2 ( ω 3 + ω 2 2 ω 1 ) = 1 ( 2 / T 2 ) + i ( ω 3 + ω 2 2 ω 1 ) .
ρ 12 ( t ) = D d ω 3 d ω 2 d ω 1 C × exp [ i ( ω 3 ω c ) 2 / ( 4 π κ ) ] exp ( i ω 3 t 0 )
× S ( ω 2 ) S * ( ω 1 ) exp [ i ( ω 3 + ω 2 ω 1 ) t ] × γ 1 ( ω 2 ω 1 ) γ 2 ( ω 3 + ω 2 2 ω 1 ) .
ρ 12 ( t ) = D [ | S ( ω 2 ) | 2 γ 2 ( ω 3 ω 2 ) d ω 2 ] × C   exp [ i ( ω 3 ω c ) 2 / ( 4 π κ ) ] × exp [ i ω 3 ( t + t 0 ) ] d ω 3 .
H ( ω 3 ) = | S ( ω 2 ) | 2 γ 2 ( ω 3 ω 2 ) d ω 2 .
ρ 12 ( t ) = D H ( ω 3 ) C   exp [ i ( ω 3 ω c ) 2 / ( 4 π κ ) ] × exp [ i ω 3 ( t + t 0 ) ] d ω 3 .
ρ 12 ( t ) = D C d ω 3 H ( ω 3 ) × exp ( i 4 π κ { ω 3 + [ 2 π κ ( t + t 0 ) ω c ] } 2 ) × exp [ i π κ ( t + t 0 ) 2 ] exp [ i ω c ( t + t 0 ) ] .
ρ 12 ( t ) { [ H ( 2 π κ t ) exp ( i π κ t 2 ) ] × exp ( - i π κ t 2 ) } δ ( 2 π κ t ω c ) .
E o ( t ) H ( 2 π κ t ) exp ( - i π κ t 2 ) ,
H ( 2 π κ t ) E o ( t ) exp ( i π κ t 2 )
= [ H ( 2 π κ t ) exp ( i π κ t 2 ) ] exp ( i π κ t 2 )
= 1 { [ H ( 2 π κ t ) ] × exp [ - i ω 2 / ( 4 π κ ) ] × exp [ i ω 2 / ( 4 π κ ) ] } .
H ( 2 π κ t ) exp ( i 4 π κ t 2 ) = { [ H ( 2 π κ t ) exp ( i π κ t 2 ) ] × exp ( - i 2 π κ t 2 ) } exp ( i π κ t 2 ) .
α ( z ) = i k 2 ϵ P ( z ) ( z ) ,
d I ( z ) d z = 2   Re { α ( z , ω ) } I ( z ) ,
w ˙ ( z , ω , t ) = w ( z , ω , t ) w eq T 1 + i μ 12 ħ [ ρ 21 ( z , ω , t ) E ( z , t ) c .c . ] ,
ρ ˙ 12 ( z , ω , t ) = ( i ω + 1 T 2 ) ρ 12 ( z , ω , t ) i μ 12 2 ħ E ( z , t ) w ( z , ω , t ) ,
G ( ω ) = 1 Δ ω π   exp [ - ( ω Δ ω ) 2 ] ,
E ( z , t ) = s ( z ) exp [ i ( ω s t k s z ) ] + r ( z ) exp [ i ( ω r t k r z ) ] ,
ρ 12 ( z , ω , t ) = i μ 12 ħ w ( z , ω , t ) × { s ( z ) exp [ i ( ω s t k s z ) ] γ ( ω ω s ) + r ( z ) exp [ i ( ω r t k r z ) ] γ ( ω ω r ) } ,
γ ( ω ω s , r ) = 1 ( 1 / T 2 ) i ( ω ω s , r ) .
w ( z , ω , t ) = G ( ω ) w eq 1 + [ I s ( z ) / I sat ] ( ω ω s ) ,
( ω ω 0 ) = ( 1 / T 2 ) 2 ( 1 / T 2 ) 2 + ( ω ω 0 ) 2 .
α ( z ) = α s ( z ) + α r ( z ) .
α s ( z , ω ) = α 0 T 2 G ( ω ) γ ( ω ω s ) 1 + [ I s ( z ) / I sat ] ( ω ω s ) ,
α r ( z ; ω r , ω s ) = α 0 T 2 G ( ω ) γ ( ω ω r ) 1+ [ I s ( z ) / I sat ] ( ω ω s ) d ω .
α r ( z ; ω r = ω s ) = α 0 T 2 G ( ω r ) 1 + [ I s ( z ) / I sat ] .
i d ( L ; ω r , ω s ) = Re { exp [ 0 L 2 α r ( z ; ω r , ω s ) d z ] exp [ 2 α 0 T 2 G ( ω r ) L ] } I r ( 0 ) A ,

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