Abstract

Different architectures of rf spectral analyzers based on the spectral photography scheme in spectral-hole-burning materials are theoretically and experimentally investigated. The microscopic atomic response for the recording and reading of the rf spectra and taking into account the spatial extension of the beams is calculated for different analyzer configurations. The spectral resolution and the signal-to-noise ratio of the analyzer are derived. These predictions are experimentally tested using spectral-hole burning in Tm3+:YAG for a couple of configurations and sizes of the beams. In each case, the resolution, linear dynamic range, and bandwidth of the spectrum analyzer are determined.

© 2007 Optical Society of America

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  1. J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. V. Crozatier, V. Lavielle, F. Bretenaker, J.-L. Le Gouët, and I. Lorgeré, "High resolution radio frequency spectral analysis with phoon echoes chirp transform in an Er:YSO crystal," IEEE J. Quantum Electron. 40, 1450-1457 (2004).
    [CrossRef]
  8. 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).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. T. Chang, M. Tian, K. 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] [PubMed]
  19. Y. Sun, G. M. Wang, and R. L. Cone, "Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystal," Phys. Rev. B 62, 15443-15451 (2004).
    [CrossRef]
  20. C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
    [CrossRef]
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    [CrossRef]

2005 (4)

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, "10GHz bandwidth RF spectral analyser 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] [PubMed]

T. Chang, M. Tian, K. 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] [PubMed]

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]

2004 (5)

T. Chang, K. K. 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]

Y. Sun, G. M. Wang, and R. L. Cone, "Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystal," Phys. Rev. B 62, 15443-15451 (2004).
[CrossRef]

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

V. Lavielle, F. De 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]

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

2003 (1)

2002 (3)

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

L. Levin, "Mode-hop-free electro-optically tuned diode laser," Opt. Lett. 27, 237-239 (2002).
[CrossRef]

2000 (1)

1999 (2)

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
[CrossRef]

1989 (1)

A. J. Meixner, A. Renn, and U. P. Wild, "Spectral hole-burning and holography. I. Transmission and holographic detection of spectral holes," Bell J. Chem. Phys. 91, 6728-6736 (1989).
[CrossRef]

1973 (1)

J. B. Hagen and D. T. Farley, "Digital-correlation techniques in radio science," Radio Sci. 8, 775-784 (1973).
[CrossRef]

1969 (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

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] [PubMed]

T. Chang, M. Tian, K. 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] [PubMed]

T. Chang, K. K. 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]

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (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).
[CrossRef]

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).
[CrossRef]

Bretenaker, F.

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

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]

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

Broggs, B.

C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
[CrossRef]

Cabaret, L.

Chang, T.

T. Chang, M. Tian, K. 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] [PubMed]

T. Chang, K. K. 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]

Colice, M.

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] [PubMed]

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

Cone, R. L.

Y. Sun, G. M. Wang, and R. L. Cone, "Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystal," Phys. Rev. B 62, 15443-15451 (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]

Crozatier, V.

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

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]

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

De Seze, F.

V. Lavielle, F. De 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]

Dolfi, D.

Equall, R. W.

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]

Farley, D. T.

J. B. Hagen and D. T. Farley, "Digital-correlation techniques in radio science," Radio Sci. 8, 775-784 (1973).
[CrossRef]

Gorju, G.

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

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]

Greiner, C.

C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
[CrossRef]

Hagen, J. B.

J. B. Hagen and D. T. Farley, "Digital-correlation techniques in radio science," Radio Sci. 8, 775-784 (1973).
[CrossRef]

Harris, T. L.

T. Chang, K. K. 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]

Horn, J.

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

Hutcheson, R. L.

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]

Kaplyanskii, A. A.

A. A. Kaplyanskii and R. M. McFarlane, Spectroscopy of Solids Containing Rare Earth Ions (Elsevier, 1987).

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

Kunz, C.

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

Lavielle, V.

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]

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

V. Lavielle, F. De 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]

V. Lavielle, I. Lorgeré, S. Tonda, D. Dolfi, and J.-L. Le Gouët, "Wideband versatile radio-frequency spectrum analyzer," Opt. Lett. 28, 384-386 (2003).
[CrossRef] [PubMed]

Le Gouët, J.-L.

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

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, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

V. Lavielle, F. De 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]

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

V. Lavielle, I. Lorgeré, S. Tonda, D. Dolfi, and J.-L. Le Gouët, "Wideband versatile radio-frequency spectrum analyzer," Opt. Lett. 28, 384-386 (2003).
[CrossRef] [PubMed]

L. Ménager, L. Cabaret, I. Lorgeré, and J.-L. Le Gouët, "Diode laser extended cavity for broad-range fast ramping," Opt. Lett. 25, 1246-1248 (2000).
[CrossRef]

Levin, L.

Loftus, T.

C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
[CrossRef]

Lorgere, I.

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

Lorgeré, I.

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

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]

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

V. Lavielle, F. De 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]

V. Lavielle, I. Lorgeré, S. Tonda, D. Dolfi, and J.-L. Le Gouët, "Wideband versatile radio-frequency spectrum analyzer," Opt. Lett. 28, 384-386 (2003).
[CrossRef] [PubMed]

L. Ménager, L. Cabaret, I. Lorgeré, and J.-L. Le Gouët, "Diode laser extended cavity for broad-range fast ramping," Opt. Lett. 25, 1246-1248 (2000).
[CrossRef]

McFarlane, R. M.

A. A. Kaplyanskii and R. M. McFarlane, Spectroscopy of Solids Containing Rare Earth Ions (Elsevier, 1987).

Meixner, A. J.

A. J. Meixner, A. Renn, and U. P. Wild, "Spectral hole-burning and holography. I. Transmission and holographic detection of spectral holes," Bell J. Chem. Phys. 91, 6728-6736 (1989).
[CrossRef]

Ménager, L.

Merkel, K. D.

T. Chang, M. Tian, K. 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] [PubMed]

T. Chang, K. K. 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]

Mohan, K. K.

T. Chang, M. Tian, K. 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] [PubMed]

T. Chang, K. K. 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]

Mohan, R. K.

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

Mossberg, T. W.

C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
[CrossRef]

Reibel, R.

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).
[CrossRef]

Renn, A.

A. J. Meixner, A. Renn, and U. P. Wild, "Spectral hole-burning and holography. I. Transmission and holographic detection of spectral holes," Bell J. Chem. Phys. 91, 6728-6736 (1989).
[CrossRef]

Renner, C.

Schieder, R.

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

Schlottau, F.

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] [PubMed]

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

Schmülling, F.

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

Siebertz, O.

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

Sun, Y.

Y. Sun, G. M. Wang, and R. L. Cone, "Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystal," Phys. Rev. B 62, 15443-15451 (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]

Thiel, C. W.

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.

T. Chang, M. Tian, K. 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] [PubMed]

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

Tonda, S.

Wagner, K.

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

Wagner, K. H.

Wang, G. M.

Y. Sun, G. M. Wang, and R. L. Cone, "Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystal," Phys. Rev. B 62, 15443-15451 (2004).
[CrossRef]

Wang, T.

C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
[CrossRef]

Wild, U. P.

A. J. Meixner, A. Renn, and U. P. Wild, "Spectral hole-burning and holography. I. Transmission and holographic detection of spectral holes," Bell J. Chem. Phys. 91, 6728-6736 (1989).
[CrossRef]

Winnewisser, G.

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

Bell J. Chem. Phys. (1)

A. J. Meixner, A. Renn, and U. P. Wild, "Spectral hole-burning and holography. I. Transmission and holographic detection of spectral holes," Bell J. Chem. Phys. 91, 6728-6736 (1989).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

Eur. Phys. J.: Appl. Phys. (1)

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]

Exp. Astron. (1)

J. Horn, O. Siebertz, F. Schmülling, C. Kunz, R. Schieder, and G. Winnewisser, "A 4×1GHz array acousto-optical spectrometer," Exp. Astron. 9, 17-38 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (1)

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

J. Lumin. (3)

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).
[CrossRef]

V. Lavielle, F. De 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]

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]

Opt. Lett. (5)

Phys. Rev. A (2)

T. Chang, K. K. 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]

C. Greiner, B. Broggs, T. Loftus, T. Wang, and T. W. Mossberg, "Polarization-dependent Rabi frequency beats in the coherent reponse of Tm3+ in YAG," Phys. Rev. A 60, 2657-2660 (1999).
[CrossRef]

Phys. Rev. B (1)

Y. Sun, G. M. Wang, and R. L. Cone, "Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystal," Phys. Rev. B 62, 15443-15451 (2004).
[CrossRef]

Proc. SPIE (1)

M. Colice, F. Schlottau, K. Wagner, R. K. Mohan, W. R. Babbitt, I. Lorgere, and J.-L. Le Gouët, "RF spectrum analysis in spectral hole burning media," Proc. SPIE 5557, 132-139 (2004).
[CrossRef]

Radio Sci. (1)

J. B. Hagen and D. T. Farley, "Digital-correlation techniques in radio science," Radio Sci. 8, 775-784 (1973).
[CrossRef]

Other (3)

J.N.Lee, in Optical Signal Processing, J.L.Horner, ed. (Academic, 1987), pp. l65-190.

A. A. Kaplyanskii and R. M. McFarlane, Spectroscopy of Solids Containing Rare Earth Ions (Elsevier, 1987).

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

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Figures (18)

Fig. 1
Fig. 1

(a) SHB photographic scheme spectral analyzer principles of operation, (b) Rf spectrum on an optical carrier, (c) Optically carried rf spectrum recorded in the material absorption bandwidth, (d) Instantaneous frequency of the probing laser, (e) Recovered rf spectrum as a function of time.

Fig. 2
Fig. 2

Level scheme of the Tm 3 + : YAG . κ 23 and κ 21 are the relaxations rates from the H 4 3 level to the F 4 3 and H 6 3 levels, respectively. κ 31 is the relaxation rate from level F 4 3 to the ground level H 6 3 .

Fig. 3
Fig. 3

Principles of the collinear geometry, (a) Engraving stage, (b) Reading stage.

Fig. 4
Fig. 4

Principle of the holographic architecture. (a) Engraving stage, (b) reading stage.

Fig. 5
Fig. 5

Relative amplitude of the signal E R obtained from Eq. (8) versus the engraving energy for three values of the engraving duration t W : 200 μ s (solid curve), 400 μ s (dotted curve), and 600 μ s (dashed curve). The experimental results of Ref. [10] are reproduced as circles and squares for engraving durations of 400 and 600 μ s , respectively. They were obtained by varying the engraving power between 0 and 3 mW .

Fig. 6
Fig. 6

Relative amplitude of the signal E R obtained from Eq. (10) versus the total engraving energy for three values of the engraving duration t W : 200 μ s (solid curve), 400 μ s (dotted curve), and 600 μ s (dashed curve). The engraving power varies from 0 to 3 mW in each case.

Fig. 7
Fig. 7

(a) Simulation of chirped readout ( r = 0.625 GHz ms ) of a single class of ions. (b) Same as (a) after convolution with a Gaussian of full width 1 MHz at half maximum mimicking the frequency jitter of the engraving laser.

Fig. 8
Fig. 8

Circles: simulation of chirped readout ( r = 0.625 GHz ms ) as a function of the probing Rabi frequency. The solid line corresponds to the slope of the linear section.

Fig. 9
Fig. 9

Calculated evolutions of the noises in a 3 MHz bandwidth as a function of the incident power up to P sat = 45 μ W . Dashed–dotted–dotted curve: shot noise. Dotted-dashed line: dark current noise. Dashed line: digitalization noise of our oscilloscope (Tektronix model TDS 5104, 1 mV division ). Solid curve: total noise.

Fig. 10
Fig. 10

(a) Experimental setup. AO1 and AO2 operate at 100 MHz . AO3 operates at 92 MHz , leading to a heterodyne signal at 8 MHz on the photodetector PD. The crystal is cooled at 4.5 K . The whole experiment is synchronized by a pulse generator labeled synchro. (b) Chronograms of the electrical signals send to AO1, AO2, and to the EOC during the engraving and probing phases.

Fig. 11
Fig. 11

Experimental profile of the diffracted signal versus time during the readout chirp of 1.25 GHz in 2 ms without heterodyning. The signal is on a dark background. The inset is a zoom on the peak.

Fig. 12
Fig. 12

(a) Diffracted intensity (thick curve) versus readout laser instantaneous frequency excursion for a rectangularly shaped engraved spectrum (thin curve), without any heterodyning. (b) Same as (a) in the presence of the LO shifted by 8 MHz . (c) Result of the demodulation of (b).

Fig. 13
Fig. 13

Experimental demonstration of the 10 GHz bandwidth capability of our holographic architecture. The crystal has been engraved with 15 equally spaced tones spanning 10 GHz .

Fig. 14
Fig. 14

Evolution of the measured value of readout signal amplitude versus reading laser Rabi frequency. Solid line: linear fit.

Fig. 15
Fig. 15

Evolution of the readout signal amplitude line shape versus reading laser power for the holographic configuration. The open triangles, squares, and circles have been obtained for Ω = 113 × 10 3 s 1 , Ω = 80 × 10 3 s 1 , and Ω = 40 × 10 3 s 1 , respectively.

Fig. 16
Fig. 16

Circles: measured rms noise amplitude in the (a) collinear and (b) holographic architecture versus (a) transmitted probe power and (b) LO power. The thin line is obtained from Eq. (29).

Fig. 17
Fig. 17

Experimental (squares) and theoretical (solid line) evolutions of the detected amplitude of a peak versus engraving optical energy in the collinear architecture for a beam radius (a) w = 100 μ m and (b) w = 500 μ m . The theoretical curves have been obtained from Eq. (8) with an absorption cross section σ = 5 × 10 16 cm 2 . The engraving time is 700 μ s . The inset shows the distribution of the signal value in the background absorption region.

Fig. 18
Fig. 18

Experimental (squares) and theoretical (solid line) evolutions of the detected amplitude of a peak after demodulation versus engraving optical energy in the holographic architecture for a beam radius (a) w = 100 μ m and (b) w = 500 μ m . The theoretical curves have been obtained from Eq. (10) with an absorption cross section of (a) σ = 7 × 10 16 cm 2 and (b) σ = 16 × 10 16 cm 2 . The engraving time is 700 μ s . The inset shows the distribution of the signal value in the presence of the LO only.

Equations (29)

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E e = E e 0 + δ E e ,
δ E e = E R + i E I ,
I det = E P 2 + E R 2 + E I 2 + 2 E P E R E P 2 + 2 E P E R ,
I det = E R 2 + E I 2 .
I det = E LO 2 + 2 E LO E R cos ( 2 π f LO t ) 2 E LO E I sin ( 2 π f LO t ) + E R 2 + E I 2 E LO 2 + 2 E LO E R cos ( 2 π f LO t ) 2 E LO E I sin ( 2 π f LO t ) ,
d n 1 d t = σ I h ν ( n 1 n 2 ) + κ 21 n 2 + κ 31 n 3 ,
d n 2 d t = σ I h ν ( n 1 n 2 ) κ n 2 ,
d n 3 d t = κ 23 n 2 κ 31 n 3 ,
I ( x ) = I 0 exp ( 2 x 2 w 2 ) ,
E R σ L 2 exp ( σ n L 2 ) ( n 2 w π d x exp ( 2 x 2 w 2 ) [ n 1 ( x ) n 2 ( x ) ] ) E P .
I ( x ) = 2 I 0 [ 1 + cos ( 2 π x Λ ) ] exp ( 2 x 2 w 2 ) ,
E R exp ( α 0 L 2 cos θ ) α 1 L 4 cos θ E P .
α 0 = 2 2 w π σ 0 d x exp ( 2 x 2 w 2 ) [ n 1 ( x ) n 2 ( x ) ] ,
α 1 = 4 2 w π σ 0 d x exp ( 2 x 2 w 2 ) cos ( 2 π x Λ ) [ n 1 ( x ) n 2 ( x ) ] .
E P ( t , z ) = E P 2 exp [ i ( ω 0 t + π r t 2 k z ) ] x + c.c. ,
Ω = d 12 E P ,
ρ ̃ 12 ( t , z ) = i Ω 4 π n 12 ( 0 ) 1 i r { 2 π 2 + d ω L ( ω ) exp [ i ( 2 π r t Δ ω ) 2 4 π r ] i 2 π + d ω L ( w ) + d ω exp ( i ω 2 4 π r ) 2 π r t Δ ω ω } ,
ρ ̃ 12 ( t , z ) = Ω 4 π n 12 ( 0 ) ( i Γ h 2 ( 2 π r t Δ ) 2 + ( Γ h 2 ) 2 ( 2 π r t Δ ) ( 2 π r t Δ ) 2 + ( Γ h 2 ) 2 ) .
δ E e ( t ) = μ 0 c ω 0 2 Ω 4 π d 12 N V π ln 2 Γ h Γ inh n 12 ( 0 ) [ Γ h 2 ( 2 π r t Δ ) 2 + ( Γ h 2 ) 2 + i ( 2 π r t Δ ) ( 2 π r t Δ ) 2 + ( Γ h 2 ) 2 ] [ 1 exp [ α L 2 ] α 2 ] ,
E R E P = β c , h t W P W ,
V = S P in G .
V shot = G R T 2 q S P det R T Δ f ,
V NEP = G NEP Δ f ,
V noise = V shot 2 + V NEP 2 + V osc 2 .
P P < P sat .
SNR c = 2 β c t W P W S P sat 2 q R T Δ f .
SNR h = β h t W P W S P P 2 q R T Δ f .
( β h t W P W ) 2 P P P sat 4 .
SNR h = S P sat 8 q R T Δ f .

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