Abstract

We numerically analyze phase-sensitive parametric amplification and de-amplification of a multimode field representing a multi-pixel text image. We optimize pumping configuration and demonstrate that ~10-dB gain is achievable with relatively moderate ~10-kW total pump peak power available from compact pump sources.

© 2009 Optical Society of America

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References

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  1. C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D. 26, 1817-1839 (1982).
    [CrossRef]
  2. D. Levandovsky, M. Vasilyev, and P. Kumar, "Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier," Opt. Lett. 24, 984-986 (1999).
    [CrossRef]
  3. D. Levandovsky, M. Vasilyev, and P. Kumar, "Near-noiseless amplification of light by a phase-sensitive fibre amplifier," PRAMANA-J. Phys. 56, 281-285 (2001).
    [CrossRef]
  4. W. Imajuku, A. Takada, and Y. Yamabayashi, "Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier," Electron. Lett. 35, 1954-1955 (1999).
    [CrossRef]
  5. H. P. Yuen, "Reduction Of Quantum Fluctuation And Suppression Of The Gordon-Haus Effect With Phase-Sensitive Linear-Amplifiers," Opt. Lett. 17, 73-75 (1992).
    [CrossRef] [PubMed]
  6. J. N. Kutz, W. L. Kath, R.-D. Li, and P. Kumar, "Long-distance propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers," Opt. Lett. 18, 802-804 (1993).
    [CrossRef] [PubMed]
  7. G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photon. Technol. Lett. 9, 1020-1022 (1997).
    [CrossRef]
  8. K. Croussore, I. Kim, Y. Han, C. Kim, G. Li, and S. Radic, "Demonstration of phase-regeneration of DPSK signals based on phase-sensitive amplification," Opt. Express 13, 3945-3950 (2005).
    [CrossRef] [PubMed]
  9. M. Vasilyev, "Distributed phase-sensitive amplification," Opt. Express 13, 7563-7571 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7563.
    [CrossRef] [PubMed]
  10. R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, "In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber," Opt. Express 16, 9046-9053 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-9046.
    [CrossRef] [PubMed]
  11. E. Lantz and F. Devaux, "Parametric Amplification of Images: From Time Gating to Noiseless Amplification," J. Sel. Top. Quantum Electron. 14, 635-647 (2008).
    [CrossRef]
  12. M. Kolobov, "The spatial behavior of nonclassical light," Rev. Mod. Phys. 71, 1539-1589 (1999).
    [CrossRef]
  13. K. Wang, G. Yang, A. Gatti, and L. Lugiato, "Controlling the signal-to-noise ratio in optical parametric image amplification," J. Opt. B: Quantum Semiclass. Opt. 5, S535-S544 (2003).
    [CrossRef]
  14. S.-K. Choi, M. Vasilyev, and P. Kumar, "Noiseless Optical Amplification of Images," Phys. Rev. Lett. 83, 1938-1941 (1999); erratum: Ibid.,  84, 1361-1361 (2000).
    [CrossRef]
  15. A. Mosset, F. Devaux, and E. Lantz, "Spatially noiseless optical amplification of images," Phys. Rev. Lett. 94, 223603-1-223603-4 (2005).
    [CrossRef]
  16. P. Kumar, V. Grigoryan, and M. Vasilyev, "Noise-Free Amplification: Towards Quantum Laser Radar," the 14th Coherent Laser Radar Conference, Snowmass, CO, July 2007.
  17. S.-K. Choi, R.-D. Li, C. Kim, and P. Kumar, "Traveling-wave optical parametric amplifier: investigation of its phase-sensitive and phase-insensitive gain response," J. Opt. Soc. Am. B 14, 1564-1575 (1997).
    [CrossRef]
  18. C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
    [CrossRef]
  19. K. G. Köprülü and O. Aytür, "Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states," Phys. Rev. A 60, 4122-4134 (1999).
    [CrossRef]
  20. K. G. Köprülü and O. Aytür, "Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers," J. Opt. Soc. Am. B 18, 846-854 (2001).
    [CrossRef]
  21. E. Lantz and F. Devaux, "Numerical simulation of spatial fluctuations in parametric image amplification," Eur. Phys. J. D 17, 93-98 (2001).
    [CrossRef]
  22. M. Kolobov, ed., Quantum Imaging, (Springer Verlag, New York, 2007).
    [CrossRef]
  23. A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
    [CrossRef]
  24. M. L. Marable, S.-K. Choi, and P. Kumar, "Measurement of quantum-noise correlations in parametric image amplication," Opt. Express 2, 84-92 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-2-3-84.
    [CrossRef] [PubMed]
  25. M. Vasilyev, N. Stelmakh, and P. Kumar, "Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump," to appear in J. Mod. Opt.

2008 (2)

2005 (2)

2003 (1)

K. Wang, G. Yang, A. Gatti, and L. Lugiato, "Controlling the signal-to-noise ratio in optical parametric image amplification," J. Opt. B: Quantum Semiclass. Opt. 5, S535-S544 (2003).
[CrossRef]

2001 (3)

K. G. Köprülü and O. Aytür, "Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers," J. Opt. Soc. Am. B 18, 846-854 (2001).
[CrossRef]

E. Lantz and F. Devaux, "Numerical simulation of spatial fluctuations in parametric image amplification," Eur. Phys. J. D 17, 93-98 (2001).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, "Near-noiseless amplification of light by a phase-sensitive fibre amplifier," PRAMANA-J. Phys. 56, 281-285 (2001).
[CrossRef]

2000 (1)

S.-K. Choi, M. Vasilyev, and P. Kumar, "Noiseless Optical Amplification of Images," Phys. Rev. Lett. 83, 1938-1941 (1999); erratum: Ibid.,  84, 1361-1361 (2000).
[CrossRef]

1999 (4)

M. Kolobov, "The spatial behavior of nonclassical light," Rev. Mod. Phys. 71, 1539-1589 (1999).
[CrossRef]

K. G. Köprülü and O. Aytür, "Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states," Phys. Rev. A 60, 4122-4134 (1999).
[CrossRef]

W. Imajuku, A. Takada, and Y. Yamabayashi, "Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier," Electron. Lett. 35, 1954-1955 (1999).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, "Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier," Opt. Lett. 24, 984-986 (1999).
[CrossRef]

1998 (2)

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

M. L. Marable, S.-K. Choi, and P. Kumar, "Measurement of quantum-noise correlations in parametric image amplication," Opt. Express 2, 84-92 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-2-3-84.
[CrossRef] [PubMed]

1997 (2)

S.-K. Choi, R.-D. Li, C. Kim, and P. Kumar, "Traveling-wave optical parametric amplifier: investigation of its phase-sensitive and phase-insensitive gain response," J. Opt. Soc. Am. B 14, 1564-1575 (1997).
[CrossRef]

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photon. Technol. Lett. 9, 1020-1022 (1997).
[CrossRef]

1993 (1)

1992 (1)

1987 (1)

A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
[CrossRef]

1982 (1)

C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D. 26, 1817-1839 (1982).
[CrossRef]

Aytür, O.

K. G. Köprülü and O. Aytür, "Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers," J. Opt. Soc. Am. B 18, 846-854 (2001).
[CrossRef]

K. G. Köprülü and O. Aytür, "Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states," Phys. Rev. A 60, 4122-4134 (1999).
[CrossRef]

Bartolini, G. D.

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photon. Technol. Lett. 9, 1020-1022 (1997).
[CrossRef]

Cardimona, D.

A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
[CrossRef]

Caves, C. M.

C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D. 26, 1817-1839 (1982).
[CrossRef]

Choi, S.-K.

Cohadon, P. F.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Croussore, K.

Devaux, F.

E. Lantz and F. Devaux, "Parametric Amplification of Images: From Time Gating to Noiseless Amplification," J. Sel. Top. Quantum Electron. 14, 635-647 (2008).
[CrossRef]

E. Lantz and F. Devaux, "Numerical simulation of spatial fluctuations in parametric image amplification," Eur. Phys. J. D 17, 93-98 (2001).
[CrossRef]

Devgan, P. S.

Fabre, C.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Gatti, A.

K. Wang, G. Yang, A. Gatti, and L. Lugiato, "Controlling the signal-to-noise ratio in optical parametric image amplification," J. Opt. B: Quantum Semiclass. Opt. 5, S535-S544 (2003).
[CrossRef]

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Gavrielides, A.

A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
[CrossRef]

Grigoryan, V. S.

Han, Y.

Imajuku, W.

W. Imajuku, A. Takada, and Y. Yamabayashi, "Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier," Electron. Lett. 35, 1954-1955 (1999).
[CrossRef]

Kath, W. L.

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photon. Technol. Lett. 9, 1020-1022 (1997).
[CrossRef]

J. N. Kutz, W. L. Kath, R.-D. Li, and P. Kumar, "Long-distance propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers," Opt. Lett. 18, 802-804 (1993).
[CrossRef] [PubMed]

Kim, C.

Kim, I.

Kolobov, M.

M. Kolobov, "The spatial behavior of nonclassical light," Rev. Mod. Phys. 71, 1539-1589 (1999).
[CrossRef]

Köprülü, K. G.

K. G. Köprülü and O. Aytür, "Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers," J. Opt. Soc. Am. B 18, 846-854 (2001).
[CrossRef]

K. G. Köprülü and O. Aytür, "Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states," Phys. Rev. A 60, 4122-4134 (1999).
[CrossRef]

Kumar, P.

R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, "In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber," Opt. Express 16, 9046-9053 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-9046.
[CrossRef] [PubMed]

D. Levandovsky, M. Vasilyev, and P. Kumar, "Near-noiseless amplification of light by a phase-sensitive fibre amplifier," PRAMANA-J. Phys. 56, 281-285 (2001).
[CrossRef]

S.-K. Choi, M. Vasilyev, and P. Kumar, "Noiseless Optical Amplification of Images," Phys. Rev. Lett. 83, 1938-1941 (1999); erratum: Ibid.,  84, 1361-1361 (2000).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, "Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier," Opt. Lett. 24, 984-986 (1999).
[CrossRef]

M. L. Marable, S.-K. Choi, and P. Kumar, "Measurement of quantum-noise correlations in parametric image amplication," Opt. Express 2, 84-92 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-2-3-84.
[CrossRef] [PubMed]

S.-K. Choi, R.-D. Li, C. Kim, and P. Kumar, "Traveling-wave optical parametric amplifier: investigation of its phase-sensitive and phase-insensitive gain response," J. Opt. Soc. Am. B 14, 1564-1575 (1997).
[CrossRef]

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photon. Technol. Lett. 9, 1020-1022 (1997).
[CrossRef]

J. N. Kutz, W. L. Kath, R.-D. Li, and P. Kumar, "Long-distance propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers," Opt. Lett. 18, 802-804 (1993).
[CrossRef] [PubMed]

Kutz, J. N.

Lantz, E.

E. Lantz and F. Devaux, "Parametric Amplification of Images: From Time Gating to Noiseless Amplification," J. Sel. Top. Quantum Electron. 14, 635-647 (2008).
[CrossRef]

E. Lantz and F. Devaux, "Numerical simulation of spatial fluctuations in parametric image amplification," Eur. Phys. J. D 17, 93-98 (2001).
[CrossRef]

Levandovsky, D.

D. Levandovsky, M. Vasilyev, and P. Kumar, "Near-noiseless amplification of light by a phase-sensitive fibre amplifier," PRAMANA-J. Phys. 56, 281-285 (2001).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, "Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier," Opt. Lett. 24, 984-986 (1999).
[CrossRef]

Li, G.

Li, R.-D.

Lugiato, L.

K. Wang, G. Yang, A. Gatti, and L. Lugiato, "Controlling the signal-to-noise ratio in optical parametric image amplification," J. Opt. B: Quantum Semiclass. Opt. 5, S535-S544 (2003).
[CrossRef]

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Marable, M. L.

Marte, M. A. M.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Peterson, P.

A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
[CrossRef]

Radic, S.

Ritsch, H.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Schwob, C.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Serkland, D. K.

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photon. Technol. Lett. 9, 1020-1022 (1997).
[CrossRef]

Takada, A.

W. Imajuku, A. Takada, and Y. Yamabayashi, "Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier," Electron. Lett. 35, 1954-1955 (1999).
[CrossRef]

Tang, R.

Vasilyev, M.

Wang, K.

K. Wang, G. Yang, A. Gatti, and L. Lugiato, "Controlling the signal-to-noise ratio in optical parametric image amplification," J. Opt. B: Quantum Semiclass. Opt. 5, S535-S544 (2003).
[CrossRef]

Yamabayashi, Y.

W. Imajuku, A. Takada, and Y. Yamabayashi, "Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier," Electron. Lett. 35, 1954-1955 (1999).
[CrossRef]

Yang, G.

K. Wang, G. Yang, A. Gatti, and L. Lugiato, "Controlling the signal-to-noise ratio in optical parametric image amplification," J. Opt. B: Quantum Semiclass. Opt. 5, S535-S544 (2003).
[CrossRef]

Yuen, H. P.

Appl. Phys. B (1)

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[CrossRef]

Electron. Lett. (1)

W. Imajuku, A. Takada, and Y. Yamabayashi, "Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier," Electron. Lett. 35, 1954-1955 (1999).
[CrossRef]

Eur. Phys. J. D (1)

E. Lantz and F. Devaux, "Numerical simulation of spatial fluctuations in parametric image amplification," Eur. Phys. J. D 17, 93-98 (2001).
[CrossRef]

Ibid (1)

S.-K. Choi, M. Vasilyev, and P. Kumar, "Noiseless Optical Amplification of Images," Phys. Rev. Lett. 83, 1938-1941 (1999); erratum: Ibid.,  84, 1361-1361 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photon. Technol. Lett. 9, 1020-1022 (1997).
[CrossRef]

J. Appl. Phys. (1)

A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

K. Wang, G. Yang, A. Gatti, and L. Lugiato, "Controlling the signal-to-noise ratio in optical parametric image amplification," J. Opt. B: Quantum Semiclass. Opt. 5, S535-S544 (2003).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. (1)

D. Levandovsky, M. Vasilyev, and P. Kumar, "Near-noiseless amplification of light by a phase-sensitive fibre amplifier," PRAMANA-J. Phys. 56, 281-285 (2001).
[CrossRef]

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

E. Lantz and F. Devaux, "Parametric Amplification of Images: From Time Gating to Noiseless Amplification," J. Sel. Top. Quantum Electron. 14, 635-647 (2008).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (1)

K. G. Köprülü and O. Aytür, "Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states," Phys. Rev. A 60, 4122-4134 (1999).
[CrossRef]

Phys. Rev. D. (1)

C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D. 26, 1817-1839 (1982).
[CrossRef]

Rev. Mod. Phys. (1)

M. Kolobov, "The spatial behavior of nonclassical light," Rev. Mod. Phys. 71, 1539-1589 (1999).
[CrossRef]

Other (4)

A. Mosset, F. Devaux, and E. Lantz, "Spatially noiseless optical amplification of images," Phys. Rev. Lett. 94, 223603-1-223603-4 (2005).
[CrossRef]

P. Kumar, V. Grigoryan, and M. Vasilyev, "Noise-Free Amplification: Towards Quantum Laser Radar," the 14th Coherent Laser Radar Conference, Snowmass, CO, July 2007.

M. Vasilyev, N. Stelmakh, and P. Kumar, "Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump," to appear in J. Mod. Opt.

M. Kolobov, ed., Quantum Imaging, (Springer Verlag, New York, 2007).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Phase-sensitive amplification and de-amplification gains for 3 signal modes (profiles shown on the left) with 1/e intensity radii a 0s=66 µm versus pump power; PSA crystal has d eff=6.5 pm/V and L=5.2 mm; signal wavelength is λ s =1064 nm, elliptical pump waists are a0px =141 µm, a0py =47 µm. (b)–(d) Grayscale text images before (b) and after phase-sensitive amplification (c) and de-amplification (d) for PSA with d eff=8.7 pm/V, L=2.5 cm, λs=1560 nm, a0px =440 µm, a0py =25 µm, image size ~470 µm×90 µm, and 10 kW pump power. Linear grayscales of (b) and (d) are the same, whereas the grayscale in (c) is normalized by the maximum intensity of (c), which is ~10 dB higher than that in (b).

Fig. 2.
Fig. 2.

Intensity of the text image before (a, b) and after (c, d, e) phase-sensitive amplification. Vertical scale is linear and is normalized by the peak intensity of the input image. (b) and (d) are the top views of (a) and (c), respectively. (e) is the front-side view of (c).

Fig. 3.
Fig. 3.

(a) Dependence of total power gain and brightest pixel gain on input phase detuning from -45°. (c) De-amplified text image. (b) Top view of (c). (d) Front-side view of (c).

Fig. 4.
Fig. 4.

(a) Intensity of the text image processed by the modified PSF (without the delta-function), i.e. amplified by transfer function (|µ|--1) in the spatial frequency domain; (b) and (c) are the top and front-side views of (a). Vertical scale is linear and is normalized by the peak intensity of the input image.

Fig. 5.
Fig. 5.

Same input image as that in Fig. 4, but processed by the complete PSF (with the delta-function), i.e. amplified by transfer function (|µ|-) in the spatial frequency domain; (b) and (c) are the top and front-side views of (a). Vertical scale is linear and is normalized by the peak intensity of the input image.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

Esρzz=i2ksρ2Esρz+iωsdeffnscEpρzEi*ρzeikz,
E˜qz=Eρzeiq·ρdρ,Eρz=E˜qzeiq·ρdq(2π)2·
E˜qz=E˜ q0 exp (iq22kz) ·
E˜sqz=μ(q)E˜s(q,0)+v(q)E˜i*(q,0),
μ(q)=(coshγziΔkeff2γsinhγz)×exp (iΔkeff2z)exp(iq22ksz),
v (q)=i κsγ sinh γz×exp (iΔkeff2z)exp(iq22ksz),
Δkeff=Δk+q22(1ks+1ki),
γ=κ2Δkeff24 ,
κ2=κsκi*=ωsωideff2Iρ(2ε0nsninρc3),κs,i=ωs,ideffEρ(ns,ic).
θsopt(q)=12{arg[E˜s(q˜,0)]+arg[E˜s(q,0)]}=θρ2+π4 +12 tan1 [Δkeff2γtanhγL] + 12 arg [sinhγLγ] .
GPSAopt=(μ+v)2
θsoptθp2+π4+ΔkL4+q24ksL,
Es(ρ,z)z=iκsEi* (ρ,z)eiΔkz.
μ(ρ,z)=(coshγzk2γsinhγz)×exp (iΔk2z),
v(ρ,z)=i κsγ sihh γz×exp (iΔk2z),
γ(ρ)=κ2(ρ)Δk24,κ2(ρ)=κsκi* =ωsωideff2Ip(ρ)2ε0nsninpc3,
Es(ρ,z)=μ (ρ,z)Es(ρ,0)+v(ρ,z)Ei*(ρ,0).
Δq=(4ks2κ1nL)14,
GPSAFig.5(ρ)GPSAFig.4(ρ)=2GPSAFig.4(ρ)Sin(ρ)+Sin(ρ)=2GPSAFig.5(ρ)Sin(ρ)Sin(ρ),

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