Abstract

The photorefractive recording dynamics of two-beam coupling in semi-insulating semiconductors by beams with slightly different frequencies are studied theoretically and experimentally. The influences of bulk absorption, Gaussian beam profiles, and experimental geometry on the temporal response are analyzed. These effects act to narrow the bandwidth. Measurement of the material photorefractive time constant is discussed.

© 1998 Optical Society of America

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References

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  1. B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).
  2. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  3. L. Dai, C. Gu, and P. Yeh, “Effect of position-dependent time constant on photorefractive two-wave mixing,” J. Opt. Soc. Am. B 9, 1693 (1992).
    [Crossref]
  4. Ph. Delaye, L. A. De Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154 (1995).
    [Crossref]
  5. A. Hermanns, C. Benkert, D. M. Lininger, and D. A. Anderson, “The transfer function and impulse response of photorefractive two-beam coupling,” IEEE J. Quantum Electron. 28, 750 (1992).
    [Crossref]
  6. D. Fluck, S. Brulisauer, and P. Gunter, “Photorefractive two-wave mixing with focused Gaussian beams,” Opt. Commun. 115, 626 (1995).
    [Crossref]
  7. L. Boutsikaris and F. Davidson, “Two-wave mixing of time-varying non-plane-wave optical fields in photorefractive materials,” Appl. Opt. 32, 1559 (1993).
    [Crossref] [PubMed]
  8. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, “Forward wave interactions in photorefractive materials,” Prog. Quantum Electron. 18, 377 (1994).
    [Crossref]
  9. F. Vachss, “An analytical expression for the photorefractive two beam coupling response time,” presented at the meeting on Photorefractive Materials, Effects, and Devices, cosponsored by the Optical Society of America and Societe Francaise D’Optique, 1990.
  10. G. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993). (Note that the analysis presented here is for an applied field but that for m=1 the results for no applied field are similar.)
    [Crossref]
  11. S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665 (1996).
    [Crossref]

1996 (1)

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665 (1996).
[Crossref]

1995 (2)

Ph. Delaye, L. A. De Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154 (1995).
[Crossref]

D. Fluck, S. Brulisauer, and P. Gunter, “Photorefractive two-wave mixing with focused Gaussian beams,” Opt. Commun. 115, 626 (1995).
[Crossref]

1994 (1)

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, “Forward wave interactions in photorefractive materials,” Prog. Quantum Electron. 18, 377 (1994).
[Crossref]

1993 (2)

G. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993). (Note that the analysis presented here is for an applied field but that for m=1 the results for no applied field are similar.)
[Crossref]

L. Boutsikaris and F. Davidson, “Two-wave mixing of time-varying non-plane-wave optical fields in photorefractive materials,” Appl. Opt. 32, 1559 (1993).
[Crossref] [PubMed]

1992 (2)

A. Hermanns, C. Benkert, D. M. Lininger, and D. A. Anderson, “The transfer function and impulse response of photorefractive two-beam coupling,” IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

L. Dai, C. Gu, and P. Yeh, “Effect of position-dependent time constant on photorefractive two-wave mixing,” J. Opt. Soc. Am. B 9, 1693 (1992).
[Crossref]

1978 (1)

B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).

Anderson, D. A.

A. Hermanns, C. Benkert, D. M. Lininger, and D. A. Anderson, “The transfer function and impulse response of photorefractive two-beam coupling,” IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

Benkert, C.

A. Hermanns, C. Benkert, D. M. Lininger, and D. A. Anderson, “The transfer function and impulse response of photorefractive two-beam coupling,” IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

Boutsikaris, L.

Brost, G.

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665 (1996).
[Crossref]

G. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993). (Note that the analysis presented here is for an applied field but that for m=1 the results for no applied field are similar.)
[Crossref]

Brulisauer, S.

D. Fluck, S. Brulisauer, and P. Gunter, “Photorefractive two-wave mixing with focused Gaussian beams,” Opt. Commun. 115, 626 (1995).
[Crossref]

Dai, L.

Davidson, F.

De Montmorillon, L. A.

Ph. Delaye, L. A. De Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154 (1995).
[Crossref]

Delaye, Ph.

Ph. Delaye, L. A. De Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154 (1995).
[Crossref]

Fluck, D.

D. Fluck, S. Brulisauer, and P. Gunter, “Photorefractive two-wave mixing with focused Gaussian beams,” Opt. Commun. 115, 626 (1995).
[Crossref]

Grunnet-Jepsen, A.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, “Forward wave interactions in photorefractive materials,” Prog. Quantum Electron. 18, 377 (1994).
[Crossref]

Gu, C.

Gunter, P.

D. Fluck, S. Brulisauer, and P. Gunter, “Photorefractive two-wave mixing with focused Gaussian beams,” Opt. Commun. 115, 626 (1995).
[Crossref]

Hermanns, A.

A. Hermanns, C. Benkert, D. M. Lininger, and D. A. Anderson, “The transfer function and impulse response of photorefractive two-beam coupling,” IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

Lininger, D. M.

A. Hermanns, C. Benkert, D. M. Lininger, and D. A. Anderson, “The transfer function and impulse response of photorefractive two-beam coupling,” IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

Magde, K.

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665 (1996).
[Crossref]

Odoulov, S.

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665 (1996).
[Crossref]

Roosen, G.

Ph. Delaye, L. A. De Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154 (1995).
[Crossref]

Shumelyuk, A.

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665 (1996).
[Crossref]

Solymar, L.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, “Forward wave interactions in photorefractive materials,” Prog. Quantum Electron. 18, 377 (1994).
[Crossref]

Sturman, B. I.

B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).

Vachss, F.

F. Vachss, “An analytical expression for the photorefractive two beam coupling response time,” presented at the meeting on Photorefractive Materials, Effects, and Devices, cosponsored by the Optical Society of America and Societe Francaise D’Optique, 1990.

Webb, D. J.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, “Forward wave interactions in photorefractive materials,” Prog. Quantum Electron. 18, 377 (1994).
[Crossref]

Yeh, P.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Odoulov, A. Shumelyuk, G. Brost, and K. Magde, “Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate,” Appl. Phys. Lett. 69, 3665 (1996).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Hermanns, C. Benkert, D. M. Lininger, and D. A. Anderson, “The transfer function and impulse response of photorefractive two-beam coupling,” IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

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

Opt. Commun. (3)

Ph. Delaye, L. A. De Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154 (1995).
[Crossref]

D. Fluck, S. Brulisauer, and P. Gunter, “Photorefractive two-wave mixing with focused Gaussian beams,” Opt. Commun. 115, 626 (1995).
[Crossref]

G. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993). (Note that the analysis presented here is for an applied field but that for m=1 the results for no applied field are similar.)
[Crossref]

Prog. Quantum Electron. (1)

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, “Forward wave interactions in photorefractive materials,” Prog. Quantum Electron. 18, 377 (1994).
[Crossref]

Sov. Phys. Tech. Phys. (1)

B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).

Other (2)

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

F. Vachss, “An analytical expression for the photorefractive two beam coupling response time,” presented at the meeting on Photorefractive Materials, Effects, and Devices, cosponsored by the Optical Society of America and Societe Francaise D’Optique, 1990.

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Figures (14)

Fig. 1
Fig. 1

Gain spectra for three values of α L .

Fig. 2
Fig. 2

Schematic of the beam coupling interaction: PRC, photorefractive crystal.

Fig. 3
Fig. 3

Calculated gain spectra for different crossing angles. Parameters were q = 1 , α = 1.2   cm - 1 , d = 0.6   cm , 2 ω S = 2   mm , 2 ω P = 2   mm , and ξ = 1 / 2 .

Fig. 4
Fig. 4

Calculated gain spectra for several pump beam sizes. Parameters were q = 1 , α = 1.2   cm - 1 , d = 0.6   cm , 2 ω S = 2   mm , 2 θ = 25 ° , and ξ = 1 / 2 .

Fig. 5
Fig. 5

Calculated gain spectra for three beam crossing locations. Parameters were q = 1 , α = 1.2   cm - 1 , d = 0.6   cm , 2 ω S = 2   mm , 2 ω P = 6   mm , and 2 θ = 25 ° .

Fig. 6
Fig. 6

Calculated gain spectra for three values of modulation m .

Fig. 7
Fig. 7

Configuration for the measurement of frequency and time responses of two-beam coupling: M1–M4, mirrors; λ / 2 , half-wave plate; pol, linear polarizer; BS, beam splitter; EOM, electro-optic phase modulator; BE, variable beam expander; S, mechanical shutter; PD, photodetector; ND, neutral-density filters.

Fig. 8
Fig. 8

Temporal response of the GaAs: Cr sample. 1 / e 2 beam diameters, 2.0 mm (pump) and 1.8 mm (signal). Spatially averaged beam intensities are I pump = 1.55   W / cm 2 and I signal = 2.4   mW / cm 2 . (a) Frequency response. Solid curve, fit to the absorption model; dashed curve, fit to a Lorentzian. (b) Time response. The curve is a fit to a single-exponential growth model.

Fig. 9
Fig. 9

Temporal response of the GaAs: Cr sample. 1 / e 2 beam diameters, 6.0 mm (pump) and 1.8 mm (signal). Spatially averaged beam intensities are I pump = 172   mW / cm 2 and I signal = 2.4   mW / cm 2 . (a) Frequency response. Solid curve, fit to the absorption model; dashed curve, fit to a Lorentzian. (b) Time response. The curve is a fit to a single-exponential growth model.

Fig. 10
Fig. 10

Temporal response of the GaAs: Cr sample. 1 / e 2 beam diameters, 10.7 mm (pump) and 1.8 mm (signal). Spatially averaged beam intensities are I pump = 54   mW / cm 2 and I signal = 2.4   mW / cm 2 . (a) Frequency response. Solid curve fit to the absorption model; dashed curve fit to a Lorentzian. (b) Time response. The curve is a fit to a single-exponential growth model.

Fig. 11
Fig. 11

Temporal response of the GaAs: Cr sample in the presence of a flood beam. 1 / e 2 beam diameters, 2.0 mm (pump), 1.8 mm (signal), and 13.0 mm (flood). Spatially averaged beam intensities are I pump = 1.55   W / cm 2 , I signal = 2.4   mW / cm 2 , and I flood = 142   mW / cm 2 . (a) Frequency response. Solid curve, fit to the absorption model; dashed curve, fit to a Lorentzian. (b) Time response. The curve is a fit to a single-exponential growth model.

Fig. 12
Fig. 12

Temporal response of the GaAS: Cr sample in the presence of a flood beam. 1 / e 2 beam diameters, 6.0 mm (pump), 1.8 mm (signal), and 13.0 mm (flood). Spatially averaged beam intensities are I pump = 172   mW / cm 2 , I flood = 142   mW / cm 2 . (a) Frequency response. Solid curve, fit to the absorption model; dashed curve, fit to a Lorentzian. (b) Time response. The curve is a fit to a single-exponential growth model.

Fig. 13
Fig. 13

Temporal response of the GaAs: Cr sample in the presence of a flood beam. 1 / e 2 beam diameters, 10.7 mm (pump) and 1.8 mm (signal). Spatially averaged beam intensities are I pump = 54   mW / cm 2 , I signal = 2.4   mW / cm 2 and I flood = 48   mW / cm 2 . (a) Frequency response. Solid curve, fit to the absorption model; dashed curve, fit to a Lorentzian. (b) Time response. The curve is a fit to a single-exponential growth model.

Fig. 14
Fig. 14

Fit of the data of Fig. 10(a) to the absorption coeff- icient parameter held constant at its known value of 1.2 cm - 1 .

Equations (9)

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Γ = Γ 0 [ 1 - exp ( - t / τ ) ] ,
Γ = Γ 0 / ( 1 + Ω 2 τ 2 ) ,
τ ( z ) = τ 0 [ I 0 / I ( z ) ] q = τ 0   exp ( q α z ) ,
Γ = 1 L   0 L   Γ 0 1 + Ω 2 τ 2 ( z )   d z ,
Γ = Γ 0 = 1 + 1 2 q α L   ln 1 + Ω 2 τ 0 2 1 + Ω 2 τ 0 2   exp ( 2 q α L ) .
I S ( x ,   y ,   z ) = I S 0   exp - 2 ( x 2 + y 2 ) ω S 2 exp ( - α z ) ,
I S ( x ,   y ,   z ) = I S 0   exp - 2 ( x 2 + y 2 ) ω P 2 exp ( - α z ) ,
Γ = Γ 0 2   cos ( θ ) π ω S 2 d   - ξ d cos ( θ ) ( 1 - ξ ) d cos ( θ ) - - × exp - 2 ( x 2 + y 2 ) ω S 2 d y d x d z 1 + Ω 2 + τ 0 2   exp 2 q α - sin ( 2 θ ) x + cos ( 2 θ ) y + ζ d cos ( θ ) exp 4 [ cos ( 2 θ ) x + sin ( 2 θ ) z ] 2 + 4 y 2 ω P 2 .
I sig ( z = d / cos   θ ;   pump on ) I sig ( z = d / cos   θ ;   pump off ) = exp [ - Γ ( t ) d / cos   θ ] = exp { C [ 1 - exp ( - t / τ ) ] } ,

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