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.

[Optical Society of America ]

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. B. I. Sturman , Interaction of two light waves in a crystal caused by photoelectron diffusion and drift , Sov. Phys. Tech. Phys. SPTPA3 23 , 589 ( 1978
  2. L. Dai , C. Gu , and P. Yeh , Effect of position-dependent time constant on photorefractive two-wave mixing , J. Opt. Soc. Am. B JOBPDE 9 , 1693 ( 1992
    [CrossRef]
  3. Ph. Delaye , L. A. De Montmorillon , and G. Roosen , Transmission of time modulated optical signals through an absorbing photorefractive crystal , Opt. Commun. OPCOB8 118 , 154 ( 1995
    [CrossRef]
  4. 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. IEJQA7 28 , 750 ( 1992
    [CrossRef]
  5. D. Fluck , S. Brulisauer , and P. Gunter , Photorefractive two-wave mixing with focused Gaussian beams , Opt. Commun. OPCOB8 115 , 626 ( 1995
    [CrossRef]
  6. L. Boutsikaris and F. Davidson , Two-wave mixing of time-varying non-plane-wave optical fields in photorefractive materials , Appl. Opt. APOPAI 32 , 1559 ( 1993
    [CrossRef] [PubMed]
  7. L. Solymar , D. J. Webb , and A. Grunnet-Jepsen , Forward wave interactions in photorefractive materials , Prog. Quantum Electron. PQUEAH 18 , 377 ( 1994
    [CrossRef]
  8. G. Brost , Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO , Opt. Commun. OPCOB8 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]
  9. S. Odoulov , A. Shumelyuk , G. Brost , and K. Magde , Enhancement of beam coupling in the near infrared for tin hypothiodiphosphate , Appl. Phys. Lett. APPLAB 69 , 3665 ( 1996
    [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. IEJQA7 28 , 750 ( 1992
[CrossRef]

Dai, L

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. IEJQA7 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. APPLAB 69 , 3665 ( 1996
[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. APPLAB 69 , 3665 ( 1996
[CrossRef]

Other (9)

B. I. Sturman , Interaction of two light waves in a crystal caused by photoelectron diffusion and drift , Sov. Phys. Tech. Phys. SPTPA3 23 , 589 ( 1978

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

Ph. Delaye , L. A. De Montmorillon , and G. Roosen , Transmission of time modulated optical signals through an absorbing photorefractive crystal , Opt. Commun. OPCOB8 118 , 154 ( 1995
[CrossRef]

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. IEJQA7 28 , 750 ( 1992
[CrossRef]

D. Fluck , S. Brulisauer , and P. Gunter , Photorefractive two-wave mixing with focused Gaussian beams , Opt. Commun. OPCOB8 115 , 626 ( 1995
[CrossRef]

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

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

G. Brost , Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO , Opt. Commun. OPCOB8 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]

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

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

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 ) ] } ,

Metrics