Abstract

The interference between two optical fields with nonzero spectral linewidths forms multiple moving space-charge fields inside photoconductive semiconductors that contain deep-level donors and traps. The dc components of the photocurrents generated can be expressed in terms of a convolution of a function that is characteristic of the crystal and the signal optical power spectrum when the other optical field (local oscillator) has a negligible linewidth. This permits the recovery of the optical signal power spectrum.

© 1995 Optical Society of America

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References

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  1. F. M. Davidson, C. C. Wang, C. T. Field, S. Trivedi, Opt. Lett. 19, 478 (1994).
    [CrossRef] [PubMed]
  2. F. M. Davidson, C. C. Wang, S. Trivedi, Opt. Lett. 19, 778 (1994).
  3. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
    [CrossRef]
  4. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 10, p. 344.

1994 (2)

F. M. Davidson, C. C. Wang, C. T. Field, S. Trivedi, Opt. Lett. 19, 478 (1994).
[CrossRef] [PubMed]

F. M. Davidson, C. C. Wang, S. Trivedi, Opt. Lett. 19, 778 (1994).

1990 (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Davidson, F. M.

F. M. Davidson, C. C. Wang, C. T. Field, S. Trivedi, Opt. Lett. 19, 478 (1994).
[CrossRef] [PubMed]

F. M. Davidson, C. C. Wang, S. Trivedi, Opt. Lett. 19, 778 (1994).

Field, C. T.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 10, p. 344.

Petrov, M. P.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Sokolov, I. A.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Stepanov, S. I.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Trivedi, S.

F. M. Davidson, C. C. Wang, C. T. Field, S. Trivedi, Opt. Lett. 19, 478 (1994).
[CrossRef] [PubMed]

F. M. Davidson, C. C. Wang, S. Trivedi, Opt. Lett. 19, 778 (1994).

Trofimov, G. S.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Wang, C. C.

F. M. Davidson, C. C. Wang, C. T. Field, S. Trivedi, Opt. Lett. 19, 478 (1994).
[CrossRef] [PubMed]

F. M. Davidson, C. C. Wang, S. Trivedi, Opt. Lett. 19, 778 (1994).

J. Appl. Phys. (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, J. Appl. Phys. 68, 2216 (1990).
[CrossRef]

Opt. Lett. (2)

F. M. Davidson, C. C. Wang, C. T. Field, S. Trivedi, Opt. Lett. 19, 478 (1994).
[CrossRef] [PubMed]

F. M. Davidson, C. C. Wang, S. Trivedi, Opt. Lett. 19, 778 (1994).

Other (1)

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 10, p. 344.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for the detection of photocurrents generated by moving space-charge fields. B.S.’s, beam splitters; LWE 120, LWE 122, Lightwave Electronics Series 120 and 122 nonplanar Nd:YAG ring lasers; PLL, phase-locked loop; E-O, electro-optic.

Fig. 2
Fig. 2

dc photocurrents versus carrier frequency offset, fLOfS, for the signal spectrum shown in Fig. 3. The grating spacing was Λ = 44.7 μ m, and the optical power levels were PLO = 56.9 mW/cm2, PS = 36.9 μW/cm2. The modulation frequency was fm = 496.1 kHz, and the amplitude was 2.39 rad.

Fig. 3
Fig. 3

Deduced signal spectrum from the deconvolution of the impulse response of the crystal and the experimental data shown in Fig. 2. The resolution bandwidth, which was approximately 8 kHz, was limited by the frequency spacing between two adjacent samples.

Equations (9)

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E tot ( r , t ) 2 = E LO 2 + E S 0 2 + ( E LO * E S 0 exp { j [ ( k LO - k S ) r - ω D t ] } × exp [ j Δ ϕ ( t ) ] + c . c . ) ,
d E sc T ( t ) d t + E sc T ( t ) τ g = - j E D τ M ( 1 + E D / E M ) m T ( t ) ,
j Σ T ( t ) = j m 0 2 σ 0 E D 4 ( 1 + E D / E M ) ( 1 + E D / E q ) 1 2 π × [ - d ω 1 + j ( ω D - ω ) τ g × ( - T T exp [ - j ω ( t - t ) ] × exp { j [ Δ ϕ ( t ) - Δ ϕ ( t ) ] } d t ) - c . c . ] ,
j Σ , DC T = j m 0 2 σ 0 E D 4 ( 1 + E D / E M ) ( 1 + E D / E q ) 1 2 π × ( - d ω 1 + j ( ω D - ω ) τ g × { 1 2 T - T T - T T R S ( t - t ) R LO * ( t - t ) × exp [ - j ω ( t - t ) d t d t } - c . c . ) ,
j Σ , DC = lim T j Σ , DC T = 2 σ 0 E D / ( P S + P LO ) 2 ( 1 + E D / E M ) ( 1 + E D / E q ) × - S beat ( ω ) ( ω D - ω ) τ g 1 + ( ω D - ω ) 2 τ g 2 d ω ,
j Σ , DC ( ω D ) = 2 σ 0 E D P LO / ( P S + P LO ) 2 ( 1 + E D / E M ) ( 1 + E D / E q ) × - S S ( ω ) ( ω D - ω ) τ g 1 + ( ω D - ω ) 2 τ g 2 d ω ,
T CR ( ω ) 2 σ 0 E D P LO / ( P S + P LO ) 2 ( 1 + E D / E M ) ( 1 + E D / E q ) ω τ g 1 + ( ω τ g ) 2 ,
j Σ ( t ) = lim T j Σ T ( t ) = σ 0 E D 2 ( 1 + E D / E M ) ( 1 + E D / E q ) × { i m i 2 ( ω D - ω S i ) τ g 1 + [ ( ω D - ω S i ) τ g 2 + j 2 i j m i m j * exp ( j ω i j t ) × [ 1 1 + j ( ω D - ω S j ) τ g - 1 1 - j ( ω D - ω S i ) τ g ] } ,
j Σ ( t ) = m 0 2 σ 0 E D J 0 ( Δ ) J 1 ( Δ ) 2 ( 1 + E D / E M ) ( 1 + E D / E q ) × [ j ω m τ g 1 - j ω m τ g exp ( - j ω m t ) - j ω m τ g 1 + j ω m τ g exp ( j ω m t ) ] ,

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