Abstract

A photorefractive frequency converter and phase-sensitive detector is proposed and demonstrated. Dynamic photorefractive theory is used to examine device characteristics for inputs from available types of spatial light modulator to determine which reference modulations are optimal for a given signal modulation. The output linearity is determined for pairs of signal and reference modulation types, and both spatial and temporal intensity variations are analyzed. Photorefractive response times are measured from the frequency-conversion bandwidth.

© 1993 Optical Society of America

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References

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  1. M. L. Meade, Lock-in Amplifiers: Principles and Applications, (Peregrinus, London, 1983).
  2. E. Parshall, M. Cronin-Golomb, “Phase-conjugate interferometric analysis of thin films,” Appl. Opt. 30, 5090 (1991).
    [CrossRef] [PubMed]
  3. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  4. J. F. Lam, “Spectral response of nearly degenerate four-wave mixing in photorefractive media,” Appl. Phys. Lett. 42, 153 (1983).
    [CrossRef]
  5. A. B. Carlson, Communication Systems: An Introduction to Signals and Noise Electrical Communication, 2nd ed. (McGraw-Hill, New York, 1975).
  6. M. Cronin-Golomb, “Analytical solution for photorefractive two beam coupling with time varying signal,” in Photorefractive Materials, Effects and Devices, Vol. 17 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), p. 142.
  7. J. M. Heaton, L. Salymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397 (1985).
    [CrossRef]
  8. N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
    [CrossRef]
  9. T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 77, 10 (1985).
  10. H. Kogelnik, “Coupled wave theory for thick hologram qratings,” Bell Syst. Tech. J. 48, 2909 (1969).
    [CrossRef]
  11. G. C. Valley, “Erase rates in photorefractive material with two photoactive species,” Appl. Opt. 22, 3160 (1983).
    [CrossRef]
  12. L. M. Bernardo, J. C. Lopes, O. D. Soares, “Hole–electron competition with fast and slow gratings in Bi12SiO20crystals,” Appl. Opt. 29, 12 (1990).
    [CrossRef] [PubMed]

1991

1990

1985

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 77, 10 (1985).

J. M. Heaton, L. Salymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397 (1985).
[CrossRef]

1984

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

1983

J. F. Lam, “Spectral response of nearly degenerate four-wave mixing in photorefractive media,” Appl. Phys. Lett. 42, 153 (1983).
[CrossRef]

G. C. Valley, “Erase rates in photorefractive material with two photoactive species,” Appl. Opt. 22, 3160 (1983).
[CrossRef]

1979

N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[CrossRef]

1969

H. Kogelnik, “Coupled wave theory for thick hologram qratings,” Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Bernardo, L. M.

Carlson, A. B.

A. B. Carlson, Communication Systems: An Introduction to Signals and Noise Electrical Communication, 2nd ed. (McGraw-Hill, New York, 1975).

Connors, L. M.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 77, 10 (1985).

Cronin-Golomb, M.

E. Parshall, M. Cronin-Golomb, “Phase-conjugate interferometric analysis of thin films,” Appl. Opt. 30, 5090 (1991).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

M. Cronin-Golomb, “Analytical solution for photorefractive two beam coupling with time varying signal,” in Photorefractive Materials, Effects and Devices, Vol. 17 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), p. 142.

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Foote, P. D.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 77, 10 (1985).

Hall, T. J.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 77, 10 (1985).

Heaton, J. M.

J. M. Heaton, L. Salymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397 (1985).
[CrossRef]

Jaura, R.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 77, 10 (1985).

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram qratings,” Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Kuktarev, N. V.

N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Lam, J. F.

J. F. Lam, “Spectral response of nearly degenerate four-wave mixing in photorefractive media,” Appl. Phys. Lett. 42, 153 (1983).
[CrossRef]

Lopes, J. C.

Markov, V. B.

N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Meade, M. L.

M. L. Meade, Lock-in Amplifiers: Principles and Applications, (Peregrinus, London, 1983).

Odulov, S. C.

N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Parshall, E.

Salymar, L.

J. M. Heaton, L. Salymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397 (1985).
[CrossRef]

Soares, O. D.

Soskin, M. S.

N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Valley, G. C.

Vinetskii, V. L.

N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. F. Lam, “Spectral response of nearly degenerate four-wave mixing in photorefractive media,” Appl. Phys. Lett. 42, 153 (1983).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram qratings,” Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Ferroelectrics

N. V. Kuktarev, V. B. Markov, S. C. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Opt. Acta

J. M. Heaton, L. Salymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397 (1985).
[CrossRef]

Prog. Quantum Electron.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 77, 10 (1985).

Other

M. L. Meade, Lock-in Amplifiers: Principles and Applications, (Peregrinus, London, 1983).

A. B. Carlson, Communication Systems: An Introduction to Signals and Noise Electrical Communication, 2nd ed. (McGraw-Hill, New York, 1975).

M. Cronin-Golomb, “Analytical solution for photorefractive two beam coupling with time varying signal,” in Photorefractive Materials, Effects and Devices, Vol. 17 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), p. 142.

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Figures (11)

Fig. 1
Fig. 1

Schematic illustrating the principle of phase-sensitive detection from a time-averaging point of view.

Fig. 2
Fig. 2

Experimental arrangement for frequency conversion and phase-sensitive detection: M3, mirror; BS’s, beam splitters.

Fig. 3
Fig. 3

(a) Top trace, oscilloscope trace of the result of mixing square phase modulation with square phase modulation. The peak-to-peak phase amplitudes result in phase-conjugate erasure. The horizontal axis is 20 ms/division. (b) Top trace, result of mixing the above square phase modulation with sine phase modulation. The peak-to-peak sine phase amplitude is 10.6 rad. The horizontal axis is 50 ms/division. The bottom traces are the electronic results.

Fig. 4
Fig. 4

Result of mixing two sine phase modulations. (a) Top trace, both inputs are modulated simultaneously with peak-to-peak phase amplitudes of 10.6 rad. (b) Top trace, one input is phase modulated with a peak-to-peak amplitude of 10.6 rad and the other with 5.3 rad. (c) Top trace, both inputs are modulated with peak-to-peak phase amplitudes of 5.3 rad. The horizontal axis in all cases is 100 ms/division. The bottom traces in all the cases are the electronic results.

Fig. 5
Fig. 5

Theoretical plots of the results shown in Fig. 4.

Fig. 6
Fig. 6

Oscilloscope traces of the result of frequency conversion between amplitude and phase modulation. Top trace, mixing between sinusoidal phase modulation and chopping amplitude modulation. Bottom trace, square phase modulation with chopper amplitude modulation. The horizontal axis is 50 ms/division.

Fig. 7
Fig. 7

Phase-sensitive detection measurement, operating with sine and square phase modulations with the respective peak-to-peak amplitudes of Fig. 3. The dots represent the measurements, and the solid curve is a plot of the theoretical results.

Fig. 8
Fig. 8

Phase-sensitive detection measurement, operating with two sine phase modulations with peak-to-peak amplitudes of 10.6 rad. Again the dots represent the experiment and the solid curve the theory.

Fig. 9
Fig. 9

Bandwidth curve for operation with two sinusoidal phase modulations.

Fig. 10
Fig. 10

Amplitude of the oscillating output phase conjugate as a function of the amplitude of a sine phase-modulated beam. The other input is a peak-to-peak constant-amplitude square phase modulation of Fig. 3.

Fig. 11
Fig. 11

Same plot as in Fig. 10 with a constant peak-to-peak amplitude sine-phase reference modulation of 10.6 rad.

Equations (57)

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E 1 ( t ) = A 1 ( t ) exp [ i ( k 1 · r - ω t ) ] ,
E 2 ( t ) = A 2 ( t ) exp [ i ( k 2 · r - ω t ) ] ,
E 4 ( t ) = A 4 ( t ) exp [ i ( k 4 · r - ω t ) ] .
A 3 ( t ) z = G ( t ) A 2 ( t ) ,
A 3 ( t ) = l G ( t ) A 2 ( t ) ,
I 0 = A 1 2 + A 2 2 + A 3 2 + A 4 2 = const . ,
G ( t ) t + G ( t ) τ = γ τ I 0 A 1 ( t ) A 4 * ( t ) ,
A 1 ( t ) = - S 1 ( ω 1 ) exp ( - i ω 1 t ) d ω 1 ,
A 4 ( t ) = - S 4 ( ω 2 ) exp ( - i ω 2 t ) d ω 2 .
G ( t ) t + G ( t ) τ = γ I 0 τ - - S 1 ( ω 1 ) S 4 * ( ω 2 ) exp [ - i ω 1 - ω 2 ) t ] d ω 1 d ω 2 .
A 3 ( t ) = A 3 ( t = 0 ) exp ( - t / τ ) + γ l A 2 I 0 τ × - - S 1 ( ω 1 ) S 4 * ( ω 2 ) exp [ - i ( ω 1 - ω 2 ) t ] - i ( ω 1 - ω 2 ) + 1 / τ d ω 1 d ω 2 .
A 1 ( t ) = A 1 exp [ - i δ 1 sin ( ω 1 t + ϕ 1 ) ] = A 1 - J n ( δ 1 ) exp [ - i n ( ω 1 t - ϕ 1 ) ] ,
A 4 ( t ) = A 4 exp [ - i δ 2 sin ( ω 2 t + ϕ 2 ) ] = A 4 - J m ( δ 2 ) exp [ - i m ( ω 2 t + ϕ 2 ) ] ,
A 3 ( t ) = γ A 1 A 4 I 0 τ l A 2 ( t ) n = - m = - { J n ( δ 1 ) J m ( δ 2 ) - i ( n ω 1 - m ω 2 ) + 1 / τ × exp [ - i ( n ω 1 - m ω 2 ) t ] exp [ - i ( n ϕ 1 - m ϕ 2 ) ] } ,
( n ω 1 - m ω 2 ) τ 1.
A 3 ( t ) = γ l A 2 A 1 A 4 I 0 τ × n = - { J n ( δ 1 ) J n ( δ 2 ) i n ( Δ ω ) + 1 / τ exp [ i n ( Δ ω t + Δ ϕ ) ] } ,
A 3 ( Δ ϕ ) = γ l A 2 A 1 A 4 I 0 n = - J n ( δ 1 ) J n ( δ 2 ) exp [ i n ( Δ ϕ ) ] ,
A 1 ( t ) = A 1 sin ( ω 1 t + ϕ 1 ) ,
A 4 ( t ) = A 4 exp [ - i δ 2 sin ( ω 2 t + ϕ 2 ) ] ,
A 3 ( t ) = γ l A 2 A 1 A 4 I 0 τ J 1 ( δ 2 ) cos [ ( Δ ω ) t + ( Δ ϕ ) + α ] [ ( Δ ω ) 2 + ( 1 / τ ) 2 ] 1 / 2 ,
α = - tan - 1 ( Δ ω ) τ .
A 3 ( Δ ϕ ) = γ l A 2 A 1 A 4 I 0 J 1 ( δ 2 ) cos ( Δ ϕ ) .
A 1 ( t ) = A 1 sin ( ω 1 t + ϕ 1 + π / 2 ) ,
A 3 ( Δ ϕ ) = γ l A 2 A 1 A 4 I 0 J 1 ( δ 2 ) sin ( Δ ϕ ) ,
A 1 ( t ) = 4 A 1 π m = 0 sin l ( ω 1 t + ϕ 1 ) l ,
A 4 ( t ) = A 4 exp [ - i δ 2 sin ( ω 2 t + ϕ 2 ) ] ,
A 3 ( t ) = 4 γ l A 2 A 1 A 4 - i π I 0 τ m = 0 J l ( δ 2 ) cos [ l ( Δ ω ) t + l ( Δ ϕ ) + α l ] l [ l 2 ( Δ ω ) 2 + ( 1 / τ ) 2 ] 1 / 2 ,
α l = - tan - 1 ( Δ ω ) l τ .
A 3 ( Δ ϕ ) = 4 γ l A 2 A 1 A 4 - i π I 0 m = 0 J l ( δ 2 ) l cos [ l ( Δ ϕ ) ] .
A 3 ( t ) = 8 γ l A 2 A 1 A 4 - i π I 0 τ m = 0 cos [ l ( Δ ω ) t + l ( Δ ϕ ) + α l ] l 2 [ l 2 ( Δ ω ) 2 + ( 1 / τ ) 2 ] 1 / 2 ,
α l = - tan - 1 ( Δ ω ) l τ .
A 3 ( Δ ϕ ) = 8 γ l A 2 A 1 A 4 - i π I 0 m = 0 cos [ l ( Δ ϕ ) ] l 2 = 2 G A 1 A 2 - i I 0 triangle ( Δ ϕ ) ,
A 3 = ( 1 + A E ) / 4 ,
A 3 ( t ) = 2 γ l A 2 A 1 A 4 - π I 0 τ cos [ ( Δ ω ) t + ( Δ ϕ ) + α ] [ ( Δ ω ) 2 + ( 1 / τ ) 2 ] 1 / 2 .
A 3 ( Δ ϕ ) = 2 γ l A 2 A 1 A 4 - π I 0 cos [ ( Δ ϕ ) + α ] .
G N ( t ) = G L + δ G .
G L = η A 1 ( t ) A 4 * ( t ) / I 0 ,
δ F t + G L + δ G τ 0 + δ τ ( t ) = G L I 0 τ I ,
δ G t + δ G τ = δ τ τ τ 0 G L ,
I = I 0 + δ I = I 0 [ 1 + 0.5 β cos ( 2 ω t ) ] ,
δ τ = - 0.5 τ 0 β cos ( 2 ω t ) ,
δ G / G L = - 0.5 β cos ( 2 ω t + γ ) [ ( 2 ω τ 0 ) 2 + 1 ] 1 / 2 β sin ( 2 ω t ) 4 ω τ 0 ,
γ = - tan - 1 ( 2 ω τ 0 ) - π / 2 ,
( 1 / τ ) = ( 1 / τ 1 ) + i ω g .
A 3 ( t ) = A 3 ( t = 0 ) exp [ ( - t / τ 1 ) + i ω g t ] + γ l A 2 I 0 ( 1 τ 1 + i ω g ) + - - S 1 ( ω 1 ) S 4 * ( ω 2 ) exp [ - i ( ω 1 - ω 2 ) t ] - i ( ω 1 - ω 2 + ω g ) + 1 / τ 1 d ω 1 d ω 2 .
A 3 ( t ) = γ l A 2 A 1 A 4 I 0 τ n = - τ J n ( δ 1 ) J n ( δ 2 ) exp ( - i n Δ ω t ) 1 - i n ( Δ ω ) τ ,
P 3 = 2 π A 3 2 r d r
I I p exp ( - u ) = I p exp [ - ( r / r p ) 2 ]
P 3 = π r p 2 I 3 p ,
τ = τ p exp ( r / r p ) 2 ,
η P P 3 P 2 = l 2 G M 2 0 exp ( - u ) | n = - J n ( δ 1 ) J n ( δ 2 ) 1 - i n ( Δ ω ) τ p exp ( u ) | 2 d u ,
G M = γ A 1 A 4 I 0 .
1 ( 1 - i n Δ ω τ p exp ( u ) ) ( 1 + i m Δ ω τ p exp ( u ) ) = n m + n 1 1 - i n Δ ω τ p exp ( u ) + m m + n 1 1 + i m Δ ω τ p exp ( u ) ,
η P = l 2 G M 2 m , n = - B n B m * × ( 1 + m i Δ ω τ p m + n C - n C m exp [ - i ( n - m ) Δ ω τ p ] ) ,
B m = J n ( δ 1 ) J n ( δ 2 ) ,
C m = ( 1 - 1 i n Δ ω τ p ) m 2 .
η P = l 2 G M 2 [ B 0 2 + 2 n = 1 B n 2 ( 1 - n Δ ω τ p tan - 1 1 n Δ ω τ p ) ]

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