Abstract

In earlier work, the transient response of a four-wave optical phase conjugator was studied. Here we study the inverse problem, namely: How must we tailor the input pulse in order to obtain a prescribed conjugator output? We find that an arbitrarily short output pulse can be obtained and show how the input, or probe, must be programmed in order to achieve this result.

© 1983 Optical Society of America

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  1. T. R. O'Meara and A. Yariv, "Time-domain signal processing via four-wave mixing in nonlinear delay lines," Opt. Eng. 21, 237–242 (1982).
  2. R. A. Fisher, B. R. Suydam, and B. J. Feldman, "Transient analysis of Kerr-like phase conjugation using frequency domain techniques," Phys. Rev. A. 23, 3071–3083 (1981).
  3. R. W. Hellwarth, "Generation of time-reversed wavefronts by nonlinear refraction," J. Opt. Soc. Am. 67, 1–3 (1977).
  4. D. L. Bobroff and H. A. Haus, "Impulse response of active coupled wave systems," J. Appl. Phys. 38, pp. 390–403 (1967).
  5. D. M. Pepper and R. L. Abrams, "Narrow optical bandpass filter via nearly degenerate four-wave mixing," Opt. Lett. 3, 212–214 (1978).
  6. J. H. Marburger, "Optical pulse integration and chirp reversal in degenerate four-wave mixing," Appl. Phys. Lett. 32, 372–374 (1978).
  7. D. L. Bobroff, "Coupled-modes analysis of the phonon–photon parametric backward-wave oscillator," J. Appl. Phys. 36, 1760–1769 (1965).
  8. J. H. Marburger and R. Shockley, "Nonresonant chirp compensation with counterpropagating optical pulses," Appl. Phys. Lett. 30, 441–443 (1977).
  9. A. Yariv, D. Fekete, and D. M. Pepper, "Compensation for channel dispersion by nonlinear optical phase conjugation," Opt. Lett. 4, 52–54 (1979).
  10. W. W. Rigrod, R. A. Fisher, and B. J. Feldman, "Transient analysis of nearly degenerate four-wave mixing," Opt. Lett. 5, 105–107 (1980).
  11. B. Ya. Zel'dovich, M. A. Orlova, and V. V. Shkunov, "Nonstationary theory and calculation of the time of establishment of four-wave wavefront reversal," Dokl. Akad. Nauk SSSR 252, 592–594 (1980) [Sov. Phys. Dokl. 25, 390–391 (1980)].
  12. R. C. Shockley, "Simplified theory of the impulse response of an optical degenerate four-wave mixing cell," Opt. Commun. 39, 221–224 (1981).
  13. S. A. Shakir, "Zero area optical pulse processing by degenerate four-wave mixing," Opt. Commun. 40, 151–155 (1981).
  14. B. R. Suydam and R. A. Fisher, "Transient response of Kerr-like conjugators: a review," Opt. Eng. 21, 184–189 (1982). For a preliminary version of the present paper, see B. R. Suydam, "Can optical phase conjugators produce a very short conjugate pulse," in Proceedings of the International Conference on Lasers '80, C. B. Collins, ed. (STS, McLean, Va., 1981), pp. 319–322.
  15. Studies of the transient response of four-wave conjugators all show that the output pulse is not truly the phase conjugate of a transient probe signal. For example, chirp reversal is inevitably imperfect.2,6 Nevertheless, we call the four-wave mixing device a phase conjugator for convenience and because it can produce healing in the sense of phase-front reversal.
  16. Mathematically stated, the input envelope must belong to L2, that is, if F(t) represent this envelope, then the integral [equation] must converge.
  17. N. Wiener, The Fourier Integral and Certain of Its Applications (Dover, New York, 1958). For the definition and elementary properties of almost periodic functions, see the section starting on p. 185. For a more complete work, see A. S. Besicovitch, Almost Periodic Functions (Cambridge U. Press, Cambridge, 1932).
  18. D. A. B. Miller, "Time reversal of optical pulses by four-wave mixing," Opt. Lett. 5, 300–302 (1980).

1982 (1)

T. R. O'Meara and A. Yariv, "Time-domain signal processing via four-wave mixing in nonlinear delay lines," Opt. Eng. 21, 237–242 (1982).

1981 (3)

R. A. Fisher, B. R. Suydam, and B. J. Feldman, "Transient analysis of Kerr-like phase conjugation using frequency domain techniques," Phys. Rev. A. 23, 3071–3083 (1981).

R. C. Shockley, "Simplified theory of the impulse response of an optical degenerate four-wave mixing cell," Opt. Commun. 39, 221–224 (1981).

S. A. Shakir, "Zero area optical pulse processing by degenerate four-wave mixing," Opt. Commun. 40, 151–155 (1981).

1980 (3)

B. Ya. Zel'dovich, M. A. Orlova, and V. V. Shkunov, "Nonstationary theory and calculation of the time of establishment of four-wave wavefront reversal," Dokl. Akad. Nauk SSSR 252, 592–594 (1980) [Sov. Phys. Dokl. 25, 390–391 (1980)].

W. W. Rigrod, R. A. Fisher, and B. J. Feldman, "Transient analysis of nearly degenerate four-wave mixing," Opt. Lett. 5, 105–107 (1980).

D. A. B. Miller, "Time reversal of optical pulses by four-wave mixing," Opt. Lett. 5, 300–302 (1980).

1979 (1)

1978 (2)

D. M. Pepper and R. L. Abrams, "Narrow optical bandpass filter via nearly degenerate four-wave mixing," Opt. Lett. 3, 212–214 (1978).

J. H. Marburger, "Optical pulse integration and chirp reversal in degenerate four-wave mixing," Appl. Phys. Lett. 32, 372–374 (1978).

1977 (2)

J. H. Marburger and R. Shockley, "Nonresonant chirp compensation with counterpropagating optical pulses," Appl. Phys. Lett. 30, 441–443 (1977).

R. W. Hellwarth, "Generation of time-reversed wavefronts by nonlinear refraction," J. Opt. Soc. Am. 67, 1–3 (1977).

1967 (1)

D. L. Bobroff and H. A. Haus, "Impulse response of active coupled wave systems," J. Appl. Phys. 38, pp. 390–403 (1967).

1965 (1)

D. L. Bobroff, "Coupled-modes analysis of the phonon–photon parametric backward-wave oscillator," J. Appl. Phys. 36, 1760–1769 (1965).

Abrams, R. L.

Bobroff, D. L.

D. L. Bobroff and H. A. Haus, "Impulse response of active coupled wave systems," J. Appl. Phys. 38, pp. 390–403 (1967).

D. L. Bobroff, "Coupled-modes analysis of the phonon–photon parametric backward-wave oscillator," J. Appl. Phys. 36, 1760–1769 (1965).

Fekete, D.

Feldman, B. J.

R. A. Fisher, B. R. Suydam, and B. J. Feldman, "Transient analysis of Kerr-like phase conjugation using frequency domain techniques," Phys. Rev. A. 23, 3071–3083 (1981).

W. W. Rigrod, R. A. Fisher, and B. J. Feldman, "Transient analysis of nearly degenerate four-wave mixing," Opt. Lett. 5, 105–107 (1980).

Fisher, R. A.

R. A. Fisher, B. R. Suydam, and B. J. Feldman, "Transient analysis of Kerr-like phase conjugation using frequency domain techniques," Phys. Rev. A. 23, 3071–3083 (1981).

W. W. Rigrod, R. A. Fisher, and B. J. Feldman, "Transient analysis of nearly degenerate four-wave mixing," Opt. Lett. 5, 105–107 (1980).

B. R. Suydam and R. A. Fisher, "Transient response of Kerr-like conjugators: a review," Opt. Eng. 21, 184–189 (1982). For a preliminary version of the present paper, see B. R. Suydam, "Can optical phase conjugators produce a very short conjugate pulse," in Proceedings of the International Conference on Lasers '80, C. B. Collins, ed. (STS, McLean, Va., 1981), pp. 319–322.

Haus, H. A.

D. L. Bobroff and H. A. Haus, "Impulse response of active coupled wave systems," J. Appl. Phys. 38, pp. 390–403 (1967).

Hellwarth, R. W.

Marburger, J. H.

J. H. Marburger, "Optical pulse integration and chirp reversal in degenerate four-wave mixing," Appl. Phys. Lett. 32, 372–374 (1978).

J. H. Marburger and R. Shockley, "Nonresonant chirp compensation with counterpropagating optical pulses," Appl. Phys. Lett. 30, 441–443 (1977).

Miller, D. A. B.

O’Meara, T. R.

T. R. O'Meara and A. Yariv, "Time-domain signal processing via four-wave mixing in nonlinear delay lines," Opt. Eng. 21, 237–242 (1982).

Orlova, M. A.

B. Ya. Zel'dovich, M. A. Orlova, and V. V. Shkunov, "Nonstationary theory and calculation of the time of establishment of four-wave wavefront reversal," Dokl. Akad. Nauk SSSR 252, 592–594 (1980) [Sov. Phys. Dokl. 25, 390–391 (1980)].

Pepper, D. M.

Rigrod, W. W.

Shakir, S. A.

S. A. Shakir, "Zero area optical pulse processing by degenerate four-wave mixing," Opt. Commun. 40, 151–155 (1981).

Shkunov, V. V.

B. Ya. Zel'dovich, M. A. Orlova, and V. V. Shkunov, "Nonstationary theory and calculation of the time of establishment of four-wave wavefront reversal," Dokl. Akad. Nauk SSSR 252, 592–594 (1980) [Sov. Phys. Dokl. 25, 390–391 (1980)].

Shockley, R.

J. H. Marburger and R. Shockley, "Nonresonant chirp compensation with counterpropagating optical pulses," Appl. Phys. Lett. 30, 441–443 (1977).

Shockley, R. C.

R. C. Shockley, "Simplified theory of the impulse response of an optical degenerate four-wave mixing cell," Opt. Commun. 39, 221–224 (1981).

Suydam, B. R.

R. A. Fisher, B. R. Suydam, and B. J. Feldman, "Transient analysis of Kerr-like phase conjugation using frequency domain techniques," Phys. Rev. A. 23, 3071–3083 (1981).

B. R. Suydam and R. A. Fisher, "Transient response of Kerr-like conjugators: a review," Opt. Eng. 21, 184–189 (1982). For a preliminary version of the present paper, see B. R. Suydam, "Can optical phase conjugators produce a very short conjugate pulse," in Proceedings of the International Conference on Lasers '80, C. B. Collins, ed. (STS, McLean, Va., 1981), pp. 319–322.

Wiener, N.

N. Wiener, The Fourier Integral and Certain of Its Applications (Dover, New York, 1958). For the definition and elementary properties of almost periodic functions, see the section starting on p. 185. For a more complete work, see A. S. Besicovitch, Almost Periodic Functions (Cambridge U. Press, Cambridge, 1932).

Yariv, A.

T. R. O'Meara and A. Yariv, "Time-domain signal processing via four-wave mixing in nonlinear delay lines," Opt. Eng. 21, 237–242 (1982).

A. Yariv, D. Fekete, and D. M. Pepper, "Compensation for channel dispersion by nonlinear optical phase conjugation," Opt. Lett. 4, 52–54 (1979).

Zel’dovich, B. Ya.

B. Ya. Zel'dovich, M. A. Orlova, and V. V. Shkunov, "Nonstationary theory and calculation of the time of establishment of four-wave wavefront reversal," Dokl. Akad. Nauk SSSR 252, 592–594 (1980) [Sov. Phys. Dokl. 25, 390–391 (1980)].

Appl. Phys. Lett. (2)

J. H. Marburger, "Optical pulse integration and chirp reversal in degenerate four-wave mixing," Appl. Phys. Lett. 32, 372–374 (1978).

J. H. Marburger and R. Shockley, "Nonresonant chirp compensation with counterpropagating optical pulses," Appl. Phys. Lett. 30, 441–443 (1977).

Dokl. Akad. Nauk SSSR (1)

B. Ya. Zel'dovich, M. A. Orlova, and V. V. Shkunov, "Nonstationary theory and calculation of the time of establishment of four-wave wavefront reversal," Dokl. Akad. Nauk SSSR 252, 592–594 (1980) [Sov. Phys. Dokl. 25, 390–391 (1980)].

J. Appl. Phys. (2)

D. L. Bobroff, "Coupled-modes analysis of the phonon–photon parametric backward-wave oscillator," J. Appl. Phys. 36, 1760–1769 (1965).

D. L. Bobroff and H. A. Haus, "Impulse response of active coupled wave systems," J. Appl. Phys. 38, pp. 390–403 (1967).

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

R. C. Shockley, "Simplified theory of the impulse response of an optical degenerate four-wave mixing cell," Opt. Commun. 39, 221–224 (1981).

S. A. Shakir, "Zero area optical pulse processing by degenerate four-wave mixing," Opt. Commun. 40, 151–155 (1981).

Opt. Eng. (1)

T. R. O'Meara and A. Yariv, "Time-domain signal processing via four-wave mixing in nonlinear delay lines," Opt. Eng. 21, 237–242 (1982).

Opt. Lett. (4)

Phys. Rev. A. (1)

R. A. Fisher, B. R. Suydam, and B. J. Feldman, "Transient analysis of Kerr-like phase conjugation using frequency domain techniques," Phys. Rev. A. 23, 3071–3083 (1981).

Other (4)

B. R. Suydam and R. A. Fisher, "Transient response of Kerr-like conjugators: a review," Opt. Eng. 21, 184–189 (1982). For a preliminary version of the present paper, see B. R. Suydam, "Can optical phase conjugators produce a very short conjugate pulse," in Proceedings of the International Conference on Lasers '80, C. B. Collins, ed. (STS, McLean, Va., 1981), pp. 319–322.

Studies of the transient response of four-wave conjugators all show that the output pulse is not truly the phase conjugate of a transient probe signal. For example, chirp reversal is inevitably imperfect.2,6 Nevertheless, we call the four-wave mixing device a phase conjugator for convenience and because it can produce healing in the sense of phase-front reversal.

Mathematically stated, the input envelope must belong to L2, that is, if F(t) represent this envelope, then the integral [equation] must converge.

N. Wiener, The Fourier Integral and Certain of Its Applications (Dover, New York, 1958). For the definition and elementary properties of almost periodic functions, see the section starting on p. 185. For a more complete work, see A. S. Besicovitch, Almost Periodic Functions (Cambridge U. Press, Cambridge, 1932).

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