Abstract

It is shown that a nearly degenerate four-wave mixing process is capable of yielding a real-time optical bandpass filter. The filter has a large field of view and is capable of providing an amplified bandpass. Moreover, the conjugate nature of the output field can be utilized to increase the signal-to-noise ratio of the device. For a 1-cm interaction length in a nondispersive medium, the optical bandpass at 5000 Å can be varied from ~9 GHz down to the linewidth of the exciting laser.

© 1978 Optical Society of America

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References

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  1. R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
    [CrossRef]
  2. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  3. R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978).
    [CrossRef] [PubMed]
  4. D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
    [CrossRef]
  5. S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978), and reference therein.
    [CrossRef] [PubMed]
  6. D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
    [CrossRef] [PubMed]
  7. A. Yariv, Opt. Commun. 25, 23 (1978).
    [CrossRef]
  8. D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978).
    [CrossRef] [PubMed]
  9. D. M. Bloom, C. V. Shank, R. L. Fork, O. Teschke, “Subpicosecond optical gating and wavefront conjugation by four-wave mixing,” in Proceedings of the First Topical Meeting on Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978).
  10. A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 421–432.
  11. See, for example, F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 338–339.
  12. R. P. Feynman, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I, p. 30-36.
  13. A. Yariv, California Institute of Technology, Pasadena, Calif. 91125, unpublished.

1978 (5)

R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978).
[CrossRef] [PubMed]

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978), and reference therein.
[CrossRef] [PubMed]

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
[CrossRef] [PubMed]

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978).
[CrossRef] [PubMed]

1977 (3)

Abrams, R. L.

AuYeung, J.

Bjorklund, G. C.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

Bloom, D. M.

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
[CrossRef] [PubMed]

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

D. M. Bloom, C. V. Shank, R. L. Fork, O. Teschke, “Subpicosecond optical gating and wavefront conjugation by four-wave mixing,” in Proceedings of the First Topical Meeting on Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978).

Economou, N. P.

Fekete, D.

Feynman, R. P.

R. P. Feynman, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I, p. 30-36.

Fork, R. L.

D. M. Bloom, C. V. Shank, R. L. Fork, O. Teschke, “Subpicosecond optical gating and wavefront conjugation by four-wave mixing,” in Proceedings of the First Topical Meeting on Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978).

Hellwarth, R. W.

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978), and reference therein.
[CrossRef] [PubMed]

R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
[CrossRef]

Jenkins, F.

See, for example, F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 338–339.

Jensen, S. M.

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978), and reference therein.
[CrossRef] [PubMed]

Liao, P. F.

Lind, R. C.

Pepper, D. M.

Shank, C. V.

D. M. Bloom, C. V. Shank, R. L. Fork, O. Teschke, “Subpicosecond optical gating and wavefront conjugation by four-wave mixing,” in Proceedings of the First Topical Meeting on Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978).

Teschke, O.

D. M. Bloom, C. V. Shank, R. L. Fork, O. Teschke, “Subpicosecond optical gating and wavefront conjugation by four-wave mixing,” in Proceedings of the First Topical Meeting on Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978).

White, H.

See, for example, F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 338–339.

Yariv, A.

D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978).
[CrossRef] [PubMed]

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

A. Yariv, California Institute of Technology, Pasadena, Calif. 91125, unpublished.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 421–432.

Appl. Phys. Lett. (2)

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978); D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978); P. F. Liao, D. M. Bloom, Opt. Lett. 3, 4 (1978), and reference therein.
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

Opt. Lett. (4)

Other (5)

D. M. Bloom, C. V. Shank, R. L. Fork, O. Teschke, “Subpicosecond optical gating and wavefront conjugation by four-wave mixing,” in Proceedings of the First Topical Meeting on Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978).

A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 421–432.

See, for example, F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), pp. 338–339.

R. P. Feynman, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I, p. 30-36.

A. Yariv, California Institute of Technology, Pasadena, Calif. 91125, unpublished.

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Figures (3)

Fig. 1
Fig. 1

Nearly degenerate four-wave mixing geometry. The pump waves (at frequency ω) are assumed nondepleted. The probe field A4 is at frequency ω + δ.

Fig. 2
Fig. 2

Power reflectivity R versus normalized wavelength detuning Ψ for several values of the nonlinear gain |κ|L. For the example given in the text, unity along the abscissa corresponds to Δλ/2 = 0.0772 Å, or Δν = 9.26 GHz. Note that Ψ = [(Δλ/2)(2nL2)].

Fig. 3
Fig. 3

Power reflectivity versus normalized wavelength detuning Ψ for several values of the nonlinear gain |κ|L. All curves are normalized to unity power reflectivity to emphasize the frequency bandpass of the interaction.

Equations (9)

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E i ( r , t ) = 1 2 A i ( r i ) exp [ i ( ω i t - k i · r ) ] + c . c . ,
P NL ( ω 3 = ω - δ ) = 1 2 χ NL ( 3 ) A 1 A 2 A 4 * exp ( i { [ ω + ω - ( ω + δ ) ] t - [ k 1 + k 2 - k 4 ] · r } ) + c . c .
d A 3 / d z = i κ 3 * A 4 * exp ( i Δ k z ) , d A 4 * / d z = i κ 4 A 3 exp ( - i Δ k z ) ,
Δ k = 2 n π ( Δ λ / λ 2 ) = 2 n δ / c .
A 3 ( z ) = exp ( i Δ k z / 2 ) / D { exp ( - i Δ k L / 2 ) [ β cos ( β z ) - ( i Δ k / 2 ) sin ( β z ) ] A 3 ( L ) + i κ 3 * s i n [ β ( z - L ) ] × A 4 * ( 0 ) } , A 4 * ( z ) = exp ( - i Δ k z / 2 ) / D ( i κ 4 × exp ( - i Δ k L / 2 ) sin ( β z ) A 3 ( L ) + { β cos [ β ( z - L ) ] + ( i Δ k / 2 ) sin [ β ( z - L ) ] } A 4 * ( 0 ) ) ,
A 3 ( 0 ) = - i κ 3 * tan ( β L ) A 4 * ( 0 ) β - ( i Δ k / 2 ) tan ( β L ) .
R | A 3 ( 0 ) A 4 ( 0 ) | 2 ,
R κ L 2 [ sin ( Δ k L / 2 ) ( Δ k L / 2 ) ] 2 .
R = κ L 2 tan 2 ( β L ) κ L 2 + ( Δ k L / 2 ) 2 sec 2 ( β L ) .

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