Abstract

An analytical solution of the short-pulse four-wave mixing phenomenon is obtained in the undepleted-pump approximation for an instantaneously responding Kerr medium.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 2.
  2. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  3. B. R. Suydam, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 3.
  4. J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
    [CrossRef]
  5. W. W. Rigrod, R. A. Fisher, B. J. Feldman, Opt. Lett. 5, 105 (1980).
    [CrossRef] [PubMed]
  6. R. C. Shockley, Opt. Commun. 38, 221 (1981).
    [CrossRef]
  7. D. A. B. Miller, Opt. Lett. 5, 300 (1980).
    [CrossRef] [PubMed]
  8. I. C. McMichael, “Degenerate four-wave mixing of short and ultrashort light pulses,” Ph.D. dissertation (North Texas State University, Denton, Texas, 1984).
  9. D. Jean-Claude, I. C. McMichael, H. A. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).
  10. J. Menders, C. Shih, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper FBB5.
  11. B. W. Wherrett, A. L. Smirl, T. F. Boggess, IEEE J. Quantum Electron. QE-19, 680 (1983).
    [CrossRef]
  12. C. Shih, Proc. Soc. Photo-Opt. Instrum. Eng.642 (to be published).

1984

D. Jean-Claude, I. C. McMichael, H. A. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).

1983

B. W. Wherrett, A. L. Smirl, T. F. Boggess, IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

1981

R. C. Shockley, Opt. Commun. 38, 221 (1981).
[CrossRef]

1980

1978

J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
[CrossRef]

1977

Boggess, T. F.

B. W. Wherrett, A. L. Smirl, T. F. Boggess, IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

Feldman, B. J.

Fisher, R. A.

W. W. Rigrod, R. A. Fisher, B. J. Feldman, Opt. Lett. 5, 105 (1980).
[CrossRef] [PubMed]

B. R. Suydam, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 3.

Jean-Claude, D.

D. Jean-Claude, I. C. McMichael, H. A. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).

Marburger, J. H.

J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
[CrossRef]

McMichael, I. C.

D. Jean-Claude, I. C. McMichael, H. A. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).

I. C. McMichael, “Degenerate four-wave mixing of short and ultrashort light pulses,” Ph.D. dissertation (North Texas State University, Denton, Texas, 1984).

Menders, J.

J. Menders, C. Shih, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper FBB5.

Miller, D. A. B.

Pepper, D. M.

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

D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 2.

Rigrod, W. W.

Shih, C.

J. Menders, C. Shih, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper FBB5.

C. Shih, Proc. Soc. Photo-Opt. Instrum. Eng.642 (to be published).

Shockley, R. C.

R. C. Shockley, Opt. Commun. 38, 221 (1981).
[CrossRef]

Smirl, A. L.

B. W. Wherrett, A. L. Smirl, T. F. Boggess, IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

Suydam, B. R.

B. R. Suydam, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 3.

Vanherzeele, H. A.

D. Jean-Claude, I. C. McMichael, H. A. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).

Wherrett, B. W.

B. W. Wherrett, A. L. Smirl, T. F. Boggess, IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

Yariv, A.

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

D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 2.

Appl. Phys. Lett.

J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
[CrossRef]

IEEE J. Quantum Electron.

D. Jean-Claude, I. C. McMichael, H. A. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).

B. W. Wherrett, A. L. Smirl, T. F. Boggess, IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

Opt. Commun.

R. C. Shockley, Opt. Commun. 38, 221 (1981).
[CrossRef]

Opt. Lett.

Other

B. R. Suydam, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 3.

I. C. McMichael, “Degenerate four-wave mixing of short and ultrashort light pulses,” Ph.D. dissertation (North Texas State University, Denton, Texas, 1984).

J. Menders, C. Shih, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper FBB5.

C. Shih, Proc. Soc. Photo-Opt. Instrum. Eng.642 (to be published).

D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 2.

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 (3)

Fig. 1
Fig. 1

Schematic of short-pulse four-wave mixing. The pulse interaction is assumed to be well within the medium cell so that the boundaries can be placed at z = −∞, ∞, with initial and final states defined at t = −∞ and t = ∞, respectively.

Fig. 2
Fig. 2

Reflectivity versus η in linear scale. The dotted line is the lowest-order approximation of the exact expression (solid line).

Fig. 3
Fig. 3

Reflectivity versus η in logarithm scale. The dots are the result of two-dimensional four-wave mixing simulation. The result also shows the saturation phenomenon due to pump depletion.

Equations (19)

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

E 1 ( z , t ) = ½ A 1 ( z - v t ) exp [ i ( ω 1 t - k 1 z ) ] + c . c . , E 2 ( z , t ) = ½ A 2 ( z + v t ) exp [ i ( ω 2 t - k 2 z ) ] + c . c . , E p ( z , t ) = ½ A p ( z , t ) exp [ i ( ω p t - k p z ) ] + c . c . , E c ( z , t ) = ½ A c ( z , t ) exp [ i ( ω c t - k c z ) ] + c . c . ,
x = z - v t ,             y = z + v t ,
x A c = i β A 1 ( x ) A 2 ( y ) A p * × exp [ i ( k p - k 1 ) x + i ( k 2 - k c ) y ] , y A p * = i β * A 1 * ( x ) A 2 * ( y ) A c × exp [ i ( k 1 - k p ) x + i ( k c - k 2 ) y ] ,
β = ω 4 μ χ ( 3 )             ( MKS ) = π ω c n χ ( 3 )             ( Gaussian ) .
A ˜ c ( x , y ) = A c ( x , y ) / A 2 ( y ) , A ˜ p ( x , y ) = A p ( x , y ) / A 1 ( x )
p = x A 1 ( x ) 2 d x , q = - y A 2 ( y ) 2 d y .
t = - :             p = 0 , q = 0 ,
t = :             p = - A 1 ( x ) 2 d x = P 1 , q = - A 2 ( y ) 2 d y = P 2 ,
p A ˜ c ( p , q ) = - i β A ˜ p * ( p , q ) , q A ˜ p ( p , q ) = - i β * A ˜ c ( p , q ) ,
A ˜ p ( p , 0 ) = A ˜ 0 ( p ) ,             A ˜ c ( 0 , q ) = 0.
S p L p ( A ˜ c ) = - i β L p ( A ˜ p * ) , S q L q ( A ˜ p * ) - A ˜ 0 * = i β * L p ( A ˜ c ) .
L p L q ( A ˜ c ) = - i β S p S q - β 2 L p ( A ˜ 0 * ) , L p L q ( A ˜ p ) = S p S p S q - β 2 L p ( A ˜ 0 )
A ˜ c ( p , q ) = - i β 0 p A ˜ 0 * ( p - p ) I 0 ( 2 β p q ) d p , A ˜ p ( p , q ) = β 0 p A ˜ 0 ( p - p ) I 1 ( 2 β p q ) p d p ,
A ˜ 0 ( p ) = ( P p / P 1 ) 1 / 2 ,
A ˜ c ( P 1 , q ) = i β β ( P p / q ) 1 / 2 I 1 ( 2 β P 1 q ) .
A ˜ c ( P 1 , P 2 ) ( rear ) A ˜ c ( P 1 , 0 ) ( front ) = I 1 ( 2 β P 1 P 2 ) β P 1 P 2 .
R P c P p = 1 P p - d y A c ( - , y ) 2 = 1 P p 0 P 2 d q A ˜ c ( P 1 , q ) 2 = I 0 2 ( η ) + I 1 2 ( η ) - 1 ,
η = 2 β P 1 P 2 .
η ( CS 2 ) = 63 P 1 , 2 ( J / cm 2 ) .

Metrics