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  1. R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977); D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978); C. R. Giuliano, Phys. Today 34, 27 (1981).
    [CrossRef] [PubMed]
  2. A. Yariv, Appl. Phys. Lett. 28, 88 (1976).
    [CrossRef]
  3. A. Yariv, Opt. Commun. 21, 49 (1977).
    [CrossRef]
  4. D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978); J. O. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1981).
    [CrossRef] [PubMed]
  5. A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
    [CrossRef]
  6. J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, R. Jain, Opt. Lett. 4, 42 (1979).
    [CrossRef] [PubMed]
  7. R. W. Hellwarth, IEEE J. Quantum Electron. 15, 101 (1979).
    [CrossRef]
  8. S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 33, 404 (1978).
    [CrossRef]
  9. S. Akhmanov, A. Sukhorukov, R. Khokhlov, Zh. Eksp. Teor. Fiz. 50, 1537 (1966) [Sov. Phys. JETP 23, 1025 (1966)].
  10. M. Sodha, A. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).
    [CrossRef]
  11. B. Bendow, P. D. Gianino, N. Tzoar, J. Opt. Soc. Am. 71, 656 (1981).
    [CrossRef]

1981 (1)

1979 (2)

1978 (3)

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978); J. O. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1981).
[CrossRef] [PubMed]

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 33, 404 (1978).
[CrossRef]

1977 (2)

1976 (1)

A. Yariv, Appl. Phys. Lett. 28, 88 (1976).
[CrossRef]

1966 (1)

S. Akhmanov, A. Sukhorukov, R. Khokhlov, Zh. Eksp. Teor. Fiz. 50, 1537 (1966) [Sov. Phys. JETP 23, 1025 (1966)].

Akhmanov, S.

S. Akhmanov, A. Sukhorukov, R. Khokhlov, Zh. Eksp. Teor. Fiz. 50, 1537 (1966) [Sov. Phys. JETP 23, 1025 (1966)].

AuYeung, J.

Bendow, B.

Fekete, D.

Ghatak, A.

M. Sodha, A. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).
[CrossRef]

Gianino, P. D.

Hellwarth, R. W.

Jain, R.

Jensen, S. M.

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 33, 404 (1978).
[CrossRef]

Khokhlov, R.

S. Akhmanov, A. Sukhorukov, R. Khokhlov, Zh. Eksp. Teor. Fiz. 50, 1537 (1966) [Sov. Phys. JETP 23, 1025 (1966)].

Pepper, D. M.

Sodha, M.

M. Sodha, A. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).
[CrossRef]

Sukhorukov, A.

S. Akhmanov, A. Sukhorukov, R. Khokhlov, Zh. Eksp. Teor. Fiz. 50, 1537 (1966) [Sov. Phys. JETP 23, 1025 (1966)].

Tzoar, N.

Yariv, A.

Appl. Phys. Lett. (3)

A. Yariv, Appl. Phys. Lett. 28, 88 (1976).
[CrossRef]

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 33, 404 (1978).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. W. Hellwarth, IEEE J. Quantum Electron. 15, 101 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

Opt. Lett. (2)

Zh. Eksp. Teor. Fiz. (1)

S. Akhmanov, A. Sukhorukov, R. Khokhlov, Zh. Eksp. Teor. Fiz. 50, 1537 (1966) [Sov. Phys. JETP 23, 1025 (1966)].

Other (1)

M. Sodha, A. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Geometry of the degenerate four-wave mixing process in a waveguide.

Equations (22)

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[ 2 + ω 2 c 2 ( o r r 2 ) ] ( E S E R ) + 2 E p 1 E p 2 ( E * R E * S ) = 0 ,
E ( r , z ) = g ( z ) A 0 ( r , z ) exp [ i k S ( r , z ) ] exp [ i ( ± k z ω t ) ] ,
A o = E 0 f ( z ) exp [ r 2 2 r S 2 f 2 ( z ) ] , S = 1 2 β ( z ) r 2 + ζ ( z ) ,
2 E p 1 E p 2 ~ γ 0 + γ 1 r 2 , γ 1 / γ 0 = [ r p 2 f p 2 ( z ) ] 1 .
g S = γ 0 2 k g R f S f R { k 2 ( β S + β R ) r S 2 f S 2 cos A + [ 3 2 + ( γ 1 γ 0 1 2 r S 2 f R 2 ) r S 2 f S 2 ] sin A ,
g R = γ 0 2 k g S f R f S { k 2 ( β S + β R ) r S 2 f R 2 cos A + [ 3 2 + ( γ 1 γ 0 1 2 r S 2 f S 2 ) r S 2 f R 2 ] sin A ,
β S = f S f S g S g S + γ 0 2 k f S f R g R g S sin A ,
β R = f R f R + g R g R + γ 0 2 k f R f S g S g R sin A ,
β S = β S 2 + 1 k 2 r S 4 f S 4 r o + γ 0 2 k 2 g R f S g S f R { [ 2 γ 1 γ 0 + 1 r S 2 ( 1 f S 2 1 f R 2 ) ] cos A k ( β S + β R ) sin A } ,
β R = β R 2 1 k 2 r S 4 f R 4 + r o γ 0 2 k 2 g S f R g R f S { [ 2 γ 1 γ 0 1 r S 2 ( 1 f S 2 1 f R 2 ) ] cos A k ( β S + β R ) sin A } ,
ζ S = 1 k 2 r S 2 f S 2 + γ 0 2 k 2 cos A g R g S f S f R ,
ζ R = 1 k 2 r S 2 f R 2 γ 0 2 k 2 cos A g S g R f R f S ,
g S = γ 0 2 k g R , g R = γ 0 2 k g S ,
β S = β R = f / f ,
β S = β R = ( f / f ) 2 + ( k 2 r S 4 f 4 ) 1 r / o ,
ζ S = ζ R = ( k 2 r S 2 f 2 ) 1 .
f i 2 = ( 1 / 2 ) [ 1 + C i + ( 1 C i ) cos η ] ( i = S , R , or p ) ,
C S = C R = o ( r k 2 r S 4 ) 1 ,
η = 2 ( r / o ) 1 / 2 z .
f R 2 ( z ) = f S 2 ( z ) / Q ( z ) , g R ( z ) = γ 0 2 k Q 1 / 2 ( z ) , Q 1 + 2 r S 2 f S 2 r p 2 f p 2 ,
g R γ 0 2 k [ 1 + 2 r S 2 ( 1 + C S ) r p 2 ( 1 + C p ) ] 1 / 2 ( L z ) .
R = | E R ( 0 ) / E S ( 0 ) | 2 = γ 0 2 L 2 4 k 2 / [ 1 + 2 r S 2 ( 1 + C S ) r p 2 ( 1 + C p ) ] , f R ( 0 ) = ( 1 + 2 r S 2 r p 2 ) 1 / 2 .

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