Abstract

A theory for oscillation in an optical resonator with photorefractive gain was formulated. The threshold conditions for the oscillation were also obtained. The result, applicable to a whole class of new devices, is a prediction for an oscillation frequency different from that of the pump beam.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  2. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
    [CrossRef]
  3. J. Feinberg, Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]
  4. H. Rajbenbach, J. P. Huignard, Opt. Lett. 10, 137 (1985).
    [CrossRef] [PubMed]
  5. J. Feinberg, G. D. Bacher, Opt. Lett. 9, 420 (1984).
    [CrossRef] [PubMed]
  6. For the sake of specificity we consider the case of a ring resonator. The analysis is more general and applies to any resonator with photorefractive gain.
  7. J. C. Slater, Microwave Electronics (Van Nostrand, Princeton, N.J., 1950).
  8. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  9. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  10. M. Cronin-Golomb, Ph.D. dissertation (California Institute of Technology, Pasadena, California, 1983; unpublished).
  11. J. P. Huignard, A. Marrackchi, Opt. Commun. 38, 249 (1981).
    [CrossRef]
  12. S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury, Appl. Phys. Lett. (to be published).
  13. M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
    [CrossRef] [PubMed]
  14. A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart and Winston, New York, 1985), p. 159, Eq. (6.4-13).

1985 (2)

1984 (1)

1982 (3)

J. Feinberg, Opt. Lett. 7, 486 (1982).
[CrossRef] [PubMed]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

1981 (2)

Bacher, G. D.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury, Appl. Phys. Lett. (to be published).

M. Cronin-Golomb, Ph.D. dissertation (California Institute of Technology, Pasadena, California, 1983; unpublished).

Feinberg, J.

Fischer, B.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

Huignard, J. P.

H. Rajbenbach, J. P. Huignard, Opt. Lett. 10, 137 (1985).
[CrossRef] [PubMed]

J. P. Huignard, A. Marrackchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Kwong, S. K.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury, Appl. Phys. Lett. (to be published).

Marrackchi, A.

J. P. Huignard, A. Marrackchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Rajbenbach, H.

Slater, J. C.

J. C. Slater, Microwave Electronics (Van Nostrand, Princeton, N.J., 1950).

Ury, I.

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury, Appl. Phys. Lett. (to be published).

White, J. O.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

Yariv, A.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart and Winston, New York, 1985), p. 159, Eq. (6.4-13).

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury, Appl. Phys. Lett. (to be published).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Appl. Phys. Lett. (2)

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Opt. Commun. (1)

J. P. Huignard, A. Marrackchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Opt. Lett. (5)

Other (6)

For the sake of specificity we consider the case of a ring resonator. The analysis is more general and applies to any resonator with photorefractive gain.

J. C. Slater, Microwave Electronics (Van Nostrand, Princeton, N.J., 1950).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart and Winston, New York, 1985), p. 159, Eq. (6.4-13).

M. Cronin-Golomb, Ph.D. dissertation (California Institute of Technology, Pasadena, California, 1983; unpublished).

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury, Appl. Phys. Lett. (to be published).

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 (1)

Fig. 1
Fig. 1

Schematic diagram of a photorefractively pumped unidirectional ring resonator.

Equations (27)

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

E i ( r , t ) = ½ E i 0 ( r ) exp ( i ω 0 t ) + c . c . ,
E ( r , t ) = a - 1 p a ( t ) E a ( r ) , H ( r , t ) = a 1 μ ω a q a ( t ) H a ( r ) ,
× E a = k a H a , × H a = k a E a ,
V res E a · E b d V = δ ab ,             V res H a · H b d V = δ ab .
p ¨ a + ω a Q a p ˙ a + ω a 2 p a = 1 2 t 2 V res P NL ( r , t ) · E a ( r ) d V ,
P NL ( r , t ) = 4 0 Δ n ( r ) E i ( r , t ) = - 0 γ p a ( t ) [ E i 0 * · E a ( r ) ] E i 0 ( r ) E i 0 2 + 1 p a E a 2 + c . c . ,
Δ n ( r , t ) = - γ 2 p a ( t ) [ E i 0 * · E a ( r ) ] exp ( - i ω 0 t ) E i 0 2 + 1 p a E a 2 + c . c .
γ = r eff n 0 3 2 i E p ( E + i E d ) [ E - ( ω - ω 0 ) t 0 ( E d + E μ ) ] + i [ E d + E p + ( ω - ω 0 ) t 0 E ] ,
γ = i γ 0 1 + i ( ω - ω 0 ) τ ,
γ 0 = r eff n 0 3 2 E p E d ( E p + E d )
τ = t 0 ( E d + E μ E d + E p ) .
p a ( t ) = p a 0 ( t ) e i ω t .
{ [ ( ω a 2 - ω 2 ) + i ω a ω Q a ] p a 0 ( t ) + ( 2 i ω + ω a Q a ) p ˙ a 0 + p ¨ a 0 } e i ω t = - 0 2 t 2 V crystal γ p a 0 ( t ) E i 0 * · E a 2 E i 0 2 + 1 p a 0 ( t ) E a ( r ) 2 e i τ d v .
( ω a 2 - ω 2 ) + i ω a ω Q a = 0 ω 2 γ f = i 0 ω 2 f γ 0 1 + i ( ω - ω 0 ) τ ,
f = V crystal E i 0 * ( r ) · E a ( r ) 2 E i 0 ( r ) 2 + 1 p a 0 ( ) E a ( r ) 2 d V ,
ω a 2 - ω 2 = 0 f γ 0 ω 2 ( ω - ω 0 ) τ [ 1 + ( ω - ω 0 ) 2 τ 2 ]
ω a ω Q a = 0 f γ 0 ω 2 [ 1 + ( ω - ω 0 ) 2 τ 2 .
ω a - ω = 0 f γ 0 ω 0 ( ω - ω 0 ) τ 2 [ 1 + ( ω - ω 0 ) 2 τ 2 ] .
( ω - ω 0 ) 2 t a τ ( ω a - ω 0 ) .
f E i 0 * ( r ) · E a ( r ) 2 E i 0 ( r ) 2 + E osc ( r ) 2 d V
1 1 + E osc 2 E i 0 2 V c E i 0 * ( r ) · E a ( r ) 2 E i 0 2 d V ,
E osc ( r ) = - 1 p a 0 ( ) E a ( r )
f = f 0 1 + E osc 2 E i 0 2 ,
f 0 E i 0 * ( r ) · E a ( r ) 2 E i 0 2 d V
1 ω a t a = n 2 γ 0 f 0 1 + 4 ( ω 0 - ω a ) 2 t a 2 ( 1 1 + E osc 2 E i 0 2 ) ,
γ 0 1 + 4 ( ω 0 - ω a ) 2 t a 2 n 2 f 0 ω a t a
E osc 2 = E i 0 2 [ n 2 γ 0 f 0 ω a t a 1 + 4 ( ω 0 - ω a ) 2 t a 2 - 1 ] ,

Metrics