Abstract

Conversion efficiency for cw harmonic generation is calculated for the situation in which both fundamental and harmonic waves are resonant. Compared with the situation of a singly resonant cavity at the fundamental, the doubly resonant geometry can lead to an increase of the effective nonlinear coefficient. High conversion efficiency can thus be achieved with nonlinear crystals of relatively low nonlinear coefficients and with modest pump power for the fundamental input.

© 1993 Optical Society of America

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  1. A. Ashkin, G. D. Boyd, J. M. Dziedzic, IEEE J. Quantum Electron. QE-2, 109 (1966).
    [CrossRef]
  2. W. J. Kozlovsky, C. D. Nabors, R. L. Byer, IEEE J. Quantum Electron. 24, 913 (1988).
    [CrossRef]
  3. W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
    [CrossRef]
  4. E. S. Polzik, H. J. Kimble, Opt. Lett. 16, 731 (1991); in Digest of Conference on Compact Blue-Green Lasers (Optical Society of America, Washington, D.C., 1992), paper ThD6.
    [CrossRef]
  5. D. C. Gerstenberger, G. E. Tye, R. W. Wallace, Opt. Lett. 16, 992 (1991); in Digest of Conference on Compact Blue-Green Lasers (Optical Society of America, Washington, D.C., 1992), paper FA4.
    [CrossRef]
  6. D. H. Jundt, M. M. Fejer, R. L. Byer, R. G. Norwood, P. F. Bordui, Opt. Lett. 16, 1856 (1991).
    [CrossRef] [PubMed]
  7. Z. Y. Ou, S. F. Pereira, E. S. Polzik, H. J. Kimble, Opt. Lett. 17, 640 (1992).
    [CrossRef] [PubMed]
  8. P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980).
    [CrossRef]
  9. L. A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
    [CrossRef]
  10. S. T. Yang, C. C. Pohalski, E. K. Gustafson, R. L. Byer, R. S. Feigelson, R. J. Raymakers, R. Route, Opt. Lett. 16, 1493 (1991).
    [CrossRef] [PubMed]
  11. S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1989).
    [CrossRef]

1992 (1)

1991 (4)

1990 (1)

W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
[CrossRef]

1989 (1)

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1989).
[CrossRef]

1988 (1)

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, IEEE J. Quantum Electron. 24, 913 (1988).
[CrossRef]

1987 (1)

1980 (1)

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, IEEE J. Quantum Electron. QE-2, 109 (1966).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, IEEE J. Quantum Electron. QE-2, 109 (1966).
[CrossRef]

Bona, G. L.

W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
[CrossRef]

Bordui, P. F.

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, IEEE J. Quantum Electron. QE-2, 109 (1966).
[CrossRef]

Byer, R. L.

Drummond, P. D.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, IEEE J. Quantum Electron. QE-2, 109 (1966).
[CrossRef]

Feigelson, R. S.

Fejer, M. M.

Gerstenberger, D. C.

Gustafson, E. K.

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1989).
[CrossRef]

Jundt, D. H.

Kimble, H. J.

Z. Y. Ou, S. F. Pereira, E. S. Polzik, H. J. Kimble, Opt. Lett. 17, 640 (1992).
[CrossRef] [PubMed]

E. S. Polzik, H. J. Kimble, Opt. Lett. 16, 731 (1991); in Digest of Conference on Compact Blue-Green Lasers (Optical Society of America, Washington, D.C., 1992), paper ThD6.
[CrossRef]

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1989).
[CrossRef]

L. A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
[CrossRef]

Kozlovsky, W. J.

W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, IEEE J. Quantum Electron. 24, 913 (1988).
[CrossRef]

Latta, E. E.

W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
[CrossRef]

Length, W.

W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
[CrossRef]

McNeil, K. J.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980).
[CrossRef]

Moser, A.

W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
[CrossRef]

Nabors, C. D.

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, IEEE J. Quantum Electron. 24, 913 (1988).
[CrossRef]

Norwood, R. G.

Ou, Z. Y.

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, E. S. Polzik, H. J. Kimble, Opt. Lett. 17, 640 (1992).
[CrossRef] [PubMed]

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1989).
[CrossRef]

Pohalski, C. C.

Polzik, E. S.

Z. Y. Ou, S. F. Pereira, E. S. Polzik, H. J. Kimble, Opt. Lett. 17, 640 (1992).
[CrossRef] [PubMed]

E. S. Polzik, H. J. Kimble, Opt. Lett. 16, 731 (1991); in Digest of Conference on Compact Blue-Green Lasers (Optical Society of America, Washington, D.C., 1992), paper ThD6.
[CrossRef]

Raymakers, R. J.

Route, R.

Tye, G. E.

Wallace, R. W.

Walls, D. F.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980).
[CrossRef]

Wu, L. A.

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1989).
[CrossRef]

L. A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
[CrossRef]

Yang, S. T.

Appl. Phys. Lett. (1)

W. J. Kozlovsky, W. Length, E. E. Latta, A. Moser, G. L. Bona, Appl. Phys. Lett. 56, 2291 (1990).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, IEEE J. Quantum Electron. QE-2, 109 (1966).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, IEEE J. Quantum Electron. 24, 913 (1988).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Acta (1)

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1989).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Geometry of doubly resonant scheme for harmonic generation.

Fig. 2
Fig. 2

Harmonic conversion efficiency η plotted as a function of input fundamental power P1,in for doubly [curves (i)–(iii)] and singly [curve (iv)] resonant schemes as derived from Eqs. (9) and (1). The parameters are ENL = 6 × 10−5 W−1, L1 = 0.017 for all four schemes, and L2 = 0.003, T1 = 0.064, T2 = 0.019 (curve i); L2 = 0.017, T1 = 0.039, T2 = 0.06 (curve ii); L2 = 0.1, T1 = 0.024, T2 = 0.18 (curve iii); T1 = 0.018 and no harmonic enhancement cavity (curve iv).

Fig. 3
Fig. 3

(a) Optimized conversion efficiency ηop and (b) optimized coupling coefficients T 1 op / L i ( β 1 - 1 ) , T 2 op / L 2 ( β 2 - 1 ) as a function of the dimensionless input power = ENLP1,in/L12L2.

Equations (20)

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η ( T 1 + L 1 + η P 1 , in E NL ) 2 = 4 T 1 P 1 , in E NL ,
η op = 4 NL P 1 , in ( 1 + 1 + 4 NL P 1 , in ) 2 ,
- Γ 1 α 1 + κ * α 1 * α 2 + 1 = 0 , - Γ 2 α 2 - 1 2 κ α 1 2 = 0.
κ 2 = E NL 4 π c 4 d 1 2 d 2 λ 1 .
P k = c ω k d k α k 2             ( k = 1 , 2 ) .
T 1 P 1 , in = 1 2 ω 1 d 1 / c ,
P 2 , out = T 2 P 2 .
η ( T 1 + L 1 + 4 η P 1 , in E NL / T 2 ) 2 = 4 T 1 T 2 T 2 + L 2 4 P 1 , in E NL / T 2 ,
E NL eff = 4 E NL / T 2 ,
T 1 eff T 1 T 2 T 2 + L 2 T 1 1 + β 2 ,
L 1 eff L 1 + T 1 β 2 1 + β 2 ,
η ( T 1 eff + L 1 eff + η P 1 , in E NL eff ) 2 = 4 T 1 eff P 1 , in E NL eff ,
η op = P ¯ [ 2 ( s + + s - ) - 1 / 3 ] ( s + + s - + 1 / 3 ) 2 ,
T 2 op T 2 op + L 2 T 1 op T 1 op + L 1 ,
β 1 - 1 T 1 op / L 1 = s + + s - + 1 / 3 ,
( 2 P ¯ ) 1 / 3 + 1 / 3 ,
β 2 - 1 T 2 op / L 2 = 2 ( s + + s - ) - 1 / 3 ,
( 2 P ¯ ) 1 / 3 - 1 / 3 ,
s ± = [ 1 / 27 + P ¯ ± P ¯ ( P ¯ + 2 / 27 ) ] 1 / 3 .
( η 1 - L 2 ) 1 / 2 [ π F 1 - π + ( 1 - π 2 F 2 ) ( η P 1 , in E NL T 2 ( 1 - L 2 ) ) 1 / 2 ] = T 1 F 2 P 1 , in E NL T 2 π ( 1 - T 1 ) ,

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