Abstract

We analyze the squeezing characteristics of a singly resonant second-harmonic-generation system, in which only the fundamental light is confined in a plain cavity resonator, with consideration for fundamental depletion in a nonlinear crystal. The system was analyzed under the mean-field approximation, which neglects the variation of the field in the crystal, and as much as 9.5 dB of squeezing was predicted in the second-harmonic output. On the basis of the self-consistent method, we analyze the system, which is driven by such an intense fundamental input that the mean-field approximation is not valid, and predict that an arbitrary amount of squeezing will be available in this regime.

© 1996 Optical Society of America

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References

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  1. M. J. Collett, D. F. WallsPhys. Rev. A 32, 2887 (1985).
    [CrossRef] [PubMed]
  2. S. F. Pereira, M. Xiao, H. J. Kimble, J. L. HallPhys. Rev. A 38, 4931 (1988).
    [CrossRef] [PubMed]
  3. P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
    [CrossRef]
  4. R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
    [CrossRef] [PubMed]
  5. T. C. Ralph, M. S. Taubman, A. G. White, D. E. McClelland, H.-A. BachorOpt. Lett. 20, 1316 (1995).
    [CrossRef] [PubMed]
  6. H. TsuchidaOpt. Lett. 20, 2240 (1995).
    [CrossRef] [PubMed]
  7. K. IkedaOpt. Commun. 30, 257 (1979).
    [CrossRef]
  8. C. W. Gardiner, C. M. SavageOpt. Commun. 50, 173 (1984).
    [CrossRef]
  9. P. Pliszka, P. P. BanerjeeOpt. Commun. 103, 130 (1993).
    [CrossRef]
  10. Z. Y. OuPhys. Rev. A 49, 2106 (1994).
    [CrossRef] [PubMed]

1995 (2)

1994 (2)

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Z. Y. OuPhys. Rev. A 49, 2106 (1994).
[CrossRef] [PubMed]

1993 (1)

P. Pliszka, P. P. BanerjeeOpt. Commun. 103, 130 (1993).
[CrossRef]

1992 (1)

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

1988 (1)

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. HallPhys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

1985 (1)

M. J. Collett, D. F. WallsPhys. Rev. A 32, 2887 (1985).
[CrossRef] [PubMed]

1984 (1)

C. W. Gardiner, C. M. SavageOpt. Commun. 50, 173 (1984).
[CrossRef]

1979 (1)

K. IkedaOpt. Commun. 30, 257 (1979).
[CrossRef]

Bachor, H. A.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Bachor, H.-A.

Banerjee, P. P.

P. Pliszka, P. P. BanerjeeOpt. Commun. 103, 130 (1993).
[CrossRef]

Collett, M.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

Collett, M. J.

M. J. Collett, D. F. WallsPhys. Rev. A 32, 2887 (1985).
[CrossRef] [PubMed]

Fiedler, K.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner, C. M. SavageOpt. Commun. 50, 173 (1984).
[CrossRef]

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. HallPhys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Ikeda, K.

K. IkedaOpt. Commun. 30, 257 (1979).
[CrossRef]

Kimble, H. J.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. HallPhys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Kürz, P.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

Leuchs, G.

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

McClelland, D. E.

Mlynek, J.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

Ou, Z. Y.

Z. Y. OuPhys. Rev. A 49, 2106 (1994).
[CrossRef] [PubMed]

Paschotta, R.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

Pereira, S. F.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. HallPhys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Pliszka, P.

P. Pliszka, P. P. BanerjeeOpt. Commun. 103, 130 (1993).
[CrossRef]

Ralph, T. C.

Savage, C. M.

C. W. Gardiner, C. M. SavageOpt. Commun. 50, 173 (1984).
[CrossRef]

Sizman, A.

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

Taubman, M. S.

Tsuchida, H.

Walls, D. F.

M. J. Collett, D. F. WallsPhys. Rev. A 32, 2887 (1985).
[CrossRef] [PubMed]

White, A. G.

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. HallPhys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Appl. Phys. B (1)

P. Kürz, R. Paschotta, K. Fiedler, A. Sizman, G. Leuchs, J. MlynekAppl. Phys. B 55, 216 (1992).
[CrossRef]

Opt. Commun. (3)

K. IkedaOpt. Commun. 30, 257 (1979).
[CrossRef]

C. W. Gardiner, C. M. SavageOpt. Commun. 50, 173 (1984).
[CrossRef]

P. Pliszka, P. P. BanerjeeOpt. Commun. 103, 130 (1993).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

Z. Y. OuPhys. Rev. A 49, 2106 (1994).
[CrossRef] [PubMed]

M. J. Collett, D. F. WallsPhys. Rev. A 32, 2887 (1985).
[CrossRef] [PubMed]

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. HallPhys. Rev. A 38, 4931 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, J. MlynekPhys. Rev. Lett. 72, 3807 (1994).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Singly resonant SH-generation system with a ring cavity. NLC, nonlinear crystal; DM, dichroic mirror that totally reflects the fundamental while transmitting 100% of the SH.

Fig. 2
Fig. 2

Calculated noise power spectra of the SH output (a) around zero frequency and (b) with a wider frequency range. Frequencies are normalized by the free spectral range (FSR). SQL, standard quantum limit.

Fig. 3
Fig. 3

Amount of squeezing at zero frequency as a function of interaction length ξ and of the required external fundamental power. Standard quantum limit (SQL) is set to 0 dB.

Equations (20)

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E 1 = i ( ћ ω 0 2 ε 0 Snc ) 1 / 2 d ω a ( z , ω ) exp [ i ω ( n z / c t ) ] + h . c . ,
E 2 = i ( ћ 2 ω 0 2 ε 0 Snc ) 1 / 2 d ω b ( z , ω ) exp [ i ω ( n z / c t ) ] + h . c . ,
[ a ( z , ω ) , a ( z , ω ) ] = δ ( ω ω ) ,
[ b ( z , ω ) , b ( z , ω ) ] = δ ( ω ω ) .
d a ( z , ω ) d z = κ d ω a ( z , ω ) b ( z , ω + ω ) ,
d b ( z , ω ) d z = κ 2 d ω a ( z , ω ) a ( z , ω ω ) ,
κ = d eff ω 0 / n c ( ω 0 / ε 0 S n c ) 1 / 2 ,
a ( z , ω 0 + δ ω ) = u ( z ) exp ( i ϕ a ) δ ( δ ω ) + Δ a ( z , δ ω ) ,
b ( z , 2 ω 0 + δ ω ) = v ( z ) exp ( i ϕ b ) δ ( δ ω ) + Δ b ( z , δ ω ) ,
Δ x 1 ( z , δ ω ) = [ Δ x ( z , δ ω ) + Δ x ( z , δ ω ) ] / 2 ,
Δ x 2 ( z , δ ω ) = [ Δ x ( z , δ ω ) Δ x ( z , δ ω ) ] / 2 i ,
u ( l , δ ω ) = N u ( 0 , δ ω ) ,
u ( z , δ ω ) = τ ( Δ a 1 , Δ a 2 , Δ b 1 , Δ b 2 ) ( z , δ ω ) ,
N 11 = 1 ξ tanh ξ cosh ξ , N 13 = 2 tanh ξ cosh ξ ,
N 22 = 1 cosh ξ , N 24 = 1 2 ( sinh ξ + ξ cosh ξ ) ,
N 31 = 1 2 ( tanh ξ + 1 cosh 2 ξ ) , N 33 = 1 cosh 2 ξ ,
N 42 = 2 tanh ξ , N 44 = 1 ξ tanh ξ ,
Δ b 1 ( l , δ ω ) = [ 1 T exp ( i δ ω τ ) N 13 N 31 1 1 T exp ( i δ ω τ ) N 11 + N 33 ] Δ b 1 ( 0 , δ ω ) + T N 31 1 1 T exp ( i δ ω τ ) N 11 Δ r 1 ( δ ω ) ,
Δ b 1 ( l , δ ω ) = 2 T ξ i δ ω τ + T / 2 + 3 ξ 2 / 2 Δ r 1 ( δ ω ) + i δ ω τ + T / 2 ξ 2 / 2 i δ ω τ + T / 2 + 3 ξ 2 / 2 Δ b 1 ( 0 , δ ω ) .
lim ξ | Δ b 1 ( l , 0 ) | 2 = T / 2 | Δ r 1 ( 0 ) | 2 T 0 0 .

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