Abstract

We present a self-consistent calculation of anomalous second-harmonic generation in glass optical fibers. Quantum interference between multiphoton absorption processes leads to asymmetric photoelectric emission from defects, creating a spatially periodic space-charge electric field. The second harmonic is found to grow exponentially along the fiber, then saturate to a maximum value proportional to the square of the fundamental intensity. The predicted conversion efficiency is in reasonable agreement with experiments.

© 1991 Optical Society of America

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    [Crossref] [PubMed]
  2. U. Österberg, W. Margulis, Opt. Lett. 12, 57 (1987).
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    [Crossref] [PubMed]
  4. M. C. Farries, P. St. J. Russell, M. E. Fermann, D. N. Payne, Electron. Lett. 23, 322 (1987).
    [Crossref]
  5. N. M. Lawandy, Phys. Rev. Lett. 65, 1745 (1990).
    [Crossref] [PubMed]
  6. V. Mizrahi, Y. Hibino, G. Stegeman, Opt. Commun. 78, 283 (1990).
    [Crossref]
  7. A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.
  8. É. A. Manykin, A. M. Afanas’ev, Sov. Phys. JETP 25, 828 (1967).
  9. B. Ya. Zel’dovich, A. N. Chudinov, JETP Lett. 50, 439 (1989).
  10. A. V. Smith, Sandia National Laboratories, Albuquerque, N. M. 87185 (personal communication, 1990).
  11. H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, A. Zavriyev, J. Phys. B 23, 2761 (1990).
    [Crossref]
  12. N. B. Baranova, A. N. Chudinov, B. Ya. Zel’dovich, Opt. Comm. 79, 116 (1990).
    [Crossref]
  13. E. M. Dianov, P. G. Kasansky, D. Yu. Stepanov, Sov. J. Quantum Electron. 16, 887 (1989).
  14. E. V. Anoikin, E. M. Dianov, P. G. Kazansky, D. Yu. Stepanov, Opt. Lett. 15, 835 (1990).
    [Crossref]
  15. É. M. Baskin, M. V. Éntin, JETP Lett. 48, 601 (1988).
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    [Crossref]
  17. L. D. Landau, E. M. Lifshitz, Quantum Mechanics—Nonrelativistic Theory (Pergamon, London, 1965).
  18. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  19. R. C. Hughes, Phys. Rev. Lett. 30, 1333 (1973).
    [Crossref]
  20. R. Adair, L. L. Chase, S. A. Payne, J. Opt. Soc. Am. B 4, 875 (1987).
    [Crossref]

1990 (6)

N. M. Lawandy, Phys. Rev. Lett. 65, 1745 (1990).
[Crossref] [PubMed]

V. Mizrahi, Y. Hibino, G. Stegeman, Opt. Commun. 78, 283 (1990).
[Crossref]

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, A. Zavriyev, J. Phys. B 23, 2761 (1990).
[Crossref]

N. B. Baranova, A. N. Chudinov, B. Ya. Zel’dovich, Opt. Comm. 79, 116 (1990).
[Crossref]

E. V. Anoikin, E. M. Dianov, P. G. Kazansky, D. Yu. Stepanov, Opt. Lett. 15, 835 (1990).
[Crossref]

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[Crossref]

1989 (2)

E. M. Dianov, P. G. Kasansky, D. Yu. Stepanov, Sov. J. Quantum Electron. 16, 887 (1989).

B. Ya. Zel’dovich, A. N. Chudinov, JETP Lett. 50, 439 (1989).

1988 (1)

É. M. Baskin, M. V. Éntin, JETP Lett. 48, 601 (1988).

1987 (4)

1986 (1)

1973 (1)

R. C. Hughes, Phys. Rev. Lett. 30, 1333 (1973).
[Crossref]

1967 (1)

É. A. Manykin, A. M. Afanas’ev, Sov. Phys. JETP 25, 828 (1967).

Adair, R.

Afanas’ev, A. M.

É. A. Manykin, A. M. Afanas’ev, Sov. Phys. JETP 25, 828 (1967).

Anoikin, E. V.

E. V. Anoikin, E. M. Dianov, P. G. Kazansky, D. Yu. Stepanov, Opt. Lett. 15, 835 (1990).
[Crossref]

Baranova, N. B.

N. B. Baranova, A. N. Chudinov, B. Ya. Zel’dovich, Opt. Comm. 79, 116 (1990).
[Crossref]

Baskin, É. M.

É. M. Baskin, M. V. Éntin, JETP Lett. 48, 601 (1988).

Bucksbaum, P. H.

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, A. Zavriyev, J. Phys. B 23, 2761 (1990).
[Crossref]

Chase, L. L.

Chudinov, A. N.

N. B. Baranova, A. N. Chudinov, B. Ya. Zel’dovich, Opt. Comm. 79, 116 (1990).
[Crossref]

B. Ya. Zel’dovich, A. N. Chudinov, JETP Lett. 50, 439 (1989).

Dianov, E. M.

E. V. Anoikin, E. M. Dianov, P. G. Kazansky, D. Yu. Stepanov, Opt. Lett. 15, 835 (1990).
[Crossref]

E. M. Dianov, P. G. Kasansky, D. Yu. Stepanov, Sov. J. Quantum Electron. 16, 887 (1989).

Éntin, M. V.

É. M. Baskin, M. V. Éntin, JETP Lett. 48, 601 (1988).

Farries, M. C.

M. C. Farries, P. St. J. Russell, M. E. Fermann, D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

Fermann, M. E.

M. C. Farries, P. St. J. Russell, M. E. Fermann, D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

Frankel, M.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Hibino, Y.

V. Mizrahi, Y. Hibino, G. Stegeman, Opt. Commun. 78, 283 (1990).
[Crossref]

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[Crossref]

Hughes, R. C.

R. C. Hughes, Phys. Rev. Lett. 30, 1333 (1973).
[Crossref]

Kamal, A.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Kasansky, P. G.

E. M. Dianov, P. G. Kasansky, D. Yu. Stepanov, Sov. J. Quantum Electron. 16, 887 (1989).

Kazansky, P. G.

E. V. Anoikin, E. M. Dianov, P. G. Kazansky, D. Yu. Stepanov, Opt. Lett. 15, 835 (1990).
[Crossref]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics—Nonrelativistic Theory (Pergamon, London, 1965).

Lawandy, N. M.

N. M. Lawandy, Phys. Rev. Lett. 65, 1745 (1990).
[Crossref] [PubMed]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics—Nonrelativistic Theory (Pergamon, London, 1965).

Manykin, É. A.

É. A. Manykin, A. M. Afanas’ev, Sov. Phys. JETP 25, 828 (1967).

Margulis, W.

Mizrahi, V.

V. Mizrahi, Y. Hibino, G. Stegeman, Opt. Commun. 78, 283 (1990).
[Crossref]

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[Crossref]

Muller, H. G.

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, A. Zavriyev, J. Phys. B 23, 2761 (1990).
[Crossref]

Nees, J.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Österberg, U.

Ozaki, K.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Payne, D. N.

M. C. Farries, P. St. J. Russell, M. E. Fermann, D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

Payne, S. A.

Russell, P. St. J.

M. C. Farries, P. St. J. Russell, M. E. Fermann, D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

Schumacher, D. W.

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, A. Zavriyev, J. Phys. B 23, 2761 (1990).
[Crossref]

Smith, A. V.

A. V. Smith, Sandia National Laboratories, Albuquerque, N. M. 87185 (personal communication, 1990).

Stegeman, G.

V. Mizrahi, Y. Hibino, G. Stegeman, Opt. Commun. 78, 283 (1990).
[Crossref]

Stegeman, G. I.

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[Crossref]

Stepanov, D. Yu.

E. V. Anoikin, E. M. Dianov, P. G. Kazansky, D. Yu. Stepanov, Opt. Lett. 15, 835 (1990).
[Crossref]

E. M. Dianov, P. G. Kasansky, D. Yu. Stepanov, Sov. J. Quantum Electron. 16, 887 (1989).

Stock, M. L.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Stolen, R. H.

Sudo, S.

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[Crossref]

Szpak, A.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Thomas, C. H.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Tom, H. W. K.

Valdmanis, J.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Weinberger, D. A.

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

Yariv, A.

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

Zavriyev, A.

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, A. Zavriyev, J. Phys. B 23, 2761 (1990).
[Crossref]

Zel’dovich, B. Ya.

N. B. Baranova, A. N. Chudinov, B. Ya. Zel’dovich, Opt. Comm. 79, 116 (1990).
[Crossref]

B. Ya. Zel’dovich, A. N. Chudinov, JETP Lett. 50, 439 (1989).

Appl. Phys. Lett. (1)

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[Crossref]

Electron. Lett. (1)

M. C. Farries, P. St. J. Russell, M. E. Fermann, D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

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

J. Phys. B (1)

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, A. Zavriyev, J. Phys. B 23, 2761 (1990).
[Crossref]

JETP Lett. (2)

É. M. Baskin, M. V. Éntin, JETP Lett. 48, 601 (1988).

B. Ya. Zel’dovich, A. N. Chudinov, JETP Lett. 50, 439 (1989).

Opt. Comm. (1)

N. B. Baranova, A. N. Chudinov, B. Ya. Zel’dovich, Opt. Comm. 79, 116 (1990).
[Crossref]

Opt. Commun. (1)

V. Mizrahi, Y. Hibino, G. Stegeman, Opt. Commun. 78, 283 (1990).
[Crossref]

Opt. Lett. (4)

Phys. Rev. Lett. (2)

R. C. Hughes, Phys. Rev. Lett. 30, 1333 (1973).
[Crossref]

N. M. Lawandy, Phys. Rev. Lett. 65, 1745 (1990).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

E. M. Dianov, P. G. Kasansky, D. Yu. Stepanov, Sov. J. Quantum Electron. 16, 887 (1989).

Sov. Phys. JETP (1)

É. A. Manykin, A. M. Afanas’ev, Sov. Phys. JETP 25, 828 (1967).

Other (4)

L. D. Landau, E. M. Lifshitz, Quantum Mechanics—Nonrelativistic Theory (Pergamon, London, 1965).

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

A. Kamal, M. L. Stock, A. Szpak, C. H. Thomas, D. A. Weinberger, M. Frankel, J. Nees, K. Ozaki, J. Valdmanis, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper PD25.

A. V. Smith, Sandia National Laboratories, Albuquerque, N. M. 87185 (personal communication, 1990).

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Figures (2)

Fig. 1
Fig. 1

Multiphoton paths to ionization, assuming a broad defect band at approximately 5 eV and a fundamental laser wavelength of 1.064 μm.

Fig. 2
Fig. 2

Steady-state growth (in space) of the SHG calculated from Eq. (9), using the experimental parameters of Ref. 2: I2ω (z = 0)/Isat = 1.2 × 10−6. The experimental data are qualitatively fit with β = 2, and G0 = 70 m−1.

Equations (10)

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E m ω ( z , t ) = E m ω ( z , t ) exp [ i ( ϕ m ω - m ω t ) ] + c . c . ,             m = 1 , 2 ,
ρ ˙ ± = R ( ( E 2 ω 4 + η 3 2 E 2 ω 2 E ω 4 + η 4 2 E ω 8 ) + { η 4 E 2 ω 2 E ω 4 exp [ 2 i ( ϕ 2 ω - 2 ϕ ω ) ] + c . c . } ± { - i η 3 E 2 ω E ω 2 ( η 4 E ω 4 - E 2 ω 2 ) × exp [ i ( ϕ 2 ω - 2 ϕ ω ) ] + c . c . } ) .
η 3 = 8 e κ 3 ω k ,             η 4 = 8 e 2 κ 4 ω 3 m .
j a = - e n d v 0 τ m ( ρ ˙ + - ρ ˙ - ) ,
σ = e n d μ e τ R ( ρ ˙ + + ρ ˙ - ) ,
E dc = - j a σ = v 0 μ e τ m τ R ρ ˙ + - ρ ˙ - ρ ˙ + + ρ ˙ - E 0 ρ ˙ + - ρ ˙ - ρ ˙ + + ρ ˙ - .
E dc = - i E 0 η 3 η 4 1 - I 2 ω / I sat 1 + β I 2 ω / I sat + ( I 2 ω / I sat ) 2 × E 2 ω E ω 2 exp [ i ( ϕ 2 ω - 2 ϕ ω ) ] + c . c . ,
E 2 ω z = i ω n 2 ω c 3 χ ( 3 ) ( 0 , ω , ω , ) E dc E ω 2 exp ( 2 i ϕ ω ) .
I 2 ω z = G 0 1 - I 2 ω / I sat 1 + β I 2 ω / I sat + ( I 2 ω / I sat ) 2 I 2 ω .
G 0 = ( 6 ω 3 e n 2 ω C ) ( κ 3 κ 4 1 μ e χ ( 3 ) ) ( τ m τ R ) .

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