Abstract

Focusing an intense laser beam and its second harmonic into a glass fiber transforms the fiber into a frequency doubler. We measure the temporal evolution of both the amplitude and the phase of the second-harmonic light produced by a germanium-doped fiber and so determine the initial phase of the second-harmonic light to be Δθ = −71° ± 3°. We demonstrate that the fiber-produced green light can exceed the seeding green light even if these two beams are 90° out of phase. We also show that cross-phase modulation in the fiber can limit the maximum useful interaction length and consequently the ultimate efficiency of second-harmonic generation in fibers.

© 1996 Optical Society of America

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References

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1995 (1)

1993 (2)

1992 (1)

E. M. Dianov, P. G. Kazansky, D. S. Starodubov, D. Yu. Stepanov, Sov. Lightwave Commun. 2, 83 (1992).

1991 (3)

1990 (3)

Yu. E. Kapitzky, B. Ya. Zel’dovich, Opt. Commun. 78, 227 (1990).
[CrossRef]

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

E. M. Dianov, P. G. Kazanskii, D. Yu. Stepanov, Sov. J. Quantum Electron. 20, 849 (1990).
[CrossRef]

1989 (2)

1987 (1)

1986 (1)

1978 (1)

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Anderson, D. Z.

Baranova, N. B.

Bolshtyansky, M. A.

Carvalho, I. C. S.

Chudinov, A. N.

Churikov, V. M.

Dianov, E. M.

E. M. Dianov, P. G. Kazansky, D. S. Starodubov, D. Yu. Stepanov, Sov. Lightwave Commun. 2, 83 (1992).

E. M. Dianov, P. G. Kazanskii, D. Yu. Stepanov, Sov. J. Quantum Electron. 20, 849 (1990).
[CrossRef]

Dominic, V.

Dyakonov, M. I.

M. I. Dyakonov, A. S. Furman, Electron. Lett. 27, 1429 (1991).
[CrossRef]

Feinberg, J.

Furman, A. S.

M. I. Dyakonov, A. S. Furman, Electron. Lett. 27, 1429 (1991).
[CrossRef]

Hibino, Y.

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

Kapitzky, Yu. E.

Kazanskii, P. G.

E. M. Dianov, P. G. Kazanskii, D. Yu. Stepanov, Sov. J. Quantum Electron. 20, 849 (1990).
[CrossRef]

Kazansky, P. G.

E. M. Dianov, P. G. Kazansky, D. S. Starodubov, D. Yu. Stepanov, Sov. Lightwave Commun. 2, 83 (1992).

Koch, K.

Lambelet, P.

Lin, C.

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Margulis, W.

Mizrahi, V.

D. Z. Anderson, V. Mizrahi, J. E. Sipe, Opt. Lett. 16, 796 (1991).
[CrossRef] [PubMed]

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

Moore, G. T.

Österberg, U.

Savchenko, A. Yu.

Shulginov, A. A.

Sipe, J. E.

Starodubov, D. S.

E. M. Dianov, P. G. Kazansky, D. S. Starodubov, D. Yu. Stepanov, Sov. Lightwave Commun. 2, 83 (1992).

Stegeman, G.

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

Stepanov, D. Yu.

E. M. Dianov, P. G. Kazansky, D. S. Starodubov, D. Yu. Stepanov, Sov. Lightwave Commun. 2, 83 (1992).

E. M. Dianov, P. G. Kazanskii, D. Yu. Stepanov, Sov. J. Quantum Electron. 20, 849 (1990).
[CrossRef]

Stolen, R. H.

Tom, H. W. K.

von der Weid, J. P.

Zel’dovich, B. Ya.

Electron. Lett. (1)

M. I. Dyakonov, A. S. Furman, Electron. Lett. 27, 1429 (1991).
[CrossRef]

Opt. Commun. (2)

Yu. E. Kapitzky, B. Ya. Zel’dovich, Opt. Commun. 78, 227 (1990).
[CrossRef]

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

Opt. Lett. (8)

Phys. Rev. A (1)

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Phys. Rev. Lett. (1)

V. Dominic, J. Feinberg, Phys. Rev. Lett. 71, 3446 (1993).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

E. M. Dianov, P. G. Kazanskii, D. Yu. Stepanov, Sov. J. Quantum Electron. 20, 849 (1990).
[CrossRef]

Sov. Lightwave Commun. (1)

E. M. Dianov, P. G. Kazansky, D. S. Starodubov, D. Yu. Stepanov, Sov. Lightwave Commun. 2, 83 (1992).

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Figures (3)

Fig. 1
Fig. 1

Setup for determining the phase of the green light generated in the fiber with respect to the green seeding light from the LBO crystal. Translating the dispersive prism shifts the relative phase of the green beam (either LBO-generated or fiber-generated) compared with that of a common phase-reference green beam from the KTP crystal.9

Fig. 2
Fig. 2

Variation of the measured phase θ of the fiber-produced green light for different reading infrared powers Pω. For Pω = 0.5 W (which corresponds to powermeter setting during writing), we set θ = 0°. As we change the infrared reading power, the phase θ varies as the result of nonlinear phase modulation in the fiber. This effect eventually limits the efficiency of frequency doubling in a long fiber.

Fig. 3
Fig. 3

Measurement of (a) the phase and (b) the power of the total green light (seed plus fiber-generated) from the fiber during seeding. The curves are theoretical fits from Eqs. (1). We tried Δθ0 = −50° (dashed curves), Δθ0 = −71° (solid curves), and Δθ0 = −90° (dotted curves). We used the growth rate coefficient β and the photoconductivity σ of the glass as free parameters. At time t = 0, only the seeding light is present, and the green phase is θ = 0° by convention.

Equations (2)

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δ E dc δ t + σ 0 E dc = β E 2 ω ( E ω * ) 2 × exp [ i ( k 2 ω 2 k ω ) z + ϕ β ] + c . c . ,
δ E 2 ω δ z = i 3 ω 2 c n 2 ω χ ( 3 ) E dc ( E ω ) 2 exp [ i ( k 2 ω 2 k ω ) z ] .

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