Abstract

We present theoretical and experimental studies of the process of two-wave mixing of broadband radiation in BaTiO3. We show that the energy exchange in such a process can be calculated on the basis of a system of coupled-wave equations in which phase-mismatch diffraction processes are taken into account. Good agreement of the model predictions and measurements performed with a variable-bandwidth Ti:sapphire laser is reported. Reasonable amplification of light with a FWHM spectrum of as much as 10 nm is reported in a standard copropagation scheme; above this value a considerable gain decrease and significant spatial profile changes occur.

© 1999 Optical Society of America

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References

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1998 (1)

M. B. Danailov, K. Diomande, P. Apai, and R. Szipocs, “Phase conjugation of broad-band laser pulses in BaTiO3,” J. Mod. Opt. 45, 5–9 (1998).
[CrossRef]

1997 (2)

1996 (1)

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1992 (2)

1991 (3)

1990 (3)

1989 (1)

1986 (1)

Y. Fainman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. (Bellingham) 25, 228–234 (1986).
[CrossRef]

Acioli, L. H.

Apai, P.

M. B. Danailov, K. Diomande, P. Apai, and R. Szipocs, “Phase conjugation of broad-band laser pulses in BaTiO3,” J. Mod. Opt. 45, 5–9 (1998).
[CrossRef]

Bacher, G. D.

Bogodaev, N. V.

Chen, B. S.

Cronin-Golomb, M.

Danailov, M. B.

M. B. Danailov, K. Diomande, P. Apai, and R. Szipocs, “Phase conjugation of broad-band laser pulses in BaTiO3,” J. Mod. Opt. 45, 5–9 (1998).
[CrossRef]

De La Cruz, S.-Ch.

Diomande, K.

M. B. Danailov, K. Diomande, P. Apai, and R. Szipocs, “Phase conjugation of broad-band laser pulses in BaTiO3,” J. Mod. Opt. 45, 5–9 (1998).
[CrossRef]

Eason, R. W.

Fainman, Y.

Y. Fainman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. (Bellingham) 25, 228–234 (1986).
[CrossRef]

Feinberg, J.

Feldman, B. J.

Fujimoto, J. G.

Gu, C.

He, Q. B.

Hofmeister, R.

Hsu, K. Y.

Ippen, E. P.

Ivleva, L. I.

Klancnik, E.

Y. Fainman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. (Bellingham) 25, 228–234 (1986).
[CrossRef]

Klein, M. B.

Kong, H.

Korshunov, A. S.

Krolikowski, W.

Lan, G.

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

Lang, R. J.

Lee, S. H.

Y. Fainman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. (Bellingham) 25, 228–234 (1986).
[CrossRef]

Lin, S.

Liu, H.-K.

Liu, S.

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

MacCormack, S.

McMichael, I.

O’Brien, S.

Polozkov, N. M.

Rabinovich, W. S.

Saxena, R.

Shkunov, V. V.

Sun, Q.

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

Szipocs, R.

M. B. Danailov, K. Diomande, P. Apai, and R. Szipocs, “Phase conjugation of broad-band laser pulses in BaTiO3,” J. Mod. Opt. 45, 5–9 (1998).
[CrossRef]

Ulman, M.

Vachss, F.

Wechsler, B. A.

Wu, C.

Xu, J.

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

Yagi, Sh.

Yang, Ch.

Yariv, A.

Yeh, P.

Yi, X.

Zhang, Ch.

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

Zhank, G.

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

J. Mod. Opt. (1)

M. B. Danailov, K. Diomande, P. Apai, and R. Szipocs, “Phase conjugation of broad-band laser pulses in BaTiO3,” J. Mod. Opt. 45, 5–9 (1998).
[CrossRef]

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

J. Opt. Soc. Am. B (6)

Opt. Commun. (2)

Q. Sun, J. Xu, S. Liu, G. Lan, Ch. Zhang, and G. Zhank, “The influence of longitudinal modes of lasers on the photorefractive two-wave coupling,” Opt. Commun. 129, 189–192 (1996).
[CrossRef]

M. Cronin-Golomb, “Whole beam method for photorefractive nonlinear optics,” Opt. Commun. 89, 276–282 (1992).
[CrossRef]

Opt. Eng. (Bellingham) (1)

Y. Fainman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. (Bellingham) 25, 228–234 (1986).
[CrossRef]

Opt. Lett. (6)

Other (2)

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

M. B. Danailov, A. Pecchia, and M. Laurito, “Broad spectrum two-wave-mixing in BaTiO3,” presented at CLEO/Europe, Glasgow, Scotland, September 14–18, 1998, paper CWK5.

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Figures (4)

Fig. 1
Fig. 1

k-vector space diagrams of the wave mixing for two frequencies, j and m. (a) k-vectors of the initial beams and gratings (solid lines) and of the first-order beams kaj(1, m) and kam(1, l) (dashed lines) generated by diffraction of kbj(0) and kbm(0), respectively. Δαjm is the phase mismatch. (b) Second-order beam generation by diffraction of kbj(0) on the new grating created by kam(1, l) and kbm(0). The new beam and grating are plotted by dotted lines.

Fig. 2
Fig. 2

Experimental setup: CM1–CM4, cavity mirrors; S, variable slit; other abbreviations defined in text.

Fig. 3
Fig. 3

Experimental and calculated gain curves at several spectral widths.

Fig. 4
Fig. 4

Input (solid curves), calculated amplified (dashed curves), and measured amplified (dotted–dashed curves) spectra for 10- and 6-nm spectral widths.

Equations (26)

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Es=j,(n)Aj(n) exp{i[ωjt-kaj(n)·r]}
Ep=jBj exp[i(ωjt-kbj·r)],
kaj(n)=αaj(n)xˆ+βaj(n)zˆ,
kbj=αbjxˆ+βbjzˆ
I=I0+j(n)Aj(n)Bj* exp{i[kaj(n)-kbj]·r}+c.c.+j(n)(n)Aj(n)Aj(n)* exp{i[kaj(n)-kaj(n)]·r},
I0=j(n)|Aj(n)|2+j|Bj|2.
EsjAj(0)+(m)(0)Aj(1,m)+(m),(l)(0)Aj(2,m,l)×exp{i[ωjt-kaj(0)·r]}=jAj exp{i[ωjt-kaj(0)·r]}.
AjAj(0)+(m)(0)Aj(1,m)+(m),(l)(0)Aj(2,m,l)(n)Aj(n),
I0=j(n)Aj(n)2+j|Bj|2=j|Aj|2+|Bj|2.
n=n0+m,(n)n1[kam(n)-kbm]Am(n)Bm*I0×exp(iϕ)exp{-i[kam(n)-kbm]·r}+c.c.,
n1[kam(n)-kbm]Δn.
2ij,(p)αaj(p)ddxAj(p) exp{i[ωjt-kaj(p)·r]}+αbjddxBj exp[i(ωjt-kbj·r)]
=n0Δnc2I0(n),mAm(n)Bm* exp(iϕ)exp{-i[kam(n)-kbm]
·r}+c.c.j,(q)ωj2(Aj(q) exp{i[ωjt-kaj(q)·r]}
+Bj exp[i(ωjt-kbj·r)]).
ddx(n)Aj(n)
=ω2n0Δn2c2I0αj(0)Aj(0)Bj*Bj+mjAm(0)Bm*Bj exp(iΔαmjx)+mjAj(1,m)Bj*Bj+mjAm(1,l)Bm*Bj exp(iΔαmjlx)+mjlmAj(2,m,l)Bj*Bj,
Δαmj=αam(0)-αbm(0)+αbj(0)-αaj(1,m),
Δαmjl=αam(1,l)-αbm(0)+αbj(0)-αaj(2,m,l).
ddx(n)Aj(n)=ω2n0Δn2c2I0αj(0)(n)Aj(n)Bj*Bj+mjAm(0)+lmAm(1,l)Bm*Bj exp(iΔαmjx),
Aj(0)+mjAj(1,m)(n)Aj(n),
ddxAj=γ2I0m[AmBm* exp(iΔαmjx)]Bj.
ddxBj=-γ2I0m[Am*Bm exp(-iΔαmjx)]Aj.
γ=2πn1λcos ϑ.
Δαmj=4πncsin2 θcos θ(νm-νj).
ddx(Iaj+Ibj)=0,

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