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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    [CrossRef]
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    [CrossRef]
  18. 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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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]

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.

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.

Laurito, M.

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.

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.

Pecchia, A.

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.

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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