Abstract

By introducing sinusoidal chirping into a periodic nonlinear optical susceptibility, we propose that the Čerenkov radiative second-harmonic generation is greatly enhanced in theoretical calculations, and this is demonstrated with an organic copolymer. The use of nonlinear optical chirping with an average χ(2) period of 20 μm, a modulation period 200 μm (modulation index ≃9), and a total length of 2 mm with the VDCN/VAc copolymer film yields enhanced second-harmonic generation by a factor of ~7. This enhancement is much greater than that with a uniform periodic χ(2) film with a period of 60 μm, which is consistent with the theoretical estimates.

© 1994 Optical Society of America

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References

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  1. H. Itoh, K. Hotta, H. Takada, K. Sasaki, Appl. Opt. 25, 1491 (1986)
    [CrossRef] [PubMed]
  2. K. Hayata, K. Yanagawa, M. Koshiba, Opt. Lett. 15, 999 (1990).
    [CrossRef] [PubMed]
  3. Y. Azumai, I. Seo, H. Sato, Nonlin. Opt. 1, 129 (1991).
  4. Y. Azumai, I. Seo, H. Sato, IEEE J. Quantum Electron. 28, 231 (1992).
    [CrossRef]
  5. Y. Azumai, M. Kishimoto, H. Sato, Jpn. J. Appl. Phys. 31, 1358 (1992).
    [CrossRef]
  6. Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
    [CrossRef]
  7. H. Sato, Y. Azumai, J. Opt. Soc. Am. B 10, 894 (1993).
    [CrossRef]
  8. H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971), Chap. 4.
  9. Y. Azumai, H. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

1993 (2)

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

H. Sato, Y. Azumai, J. Opt. Soc. Am. B 10, 894 (1993).
[CrossRef]

1992 (2)

Y. Azumai, I. Seo, H. Sato, IEEE J. Quantum Electron. 28, 231 (1992).
[CrossRef]

Y. Azumai, M. Kishimoto, H. Sato, Jpn. J. Appl. Phys. 31, 1358 (1992).
[CrossRef]

1991 (1)

Y. Azumai, I. Seo, H. Sato, Nonlin. Opt. 1, 129 (1991).

1990 (1)

1986 (1)

Azumai, Y.

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

H. Sato, Y. Azumai, J. Opt. Soc. Am. B 10, 894 (1993).
[CrossRef]

Y. Azumai, M. Kishimoto, H. Sato, Jpn. J. Appl. Phys. 31, 1358 (1992).
[CrossRef]

Y. Azumai, I. Seo, H. Sato, IEEE J. Quantum Electron. 28, 231 (1992).
[CrossRef]

Y. Azumai, I. Seo, H. Sato, Nonlin. Opt. 1, 129 (1991).

Y. Azumai, H. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

Hayata, K.

Hotta, K.

Itoh, H.

Kishimoto, M.

Y. Azumai, M. Kishimoto, H. Sato, Jpn. J. Appl. Phys. 31, 1358 (1992).
[CrossRef]

Koshiba, M.

Sasaki, K.

Sato, H.

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

H. Sato, Y. Azumai, J. Opt. Soc. Am. B 10, 894 (1993).
[CrossRef]

Y. Azumai, M. Kishimoto, H. Sato, Jpn. J. Appl. Phys. 31, 1358 (1992).
[CrossRef]

Y. Azumai, I. Seo, H. Sato, IEEE J. Quantum Electron. 28, 231 (1992).
[CrossRef]

Y. Azumai, I. Seo, H. Sato, Nonlin. Opt. 1, 129 (1991).

Y. Azumai, H. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

Schilling, D. L.

H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971), Chap. 4.

Seo, I.

Y. Azumai, I. Seo, H. Sato, IEEE J. Quantum Electron. 28, 231 (1992).
[CrossRef]

Y. Azumai, I. Seo, H. Sato, Nonlin. Opt. 1, 129 (1991).

Takada, H.

Taub, H.

H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971), Chap. 4.

Yanagawa, K.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

Y. Azumai, I. Seo, H. Sato, IEEE J. Quantum Electron. 28, 231 (1992).
[CrossRef]

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

Jpn. J. Appl. Phys. (2)

Y. Azumai, M. Kishimoto, H. Sato, Jpn. J. Appl. Phys. 31, 1358 (1992).
[CrossRef]

Y. Azumai, H. Sato, Jpn. J. Appl. Phys. 32, 800 (1993).
[CrossRef]

Nonlin. Opt. (1)

Y. Azumai, I. Seo, H. Sato, Nonlin. Opt. 1, 129 (1991).

Opt. Lett. (1)

Other (2)

H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971), Chap. 4.

Y. Azumai, H. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

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Figures (6)

Fig. 1
Fig. 1

Theoretical model of chirped NLO χ(2) corrugation.

Fig. 2
Fig. 2

Numerical calculations of relative SHG power as a function (a) of NLO film thickness d and the modulation index ϕm and (b) of ϕm and the average modulation period Λso.

Fig. 3
Fig. 3

(a) Schematic showing the experimental setup: M1, M2, mirrors forming the resonator; F1, F2, filters; B.S., beam splitter; ATT., attenuator; CRT, cathode-ray tube, (b) The electrode pattern used for poling, where the modulation index ϕm corresponds to ϕm ≃ 9.

Fig. 4
Fig. 4

Observed second-harmonic (lower curves) and fundamental (upper curves) waveforms with (a) chirped χ(2) corrugation and (b) uniform χ(2) corrugation. Upper curves, 5 mV/division; lower curves, (a) 100 mV/division and (b) 50 mV/division; time, 100 μs/division.

Fig. 5
Fig. 5

Enhanced SHG power obtained with the chirped χ(2) corrugated scheme, in which the enhancement factor was ~7, in comparison with the nonchirped (uniform period, Λs = 60 μm) scheme.

Fig. 6
Fig. 6

Comparison of the experimental results with theoretical estimates.

Equations (7)

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χ ( 2 ) ( y ) = χ o ( 2 ) [ 1 + cos ( β so y + ϕ m sin β m y ) ] ,
χ ( 2 ) ( y ) χ o ( 2 ) ( 1 + 1 2 p = ( ϕ m + 1 ) ϕ m + 1 J p ( ϕ m ) × { exp [ i ( β so + p β m ) y ] + exp [ i ( β so + p β m ) y ] } ) ,
P 2 ω = L 4 ω μ o [ β 2 ω | A ˜ u , 2 ω | 2 tan θ c + p = ( β 2 ω , p + | A ˜ u , 2 ω , p + | 2 tan θ c , p + + β 2 ω , p | A ˜ u , 2 ω , p | 2 tan θ c , p + p = ( ϕ m + 1 ) ϕ m + 1 ( Re { A ˜ u , 2 ω * A ˜ u , 2 ω , p exp [ i ( β 2 ω β 2 ω , p ) L ] ( β 2 ω + β 2 ω , p ) tan θ c } + Re { A ˜ u , 2 ω , p + * A ˜ u , 2 ω exp [ i ( β 2 ω , p + β 2 ω ) L ] ( β 2 ω , p + + β 2 ω ) tan θ c , p + } + q = ( ϕ m + 1 ) ϕ m + 1 { Re { A ˜ u , 2 ω , p + * A ˜ u , 2 ω , q exp [ i ( β 2 ω , p + β 2 ω , q ) L ] ( β 2 ω , p + + β 2 ω , q ) tan θ c , p + } ) ] ,
θ c = cos 1 ( β 2 ω / k o , 2 ω n u , 2 ω ) ,
θ c , p ± = cos 1 ( β 2 ω , p ± / k o , 2 ω n u , 2 ω ) , p = ( ϕ m + 1 ) ( ϕ m + 1 ) .
β 2 ω = 2 β ω ,
β 2 ω = β 2 ω , p ± = 2 β ω ± ( β so + p β m ) , p = ( ϕ m + 1 ) ( ϕ m + 1 ) .

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