Abstract

We present an analytic method for obtaining phase-matching conditions for general three-wave mixing in biaxial crystals. The method is based on a rarely quoted closed-form solution to the Fresnel equation. Additionally, we show how the method can be used to obtain acceptance angles for both critical and noncritical phase matching and apply the derived formulas to two examples.

© 1992 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 14.
  2. G. A. Skripko, S. G. Bartoshevich, I. V. Mikhnyuk, I. G. Tarazevich, Opt. Lett. 16, 1726 (1991).
    [CrossRef] [PubMed]
  3. B. Wu, N. Chen, C. Chen, D. Deng, Z. Xu, Opt. Lett. 14, 1080 (1989).
    [CrossRef] [PubMed]
  4. E. U. Condon, H. Odishaw, Handbook of Physics (McGraw-Hill, New York, 1967), Chap. 14.
  5. H. Ito, N. Hatsuhiko, H. Inaba, J. Appl. Phys. 46, 3992 (1975) (we correct a typographical error in Eq. 5 of this reference).
    [CrossRef]
  6. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  7. C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, S. Lin, J. Opt. Soc. Am. B 6, 616 (1989).
    [CrossRef]
  8. K. Kato, IEEE J. Quantum Electron. 26, 1173 (1990).
    [CrossRef]

1991 (1)

1990 (1)

K. Kato, IEEE J. Quantum Electron. 26, 1173 (1990).
[CrossRef]

1989 (2)

1975 (1)

H. Ito, N. Hatsuhiko, H. Inaba, J. Appl. Phys. 46, 3992 (1975) (we correct a typographical error in Eq. 5 of this reference).
[CrossRef]

Bartoshevich, S. G.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 14.

Chen, C.

Chen, N.

Condon, E. U.

E. U. Condon, H. Odishaw, Handbook of Physics (McGraw-Hill, New York, 1967), Chap. 14.

Deng, D.

Hatsuhiko, N.

H. Ito, N. Hatsuhiko, H. Inaba, J. Appl. Phys. 46, 3992 (1975) (we correct a typographical error in Eq. 5 of this reference).
[CrossRef]

Inaba, H.

H. Ito, N. Hatsuhiko, H. Inaba, J. Appl. Phys. 46, 3992 (1975) (we correct a typographical error in Eq. 5 of this reference).
[CrossRef]

Ito, H.

H. Ito, N. Hatsuhiko, H. Inaba, J. Appl. Phys. 46, 3992 (1975) (we correct a typographical error in Eq. 5 of this reference).
[CrossRef]

Jiang, A.

Kato, K.

K. Kato, IEEE J. Quantum Electron. 26, 1173 (1990).
[CrossRef]

Li, R.

Lin, S.

Mikhnyuk, I. V.

Odishaw, H.

E. U. Condon, H. Odishaw, Handbook of Physics (McGraw-Hill, New York, 1967), Chap. 14.

Skripko, G. A.

Tarazevich, I. G.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 14.

Wu, B.

Wu, Y.

Xu, Z.

Yariv, A.

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

You, G.

IEEE J. Quantum Electron. (1)

K. Kato, IEEE J. Quantum Electron. 26, 1173 (1990).
[CrossRef]

J. Appl. Phys. (1)

H. Ito, N. Hatsuhiko, H. Inaba, J. Appl. Phys. 46, 3992 (1975) (we correct a typographical error in Eq. 5 of this reference).
[CrossRef]

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

Opt. Lett. (2)

Other (3)

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

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 14.

E. U. Condon, H. Odishaw, Handbook of Physics (McGraw-Hill, New York, 1967), Chap. 14.

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Tables (1)

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Table 1 Measured and Computed ϕ Acceptance Angles (in mrad cm) for Second-Harmonic Generation in LBO (θ = 90°)

Equations (10)

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n 1 - 2 = R 11 2 n x 2 + R 12 2 n y 2 + R 13 2 n z 2 ,
n 2 - 2 = R 21 2 n x 2 + R 22 2 n y 2 + R 23 2 n z 2 .
R = [ cos ψ sin ψ 0 - sin ψ cos ψ 0 0 0 1 ] [ cos θ 0 - sin θ 0 1 0 sin θ 0 cos θ ] × [ cos ϕ sin ϕ 0 - sin ϕ cos ϕ 0 0 0 1 ] ,
tan 2 ψ = sin 2 ϕ cos θ sin 2 ϕ - cos 2 θ cos 2 ϕ + cot 2 β sin 2 θ ,
cot 2 β = ( n y - 2 - n z - 2 ) ( n x - 2 - n y - 2 ) .
Δ k = 4 π λ 1 [ n 2 ( 2 ω ) - n 1 ( ω ) ] ,
L ϕ acc = 1.772 π d ( Δ k ) / d ϕ .
d ( Δ k ) d ϕ = 2 π λ 1 n 2 3 ( 2 ω ) sin 2 ϕ [ 1 n y 2 ( 2 ω ) - 1 n x 2 ( 2 ω ) ] .
Δ k θ = 90 ° = π λ 1 n 1 3 ( ω ) ( sin 2 θ n x 2 + cos 2 ϕ n y 2 - 1 n z 2 ) Δ θ 2 .
Δ k = 2 π [ n 2 ( ω 3 ) λ 3 - n 1 ( ω 2 ) λ 2 - n 2 ( ω 1 ) λ 1 ]

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