Abstract

A systematic evaluation of the spectral bandwidth and two acceptance angles of parametric generation processes is presented. The spectral bandwidth and acceptance angles are determined by expanding the wave vector mismatch in a Taylor series and retaining terms through second order. This allows a determination of these parameters even when the first order term vanishes. Conditions where the first order term vanishes are presented and compared with similar cases where the first order term does not vanish.

© 1976 Optical Society of America

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  1. P. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
    [CrossRef]
  2. J. A. Giordmaine, Phys. Rev. Lett. 8, 19 (1962).
    [CrossRef]
  3. J. E. Midwinter, Appl. Phys. Lett. 14, 29 (1969).
    [CrossRef]
  4. J. E. Midwinter, IEEE J. Quantum Electron. QE-4, 716 (1968).
    [CrossRef]
  5. J. Warner, Appl. Phys. Lett. 12, 222 (1968).
    [CrossRef]
  6. J. Warner, Appl. Phys. Lett. 13, 360 (1968).
    [CrossRef]
  7. R. A. Andrews, IEEE J. Quantum Electron. QE-6, 68 (1970).
    [CrossRef]
  8. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  9. G. D. Boyd, D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
    [CrossRef]
  10. S. A. Harris, Proc. IEEE 57, 2096 (1969).
    [CrossRef]
  11. R. Basu, W. H. Steier, IEEE J. Quantum Electron. QE-8, 693 (1972).
    [CrossRef]

1972

R. Basu, W. H. Steier, IEEE J. Quantum Electron. QE-8, 693 (1972).
[CrossRef]

1970

R. A. Andrews, IEEE J. Quantum Electron. QE-6, 68 (1970).
[CrossRef]

1969

J. E. Midwinter, Appl. Phys. Lett. 14, 29 (1969).
[CrossRef]

S. A. Harris, Proc. IEEE 57, 2096 (1969).
[CrossRef]

1968

G. D. Boyd, D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

J. E. Midwinter, IEEE J. Quantum Electron. QE-4, 716 (1968).
[CrossRef]

J. Warner, Appl. Phys. Lett. 12, 222 (1968).
[CrossRef]

J. Warner, Appl. Phys. Lett. 13, 360 (1968).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

J. A. Giordmaine, Phys. Rev. Lett. 8, 19 (1962).
[CrossRef]

1961

P. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Andrews, R. A.

R. A. Andrews, IEEE J. Quantum Electron. QE-6, 68 (1970).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Basu, R.

R. Basu, W. H. Steier, IEEE J. Quantum Electron. QE-8, 693 (1972).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Boyd, G. D.

G. D. Boyd, D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Franken, P.

P. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, Phys. Rev. Lett. 8, 19 (1962).
[CrossRef]

Harris, S. A.

S. A. Harris, Proc. IEEE 57, 2096 (1969).
[CrossRef]

Hill, A. E.

P. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Kleinman, D. A.

G. D. Boyd, D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Midwinter, J. E.

J. E. Midwinter, Appl. Phys. Lett. 14, 29 (1969).
[CrossRef]

J. E. Midwinter, IEEE J. Quantum Electron. QE-4, 716 (1968).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Peters, C. W.

P. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Steier, W. H.

R. Basu, W. H. Steier, IEEE J. Quantum Electron. QE-8, 693 (1972).
[CrossRef]

Warner, J.

J. Warner, Appl. Phys. Lett. 13, 360 (1968).
[CrossRef]

J. Warner, Appl. Phys. Lett. 12, 222 (1968).
[CrossRef]

Weinreich, G.

P. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Appl. Phys. Lett.

J. E. Midwinter, Appl. Phys. Lett. 14, 29 (1969).
[CrossRef]

J. Warner, Appl. Phys. Lett. 12, 222 (1968).
[CrossRef]

J. Warner, Appl. Phys. Lett. 13, 360 (1968).
[CrossRef]

IEEE J. Quantum Electron.

R. A. Andrews, IEEE J. Quantum Electron. QE-6, 68 (1970).
[CrossRef]

J. E. Midwinter, IEEE J. Quantum Electron. QE-4, 716 (1968).
[CrossRef]

R. Basu, W. H. Steier, IEEE J. Quantum Electron. QE-8, 693 (1972).
[CrossRef]

J. Appl. Phys.

G. D. Boyd, D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. Lett.

P. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

J. A. Giordmaine, Phys. Rev. Lett. 8, 19 (1962).
[CrossRef]

Proc. IEEE

S. A. Harris, Proc. IEEE 57, 2096 (1969).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

General wave vector diagram.

Fig. 2
Fig. 2

Spectral bandwidth vs ir wavelength.

Fig. 3
Fig. 3

Collinear and tangential phase matching.

Fig. 4
Fig. 4

Acceptance angles vs ir wavelength.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ω 3 = ω 1 ± ω 2 , k 3 = k 1 + k 2 ,
Δ k = k 1 ± k 2 - k 3 = k 1 cos ψ 3 ± k 2 cos ( ψ 2 - ψ 3 ) - k 3 .
η = S 3 / S 2 = η 0 sin 2 ( Δ k l / 2 ) / ( Δ k l / 2 ) 2 ,
Δ k = ± π / l .
Δ k = Δ k 0 + Δ k X Δ X + 1 2 2 Δ k X 2 Δ X 2 = ± π l
Δ k λ 2 = 2 π [ ± n 2 λ 2 cos ( ψ 2 ψ 3 ) 1 λ 2 n 3 λ 3 λ 3 λ 2 2 n 2 cos ( ψ 2 ψ 3 ) 1 λ 2 2 ± n 3 1 λ 2 2 ] , 2 Δ k λ 2 2 = 2 π [ ± 2 n 2 λ 2 2 1 λ 2 cos ( ψ 2 ψ 3 ) - 2 n 3 λ 3 2 λ 3 3 λ 2 4 ± 2 n 3 λ 3 λ 3 λ 2 3 2 n 2 λ 2 1 λ 2 2 cos ( ψ 2 ψ 3 ) ± 2 n 2 cos ( ψ 2 ψ 2 ) 1 λ 2 3 2 n 3 1 λ 2 3 ] , Δ λ 2 = λ 2 - λ 20 ,
Δ k ψ 2 = 2 π [ + n 2 θ 2 1 λ 2 cos ( ψ 2 ψ 3 ) n 2 λ 2 sin ( ψ 2 ψ 3 ) - n 3 θ 3 ψ 3 ψ 2 1 λ 3 ] , 2 Δ k ψ 2 2 = 2 π [ ± 2 n 2 θ 2 2 1 λ 2 cos ( ψ 2 ψ 3 ) - n 2 θ 2 1 λ 2 sin ( ψ 2 ψ 3 ) ( 1 ψ 3 ψ 2 ) - n 2 θ 2 1 λ 2 sin ( ψ 2 ψ 3 ) n 2 λ 2 cos ( ψ 2 ψ 3 ) ( 1 ψ 3 ψ 2 ) - 2 n 3 θ 3 2 ( ψ 3 ψ 2 ) 2 1 λ 3 - n 3 2 θ 3 ψ 3 ψ 2 2 1 λ 3 ] , ψ 3 ψ 2 cos ψ 2 [ ( λ 2 n 3 λ 3 n 2 ) 2 - sin 2 ψ 2 ] - 1 / 2 , Δ ψ 2 = ψ 2 - ψ 20 .
Δ k χ 2 = 0 , 2 Δ k χ 2 2 = 2 π [ - n 1 λ 1 cos ψ 3 ( χ 3 χ 2 ) 2 ± 2 n 2 χ 2 2 1 λ 2 cos ( ψ 2 ψ 3 ) n 2 λ 2 cos ( ψ 2 ψ 3 ) ( 1 χ 3 χ 2 ) 2 - 2 n 3 χ 3 2 1 λ 3 ( χ 3 χ 2 ) 2 ] , χ 3 χ 2 λ 3 n 2 λ 2 n 3 , Δ χ 2 = χ 2 .

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