Abstract

The quasi-stationary wave patterns inside a two-mirror optical resonator are evaluated as the sum of a progressive and a regressive wave by assuming the mirrors to be illuminated by the fundamental mode of the resonator at a resonance frequency. The progressive and the regressive waves are also evaluated in the case of the first-order mode. Calculations are made for an infinite-strip Fabry-Perot resonator, as well as for a cylindrical and a confocal resonator, with Fresnel number N = 1.

© 1971 Optical Society of America

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References

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  1. G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).
  2. A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1965).
  3. G. Toraldo di Francia, Appl. Opt. 4, 1267 (1965).
    [CrossRef]
  4. L. A. Wainstein, Open Resonators and Open Waveguides (Golem Press, Denver, 1969).
  5. G. Goubau, F. Schwering, IEEE Trans. Microwave Theory Tech. MTT-13, 749 (1965).
    [CrossRef]
  6. V. Fock, L. A. Wainstein, in Proc. Symp. on Electromagnetic Theory and Antennas (Pergamon, London, 1963), p. 11.
  7. L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 157 (1964).
  8. L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 166 (1964).
  9. A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).
  10. F. Schwering, IRE Trans. Antennas Propag. AP-10, 99 (1962).
    [CrossRef]
  11. E. Marom, J. Opt. Soc. Am. 57, 1390 (1967).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Lon-don, 1959), p. 574.
  13. A. G. Fox, T. Li, Proc. IRE 51, 80 (1963).
  14. L. A. Wainstein, High-Power Electron. 4, 106 (1965).
  15. L. A. Wainstein, High-Power Electron. 4, 130 (1965).
  16. J. P. Campbell, L. G. DeShazer, J. Opt. Soc. Am. 59, 1427 (1969).
    [CrossRef]
  17. R. G. Shell, G. Tyras, J. Opt. Soc. Am. 61, 31 (1971).
    [CrossRef]

1971 (1)

1969 (1)

1967 (1)

1965 (5)

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1965).

G. Toraldo di Francia, Appl. Opt. 4, 1267 (1965).
[CrossRef]

G. Goubau, F. Schwering, IEEE Trans. Microwave Theory Tech. MTT-13, 749 (1965).
[CrossRef]

L. A. Wainstein, High-Power Electron. 4, 106 (1965).

L. A. Wainstein, High-Power Electron. 4, 130 (1965).

1964 (2)

L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 157 (1964).

L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 166 (1964).

1963 (1)

A. G. Fox, T. Li, Proc. IRE 51, 80 (1963).

1962 (1)

F. Schwering, IRE Trans. Antennas Propag. AP-10, 99 (1962).
[CrossRef]

1961 (2)

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Arrathoon, R.

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1965).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Lon-don, 1959), p. 574.

Boyd, G. D.

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Campbell, J. P.

DeShazer, L. G.

Fock, V.

V. Fock, L. A. Wainstein, in Proc. Symp. on Electromagnetic Theory and Antennas (Pergamon, London, 1963), p. 11.

Fox, A. G.

A. G. Fox, T. Li, Proc. IRE 51, 80 (1963).

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Gordon, J. P.

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Goubau, G.

G. Goubau, F. Schwering, IEEE Trans. Microwave Theory Tech. MTT-13, 749 (1965).
[CrossRef]

Li, T.

A. G. Fox, T. Li, Proc. IRE 51, 80 (1963).

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Marom, E.

Schwering, F.

G. Goubau, F. Schwering, IEEE Trans. Microwave Theory Tech. MTT-13, 749 (1965).
[CrossRef]

F. Schwering, IRE Trans. Antennas Propag. AP-10, 99 (1962).
[CrossRef]

Shell, R. G.

Siegman, A. E.

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1965).

Toraldo di Francia, G.

Tyras, G.

Wainstein, L. A.

L. A. Wainstein, High-Power Electron. 4, 106 (1965).

L. A. Wainstein, High-Power Electron. 4, 130 (1965).

L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 157 (1964).

L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 166 (1964).

V. Fock, L. A. Wainstein, in Proc. Symp. on Electromagnetic Theory and Antennas (Pergamon, London, 1963), p. 11.

L. A. Wainstein, Open Resonators and Open Waveguides (Golem Press, Denver, 1969).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Lon-don, 1959), p. 574.

Appl. Opt. (1)

Bell Syst. Tech. J. (2)

G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

High-Power Electron. (2)

L. A. Wainstein, High-Power Electron. 4, 106 (1965).

L. A. Wainstein, High-Power Electron. 4, 130 (1965).

IEEE J. Quantum Electron. (1)

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1965).

IEEE Trans. Microwave Theory Tech. (1)

G. Goubau, F. Schwering, IEEE Trans. Microwave Theory Tech. MTT-13, 749 (1965).
[CrossRef]

IRE Trans. Antennas Propag. (1)

F. Schwering, IRE Trans. Antennas Propag. AP-10, 99 (1962).
[CrossRef]

J. Opt. Soc. Am. (3)

Proc. IRE (1)

A. G. Fox, T. Li, Proc. IRE 51, 80 (1963).

Sov. Phys. Tech. Phys. (2)

L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 157 (1964).

L. A. Wainstein, Sov. Phys. Tech. Phys. 9, 166 (1964).

Other (3)

V. Fock, L. A. Wainstein, in Proc. Symp. on Electromagnetic Theory and Antennas (Pergamon, London, 1963), p. 11.

L. A. Wainstein, Open Resonators and Open Waveguides (Golem Press, Denver, 1969).

M. Born, E. Wolf, Principles of Optics (Pergamon, Lon-don, 1959), p. 574.

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Figures (8)

Fig. 1
Fig. 1

Phase and amplitude distribution at various planes z = const of the progressive wave in the case of the fundamental mode (n = 0) of an infinite-strip resonator with N = 1. Top: Fabry-Perot resonator. Center: coaxial resonator. (Dotted lines represent the phase distribution of a cylindrical wave.) Bottom: confocal resonator. (Dotted lines represent the phase distribution of a gaussian beam.)

Fig. 2
Fig. 2

Phase and amplitude distribution at various planes z = const of the progressive wave in the case of the first-order mode (n = 1 of an infinite-strip resonator with N = 1. Top: Fabry-Perot resonator. Center: coaxial resonator. (Dotted lines represent the phase distribution of a cylindrical wave.) Bottom: confocal resonator. (Dotted lines represent the phase distribution of a gaussian beam.)

Fig. 3
Fig. 3

Quasi-stationary wave pattern of the fundamental mode in the side portion of a Fabry-Perot resonator with N = 1.

Fig. 4
Fig. 4

Quasi-stationary wave pattern of the fundamental mode in the central portion of a Fabry-Perot resonator with N = 1.

Fig. 5
Fig. 5

Quasi-stationary wave pattern of the fundamental mode in the side side portion of a coaxial resonator with N = 1.

Fig. 6
Fig. 6

Quasi-stationary wave pattern of the fundamental mode in the central portion of a coaxial resonator with N = 1.

Fig. 7
Fig. 7

Quasi-stationary wave pattern of the fundamental mode in the side portion of a confocal resonator with N = 1.

Fig. 8
Fig. 8

Quasi-stationary wave pattern of the fundamental mode in the central portion of a confocal resonator with N = 1.

Equations (8)

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K 1 ( P 0 , Q ) = exp ( i π / 4 ) [ λ ( z - z 0 ) ] 1 2 exp [ - i k ( z - z 0 ) - i π λ ( x - x 0 ) 2 z - z 0 ] ,
K 2 ( P 0 , Q ) = exp ( i π / 4 ) [ λ ( z - z ¯ 0 ) ] exp { - i k ( z - z ¯ 0 ) - i π λ ( z - z ¯ 0 ) × [ ( x - x 0 ) 2 - 1 R ( z - z ¯ 0 ) x 0 2 ] } ,
v ( Q ) = M 1 u ( P 0 ) K ( P 0 , Q ) d x .
σ n u n ( x ) = exp ( i π / 4 ) ( λ d ) 1 2 - a a u n ( x ) exp [ - i π λ d ( x - x ) 2 ] d x ,
u n ( x ) exp [ - i ( q + 1 ) π ] ,
k d = q π + arg σ n .
σ n u n ( x ) = exp ( i π / 4 ) ( λ d ) 1 2 - a a u n ( x ) exp [ i π λ d ( x + x ) 2 ] d x .
σ n u n ( x ) = exp ( i π / 4 ) ( λ d ) 1 2 - a a u n ( x ) exp ( + i 2 π λ d x x ) d x .

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