Abstract

A general description is given which allows one to determine the diffraction losses and mode structure (intensity and phase distribution) of any arbitrary TEM00 laser resonator lying in the stable region of the stability diagram. By means of equivalence relations and adaption of the aperture size to the size of the undisturbed Gaussian beam it is possible to reduce the number of characterizing parameters to two: the adapting factor s, the product (g1 · g2). Numerical results are shown. The intensity pattern of the far field is discussed.

© 1981 Optical Society of America

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Errata

H. P. Kortz and H. Weber, "Diffraction losses and mode structure of equivalent TEM00 optical resonators: errata," Appl. Opt. 21, 758_1-758 (1982)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-21-5-758_1

References

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  1. W. Koechner, Solid State Laser Engineering (Springer, New York, 1976), Chap. 5.
  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).
  3. T. Li, Bell Syst. Tech. J. 44, 917 (1965).
  4. G. D. Boyd, H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).
  5. J. C. Heurtley, W. Streifer, J. Opt. Soc. Am. 55, 1472 (1965).
    [CrossRef]
  6. W. Müller, “Optimierung eines TEM00 Nd-Lasers und Bestimmung der Beugungsverluste,” Diploma Thesis, Dept. of Physics, U. Kaiserslautern (1974).
  7. H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  8. J. P. Gordon, H. Kogelnik, Bell Syst. Tech. J. 43, 2873 (1964).
  9. W. J. Firth, Opt. Commun. 27, 267 (1978).
    [CrossRef]
  10. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

1978

W. J. Firth, Opt. Commun. 27, 267 (1978).
[CrossRef]

1966

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

1965

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

T. Li, Bell Syst. Tech. J. 44, 917 (1965).

J. C. Heurtley, W. Streifer, J. Opt. Soc. Am. 55, 1472 (1965).
[CrossRef]

1964

J. P. Gordon, H. Kogelnik, Bell Syst. Tech. J. 43, 2873 (1964).

1962

G. D. Boyd, H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

1961

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).

Boyd, G. D.

G. D. Boyd, H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

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).

Firth, W. J.

W. J. Firth, Opt. Commun. 27, 267 (1978).
[CrossRef]

Gordon, J. P.

J. P. Gordon, H. Kogelnik, Bell Syst. Tech. J. 43, 2873 (1964).

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).

Heurtley, J. C.

Koechner, W.

W. Koechner, Solid State Laser Engineering (Springer, New York, 1976), Chap. 5.

Kogelnik, H.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

J. P. Gordon, H. Kogelnik, Bell Syst. Tech. J. 43, 2873 (1964).

G. D. Boyd, H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

Li, T.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

T. Li, Bell Syst. Tech. J. 44, 917 (1965).

Müller, W.

W. Müller, “Optimierung eines TEM00 Nd-Lasers und Bestimmung der Beugungsverluste,” Diploma Thesis, Dept. of Physics, U. Kaiserslautern (1974).

Streifer, W.

Bell Syst. Tech. J.

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).

T. Li, Bell Syst. Tech. J. 44, 917 (1965).

G. D. Boyd, H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

J. P. Gordon, H. Kogelnik, Bell Syst. Tech. J. 43, 2873 (1964).

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

J. Opt. Soc. Am.

Opt. Commun.

W. J. Firth, Opt. Commun. 27, 267 (1978).
[CrossRef]

Proc. IEEE

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Other

W. Koechner, Solid State Laser Engineering (Springer, New York, 1976), Chap. 5.

W. Müller, “Optimierung eines TEM00 Nd-Lasers und Bestimmung der Beugungsverluste,” Diploma Thesis, Dept. of Physics, U. Kaiserslautern (1974).

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Figures (7)

Fig. 1
Fig. 1

Unsymmetrical spherical resonator with apertures of diameter 2ai. The Gaussian TEM00 beam has the sizes 2wi in the mirror planes F, i = 1,2.

Fig. 2
Fig. 2

Replacement of an unsymmetrical resonator with one aperture by a symmetrical resonator with two apertures.

Fig. 3
Fig. 3

Power loss per full resonator round trip for the two-aperture case for four different adapting factors of the aperture size to the Gaussian beam size (□ from Ref. 3).

Fig. 4
Fig. 4

Power loss per full resonator round trip for the one-aperture case for four different adapting factors.

Fig. 5
Fig. 5

Intensity and phase in the mirror planes. Intensity is normalized to Jmax = const. Radius r is normalized to equal size of the apertures (four different adapting factors).

Fig. 6
Fig. 6

Intensity of the first side maxima of the far-field distribution in comparison with the main maximum (four different adapting factors).

Fig. 7
Fig. 7

Halfwidth of the Gaussian-like far-field beam in comparison with the halfwidth of an undisturbed Gaussian beam.

Equations (12)

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g i = 1 L / ρ i i = 1 , 2 ; L = resonator length ; ρ i = radius of curvature of the mirrors .
w i 2 = λ L π [ g j g i ( 1 g 1 g 2 ) ] 1 / 2
L 0 = L ( 1 g 1 ) g 2 g 1 + g 2 2 g 1 g 2 .
N = a 1 a 2 λ L
γ 1 u 1 ( x 1 , y 1 ) = i λ L A 2 K u 2 ( x 2 , y 2 ) d A 2 , γ 2 u 2 ( x 2 , y 2 ) = i λ L A 1 K u 1 ( x 1 , y 1 ) d A 1 ,
K ( x 1 , x 2 , y 1 , y 2 ) = exp { i π λ L [ g 1 ( x 1 2 + y 1 2 ) + g 2 ( x 2 2 + y 2 2 ) 2 ( x 1 x 2 + y 1 y 2 ) ] } .
a i = s w i ,
N = a 1 a 2 / λ L , G 1 = g 1 ( a 1 / a 2 ) , G 2 = g 2 ( a 2 / a 1 ) .
G 1 = G 2 = g 1 g 2 ,
N = s 2 π 1 g 1 g 2 .
G 1 = G 2 = 2 g 1 g 2 1 ,
N = s 2 2 π g 1 g 2 g 1 g 2 1 .

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