Abstract

The effects of hard apertures on the transversal mode distribution and the output near and far field distributions are investigated both theoretically and experimentally. Wavefronts propagating in different directions inside a CO2 laser cavity were measured at the same plane and found to have different transversal amplitude profiles. The influence of intracavity aperture’s location and diameter on the near field distribution and far field beam quality were measured and calculated. Quantitative figures of merit are introduced to evaluate the departure of the transversal mode patterns from ideal Gaussians.

© 1990 Optical Society of America

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References

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  1. A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
  2. T. Li, “Diffraction Loss and Selection of Modes in Maser Resonator with Circular Mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965).
  3. H. P. Kortz, H. Weber, “Diffraction Losses and Mode Structure of Equivalent TEM00 Optical Resonators,” Appl. Opt. 20, 1936–1940 (1981).
    [CrossRef] [PubMed]
  4. M. Piche, P. Lavigne, F. Martin, P.-A. Belanger, “Modes of Resonators with Internal Apertures,” Appl. Opt. 22, 1999–2006 (1983).
    [CrossRef] [PubMed]
  5. A. Kellou, G. Stephan, “Etude du champ proche d’un laser diaphragme,” Appl. Opt. 26, 76–90 (1987).
    [CrossRef] [PubMed]
  6. A. E. Siegman, “Quasi Fast Hankel Transform,” Opt. Lett. 1, 13–15 (1977).
    [CrossRef] [PubMed]
  7. G. P. Agrawal, M. Lax, “End Correction to the Quasi-Fast Hankel Transform for Optical-Propagation Problems,” Opt. Lett. 6, 171–173 (1981).
    [CrossRef] [PubMed]
  8. A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel Diffraction Effects in the Design of High-Power Laser Systems,” Appl. Phys. Lett. 23, 85–87 (1973).
    [CrossRef]

1987

1983

1981

1977

1973

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel Diffraction Effects in the Design of High-Power Laser Systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

1965

T. Li, “Diffraction Loss and Selection of Modes in Maser Resonator with Circular Mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965).

1961

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Agrawal, G. P.

Belanger, P.-A.

Campillo, A. J.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel Diffraction Effects in the Design of High-Power Laser Systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Fox, A. G.

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Kellou, A.

Kortz, H. P.

Lavigne, P.

Lax, M.

Li, T.

T. Li, “Diffraction Loss and Selection of Modes in Maser Resonator with Circular Mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965).

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Martin, F.

Pearson, J. E.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel Diffraction Effects in the Design of High-Power Laser Systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Piche, M.

Shapiro, S. L.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel Diffraction Effects in the Design of High-Power Laser Systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Siegman, A. E.

Stephan, G.

Terrell, N. J.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel Diffraction Effects in the Design of High-Power Laser Systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Weber, H.

Appl. Opt.

Appl. Phys. Lett.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, “Fresnel Diffraction Effects in the Design of High-Power Laser Systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Bell Syst. Tech. J.

A. G. Fox, T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

T. Li, “Diffraction Loss and Selection of Modes in Maser Resonator with Circular Mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965).

Opt. Lett.

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Figures (8)

Fig. 1
Fig. 1

(a) Apertured resonator geometry; (b) equivalent lens guide.

Fig. 2
Fig. 2

Measurement setup.

Fig. 3
Fig. 3

Comparison between intensity patterns of wavefronts measured at the same cavity position but propagating in different directions (experimental results).

Fig. 4
Fig. 4

Variations of the figures of merit F1 and F2 along the optical cavity. (a), (b) Dashed lines correspond to use of an unapertured Gaussian as the reference function, while the solid line uses the least squares fit. (c) Effective waist variations (solid line) for the forward and backward propagating waves compared with the waist of the unapertured Gaussian (dashed line).

Fig. 5
Fig. 5

Calculated intensity profiles at locations (a)–(f) of Fig. 4 (solid line), least squares fit Gaussian (dotted line), and Gaussian of the unapertured resonator (dashed line).

Fig. 6
Fig. 6

Near field measurements at different propagating distances originating from the same cavity and with apertures of different diameter but with the same Fresnel number, N = 4.

Fig. 7
Fig. 7

Comparison between calculated (a) and measured (b) intensity pattern of an aperture-limited cavity.

Fig. 8
Fig. 8

Broadening of far field intensity patterns due to an intracavity aperture decrease in diameter.

Equations (10)

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U n ( r n ) = 0 a i U i ( r i ) ρ i ( r i ) K in ( r i , r n ) r i d r i
K in ( r i , r n ) = J k L i j 0 ( k L i r i r n ) exp [ - j k 2 L i ( r i 2 + r n 2 ) ] ,
γ 1 U 1 ( r 1 ) = 0 a 4 U 4 ( r 4 ) ρ 4 ( r 4 ) K 41 r 4 d r 4 ,
γ 2 U 2 ( r 2 ) = 0 a 1 U 1 ( r 1 ) ρ 1 ( r 1 ) K 12 r 1 d r 1 ,
γ 3 U 3 ( r 3 ) = 0 a 2 U 2 ( r 2 ) ρ 2 ( r 2 ) K 23 r 2 d r 2 ,
γ 4 U 4 ( r 4 ) = 0 a 3 U 3 ( r 3 ) ρ 3 ( r 3 ) K 34 r 3 d r 3 ,
ρ i ( r i ) = exp ( j k R i r i 2 ) for i = 1 , 3 , ρ i ( r i ) = 1 r i < a i for i = 2 , 4.
γ U 1 ( r 1 ) = 0 a 1 U 1 ( r 1 ) K 1234 r 1 d r 1
F 1 = 2 π 0 G ( r ) - I ( r ) r d r 2 π 0 G ( r ) r d r ,
F 2 = max { I ( r ) } max { G ( r ) } ,

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