Abstract

This paper describes an experiment confirming the existence of the waist shift of a Gaussian beam caused by a dielectric plate. A glass or acrylic plate was inserted in a focused laser beam with its surfaces perpendicular to the beam axis. The waist position of the transmitted beam determined from the measured spot sizes indicates that the shift does occur and its direction and magnitude are consistent with the theory.

© 1989 Optical Society of America

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References

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  1. S. Nemoto, “Waist Shift of a Gaussian Beam by Plane Dielectric Interfaces,” Appl. Opt. 27, 1833 (1988).
    [CrossRef] [PubMed]
  2. S. Nemoto, “Determination of Waist Parameters of a Gaussian Beam,” Appl. Opt. 25, 3859 (1986).
    [CrossRef] [PubMed]
  3. G. Goubau, “Optical Relations for Coherent Wave Beams,” in Electromagnetic Theory and Antennas, E. C. Jordan, Ed. (Pergamon, New York, 1963), p. 907.
  4. H. Kogelnik, “Imaging of Optical Mode Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).
  5. T. S. Chu, “Geometrical Representation of Gaussian Beam Propagation,” Bell Syst. Tech. J. 45, 287 (1966).
  6. L. D. Dickson, “Characteristics of a Propagating Gaussian Beam,” Appl. Opt. 9, 1854 (1970).
    [CrossRef] [PubMed]
  7. H. Kogelnik, “Matching of Optical Modes,” Bell Syst. Tech. J. 42, 334 (1964).
  8. D. Marcuse, Light Transmission Optics (Van Nostrand/Reinhold, New York, 1972), p. 251.
  9. J. M. Khosrofian, B. A. Garetz, “Measurement of a Gaussian Laser Beam Diameter Through the Direct Inversion of Knife-Edge Data,” Appl. Opt. 22, 3406 (1983).
    [CrossRef] [PubMed]
  10. H. R. Bilger, T. Habib, “Knife-Edge Scanning of an Astigmatic Gaussian Beam,” Appl. Opt. 24, 686 (1985).
    [CrossRef] [PubMed]

1988 (1)

1986 (1)

1985 (1)

1983 (1)

1970 (1)

1966 (1)

T. S. Chu, “Geometrical Representation of Gaussian Beam Propagation,” Bell Syst. Tech. J. 45, 287 (1966).

1965 (1)

H. Kogelnik, “Imaging of Optical Mode Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).

1964 (1)

H. Kogelnik, “Matching of Optical Modes,” Bell Syst. Tech. J. 42, 334 (1964).

Bilger, H. R.

Chu, T. S.

T. S. Chu, “Geometrical Representation of Gaussian Beam Propagation,” Bell Syst. Tech. J. 45, 287 (1966).

Dickson, L. D.

Garetz, B. A.

Goubau, G.

G. Goubau, “Optical Relations for Coherent Wave Beams,” in Electromagnetic Theory and Antennas, E. C. Jordan, Ed. (Pergamon, New York, 1963), p. 907.

Habib, T.

Khosrofian, J. M.

Kogelnik, H.

H. Kogelnik, “Imaging of Optical Mode Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).

H. Kogelnik, “Matching of Optical Modes,” Bell Syst. Tech. J. 42, 334 (1964).

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand/Reinhold, New York, 1972), p. 251.

Nemoto, S.

Appl. Opt. (5)

Bell Syst. Tech. J. (3)

H. Kogelnik, “Matching of Optical Modes,” Bell Syst. Tech. J. 42, 334 (1964).

H. Kogelnik, “Imaging of Optical Mode Resonators with Internal Lenses,” Bell Syst. Tech. J. 44, 455 (1965).

T. S. Chu, “Geometrical Representation of Gaussian Beam Propagation,” Bell Syst. Tech. J. 45, 287 (1966).

Other (2)

G. Goubau, “Optical Relations for Coherent Wave Beams,” in Electromagnetic Theory and Antennas, E. C. Jordan, Ed. (Pergamon, New York, 1963), p. 907.

D. Marcuse, Light Transmission Optics (Van Nostrand/Reinhold, New York, 1972), p. 251.

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Figures (10)

Fig. 1
Fig. 1

Waist shift of a Gaussian beam due to a dielectric plate in a medium with an index of unity. Solid and broken curves show the spot size variations.

Fig. 2
Fig. 2

Determination of waist parameters of the beam emitted from a He–Ne laser. Position z = 0 coincides with the laser head.

Fig. 3
Fig. 3

Transformation of waist parameters by a thin positive lens of focal length f.

Fig. 4
Fig. 4

Determination of waist parameters of the beam focused by the lens placed at z = 0.

Fig. 5
Fig. 5

Waist parameters of the focused beam. The plate will be located at position P1 or P2.

Fig. 6
Fig. 6

Determination of waist parameters of the beam passing through a glass plate located at P1.

Fig. 7
Fig. 7

Determination of waist parameters of the beam passing through an acrylic plate located at P1.

Fig. 8
Fig. 8

Determination of waist parameters of the beam passing through a glass or acrylic plate located at P2.

Fig. 9
Fig. 9

Displacement of the beam axis due to a tilted plate.

Fig. 10
Fig. 10

Normalized photocurrent I/I0 vs knife-edge position x for several values of tilt angle θ.

Tables (1)

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Table I Measured Beam Displacements and Refractive Indices

Equations (10)

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Δ z = ( 1 1 / n ) d , s 3 = s 1 .
d 2 / f = [ 1 + D ( D F ) ] / [ 1 + ( D F ) 2 ] ,
s 2 / s 1 = F / [ 1 + ( D F ) 2 ] 1 / 2 ,
D = d 1 / k s 1 2 , F = f / k s 1 2 ,
d 1 = f ± ( s 1 / s 2 ) [ f 2 ( k s 1 s 2 ) 2 ] 1 / 2 ,
d 2 = f ± ( s 2 / s 1 ) [ f 2 ( k s 1 s 2 ) 2 ] 1 / 2 ,
sin θ = n sin ( θ ϕ ) .
δ = A D tan ϕ = ( A C D C ) tan ϕ = ( d / cos θ δ tan θ ) tan ϕ = ( d δ sin θ ) tan ϕ / cos θ ,
ϕ = tan 1 [ δ cos θ / ( d δ sin θ ) ] .
n = sin θ / sin { θ tan 1 [ δ cos θ / ( d δ sin θ ) ] } .

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