Abstract

We analyze the transmission of a Gaussian beam of low divergence (optical beam) through a high-finesse Fabry–Perot device (R ≈ 70–80%). A detailed calculation of the parameters characterizing the beam (width and curvature radius) is given, and a discussion of the Fabry–Perot effect for low (R < 50%) and very high finesses (R > 90%) also is presented.

© 1992 Optical Society of America

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References

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  1. D. Röss, Lasers, Light Amplifiers and Oscillators (Academic, New York, 1969), Chap.10
  2. F. P. Schäfer, Dye Lasers (Springer-Verlag, New York, 1977), pp. 66–78.
  3. P. W Smith, in Lasers, A. K. Levine, A. J. De Marí, eds. (Dekker, New York, 1976), Vol. 4, Chap. 2
  4. They are usual for Ar+lasers such as the Spectra–Physics Model 2020.
  5. E. Bernabeu, J. C. Amaré, J. M. Alvarez, F. Moreno, “Intensity transmitted by a Fabry–Perot étalon with another internal Fabry–Perot interferometer,” Appl. Opt. 20, 2117–2120 (1981).
    [CrossRef] [PubMed]
  6. P. J. Valle, F. Moreno, “Theoretical study of birefringent filters as intracavity wavelength selectors,” Appl. Opt. 31, 528–535 (1992).
    [CrossRef] [PubMed]
  7. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 2.
  8. O. Svelto, Principles of Lasers (Plenum, New York, 1982), Chap. 4.

1992 (1)

1981 (1)

Alvarez, J. M.

Amaré, J. C.

Bernabeu, E.

Moreno, F.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 2.

Röss, D.

D. Röss, Lasers, Light Amplifiers and Oscillators (Academic, New York, 1969), Chap.10

Schäfer, F. P.

F. P. Schäfer, Dye Lasers (Springer-Verlag, New York, 1977), pp. 66–78.

Smith, P. W

P. W Smith, in Lasers, A. K. Levine, A. J. De Marí, eds. (Dekker, New York, 1976), Vol. 4, Chap. 2

Svelto, O.

O. Svelto, Principles of Lasers (Plenum, New York, 1982), Chap. 4.

Valle, P. J.

Appl. Opt. (2)

Other (6)

D. Röss, Lasers, Light Amplifiers and Oscillators (Academic, New York, 1969), Chap.10

F. P. Schäfer, Dye Lasers (Springer-Verlag, New York, 1977), pp. 66–78.

P. W Smith, in Lasers, A. K. Levine, A. J. De Marí, eds. (Dekker, New York, 1976), Vol. 4, Chap. 2

They are usual for Ar+lasers such as the Spectra–Physics Model 2020.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 2.

O. Svelto, Principles of Lasers (Plenum, New York, 1982), Chap. 4.

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Equations (17)

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A t = A i T exp ( i δ / 2 ) n = 0 R n exp ( i n δ ) ,
δ = k q Δ ,
A t = A i T exp ( i δ / 2 ) [ ( 1 R cos δ ) + i R sin δ ] / ( 1 + R 2 2 R cos δ ) .
δ = k q Δ = k Δ ( 1 p 2 / 2 ) .
δ = m π p 2 .
A t = 4 A i T exp ( ikqd ) [ b / ( k R 1 / 2 ) i p 2 / 2 ] / { k Δ [ ( 2 b / k ) 2 + · p 4 ] } 2 A i T exp ( ikqd ) M ( p ) × exp [ i Φ ( p ) ] / { k Δ [ ( 2 b / k ) 2 + p 4 ] } .
M ( p ) = { ( 1 + T ) [ ( 2 b / k ) 2 ] + p 4 } 1 / 2 , Φ ( p ) = tan 1 [ k R 1 / 2 p 2 / ( 2 b ) ] ,
Φ ( p ) = tan 1 ( R 1 / 2 m F p 2 ) ,
A i ( p ) = ( k w 0 ) 2 / ( 4 π ) exp [ ( k w 0 ) 2 p 2 / 4 ] .
A t ( x , z ) = + A t ( p ) exp [ i k ( p x + q z ) ] d p .
A t ( x , z ) = exp ( ikz ) + A t ( p ) exp ( ikz p 2 / 2 ) exp ( ikpx ) d p ,
tan 1 [ ( R 1 / 2 k p 2 ) / ( 2 b ) ] R 1 / 2 k p 2 / ( 2 b ) .
A t ( x , z ) = exp [ i k ( z + d ) ] × + exp { [ ( w 0 k / 2 ) 2 + i k ( z + d + R 1 / 2 / b ) / 2 ] p 2 } × M ( p ) / [ ( 2 b / k ) 2 + p 4 ] exp ( ikpx ) d p ,
A t ( x , z ) = exp [ i k ( z + d ) ] ( α + i β ) 1 / 2 exp [ x 2 / w ( z ) 2 ] × exp [ i k x 2 / 2 R ( z ) ] ,
w ( z ) 2 = w 0 2 + [ 2 ( z + d + R 1 / 2 / b ) / k w 0 ] 2 ,
R ( z ) = ( z + d + R 1 / 2 / b ) × ( 1 + { ( k w 0 / 2 ) 2 / [ k ( z + d + R 1 / 2 / b ) ] } 2 ) .
w ( z ) 2 = w 0 2 + { 2 [ z + d ( 1 + 2 R 1 / 2 F / π ) ] / k w 0 } 2 .

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