Abstract

This work combines phase perturbation techniques with resonator oscillation formalism to describe the effect of the perturbation on the beam quality of the laser radiation field. The scattering terms of the perturbation are computed to the second order and are used to determine the mode intensity ratios (MIR) and the Strehl ratios. The MIR and Strehl ratios are computed for the simple case of symmetric flat disk undergoing a symmetric linear tilt.

© 1984 Optical Society of America

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References

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  1. J. L. Remo, “Second-order Perturbation Theory for Optical Resonators,” Opt. Lett. 3, 193 (1978); “Diffraction Losses for Symmetrically Tilted Plane Reflectors in Open Resonators,” Appl. Opt. 19, 774 (1980); “Diffraction Losses for Symmetrically Perturbed Curved Reflectors in Open Resonators,” Appl. Opt. 20, 2997 (1981).
    [CrossRef] [PubMed]
  2. See, for example, B. A. Lengyel, Lasers (Wiley-Interscience, New York, 1971), pp. 61–66; or D. C. O’Shea, W. R. Callen, W. T. Rhodes, Introduction to Lasers and Their Applications (Addison-Wesley, Reading, 1978), Chap. 3, pp. 59–62.
  3. D. A. Holmes, P. V. Avizonis, “Approximate Optical System Model,” Appl. Opt. 15, 1075 (1976); B. R. Suydam, IEEE J. Quantum Electron. QE-11, 225 (1975).
    [CrossRef] [PubMed]
  4. A. E. Siegman, “Effects of Small-Scale Phase Perturbations on Laser Oscillator Beam Quality,” IEEE J. Quantum Electron. QE-13, 334 (1977).
    [CrossRef]
  5. Fm depends upon the particular active medium present within the cavity, the scattering cross sections, and the geometrical extent of the active medium.
  6. J. L. Remo, “Nonsymmetric Perturbations of Fabry-Perot Resonators,” Appl. Opt. 22, 517 (1983).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Modern Optics (Pergamon, New York, 1964), Chap. 9, pp. 460–462.
  8. Ref. 7, pp. 463–464, Eqs. (20)–(24).
  9. Ref. 7, pp. 468–473.

1983 (1)

1978 (1)

1977 (1)

A. E. Siegman, “Effects of Small-Scale Phase Perturbations on Laser Oscillator Beam Quality,” IEEE J. Quantum Electron. QE-13, 334 (1977).
[CrossRef]

1976 (1)

Avizonis, P. V.

Born, M.

M. Born, E. Wolf, Principles of Modern Optics (Pergamon, New York, 1964), Chap. 9, pp. 460–462.

Holmes, D. A.

Lengyel, B. A.

See, for example, B. A. Lengyel, Lasers (Wiley-Interscience, New York, 1971), pp. 61–66; or D. C. O’Shea, W. R. Callen, W. T. Rhodes, Introduction to Lasers and Their Applications (Addison-Wesley, Reading, 1978), Chap. 3, pp. 59–62.

Remo, J. L.

Siegman, A. E.

A. E. Siegman, “Effects of Small-Scale Phase Perturbations on Laser Oscillator Beam Quality,” IEEE J. Quantum Electron. QE-13, 334 (1977).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Modern Optics (Pergamon, New York, 1964), Chap. 9, pp. 460–462.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

A. E. Siegman, “Effects of Small-Scale Phase Perturbations on Laser Oscillator Beam Quality,” IEEE J. Quantum Electron. QE-13, 334 (1977).
[CrossRef]

Opt. Lett. (1)

Other (5)

See, for example, B. A. Lengyel, Lasers (Wiley-Interscience, New York, 1971), pp. 61–66; or D. C. O’Shea, W. R. Callen, W. T. Rhodes, Introduction to Lasers and Their Applications (Addison-Wesley, Reading, 1978), Chap. 3, pp. 59–62.

Fm depends upon the particular active medium present within the cavity, the scattering cross sections, and the geometrical extent of the active medium.

M. Born, E. Wolf, Principles of Modern Optics (Pergamon, New York, 1964), Chap. 9, pp. 460–462.

Ref. 7, pp. 463–464, Eqs. (20)–(24).

Ref. 7, pp. 468–473.

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Figures (1)

Fig. 1
Fig. 1

Two identical flat circular disk reflectors symmetrically tilted in a plane normal to the optic axis Z. The optical path length is L, and the radii of each mirror is r. Upon being slightly tilted by α, the radii are denoted by r′. For such a configuration the paraxial beam will be displaced upon each reflection so that the radiation will eventually walk-off from the original optic axis. Since the higher-order modes have a greater lateral extent, they will undergo the greater diffraction losses.

Tables (2)

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Table I Mode Intensity Ratiosa

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Table II Mode Strehl Ratiosa

Equations (21)

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R exp ( g L ) exp ( - a L ) γ 2 = 1 ,
ψ γ = K ^ ψ ,
R G ( 1 - A ) γ 2 = 1 ,
P m ( 0 ) = G m ( 1 - A m ) R m γ m ( 0 ) 2 ,
G m ( 1 - A m ) R m γ m ( 0 ) 2 = 1.
[ P m ( 0 ) ] B = G m ( 1 - A m ) ( 1 - R m ) γ m ( 0 ) 2 .
( P 1 ) B = G 1 ( 1 - A 1 ) ( 1 - R 1 ) γ 1 2 .
( P m ) B = G m ( 1 - A m ) ( 1 - R m ) γ m 2 + G 1 ( 1 - A 1 ) ( 1 - R m ) × γ 1 ( 0 ) 2 S 1 m ( 2 ) 2 F m ,
γ m = [ 1 + S m m ( 1 ) + S m m ( 2 ) + S m n ( 2 ) ] γ m ( 0 ) ,
S m m ( 1 ) = i m Φ 1 + Φ 2 m ,
S m m ( 2 ) = ½ m Φ 1 - Φ 2 m 2 - m Φ 1 2 + Φ 2 2 m ,
S m n ( 2 ) = n m n n Φ 1 + Φ 2 m 2 1 - γ m ( 0 ) / γ n ( 0 ) ,
Φ = α ( 2 π / λ ) f ( r ) ,
I m 1 ( 0 ) = G m ( 1 - A m ) ( 1 - R m ) γ m ( 0 ) 2 G 1 ( 1 - A 1 ) ( 1 - R 1 ) γ 1 ( 0 ) 2
I m 1 = G m ( 1 - A m ) ( 1 - R m ) γ m 2 + γ 1 ( 0 ) 2 S 1 m ( 2 ) 2 G 1 ( 1 - A 1 ) ( 1 - R m ) F m G 1 ( 1 - A 1 ) ( 1 - R 1 ) γ 1 2
S m = γ m 2 G m ( 1 - A m ) ( 1 - R m ) + G 1 ( 1 - A 1 ) ( 1 - R m ) γ 1 ( 0 ) 2 S 1 m ( 2 ) 2 F m γ m ( 0 ) 2 G m ( 1 - A m ) ( 1 - R m ) .
S m = γ m 2 + γ 1 ( 0 ) 2 S 1 m ( 2 ) 2 F m γ m ( 0 ) 2 .
γ m 2 = γ m ( 0 ) 2 | 1 + i m Φ m - ½ m Φ 2 m + n m n m Φ n 2 [ 1 - γ m ( 0 ) / γ n ( 0 ) ] | 2 .
S m = | 1 + i m Φ m - ½ m Φ 2 m + n m n m Φ n 2 [ 1 - γ m ( 0 ) / γ n ( 0 ) | 2 + S 1 m ( 2 ) 2 F m γ 1 ( 0 ) 2 γ m ( 0 ) 2 .
S m = | 1 + i 2 π α / λ m f m - ½ ( 2 π α / λ ) 2 m f 2 m + ( 2 π α / λ ) 2 n m n m f n 2 [ 1 - γ m ( 0 ) / γ n ( 0 ) ] | 2 + S 1 m ( 2 ) 2 F m γ 1 ( 0 ) 2 γ m ( 0 ) 2 ,
i ( p ) ~ 1 + i 2 π / λ ϕ - ½ ( 2 π / λ ) 2 ϕ 2 2 ~ 1 - ( 2 π / λ ) 2 [ ( ϕ 2 ) ¯ - ( ϕ ¯ ) 2 ] .

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