Abstract

A method is presented for finding the output phase front ψ(r,ϕ) of a large Fresnel number unstable resonator misfigures and misalignments. The technique, which is based on geometric optics, can also be with mirror used to analyze the effects of index of refraction variations. The near-field phase is then used to find the far-field on-axis intensity.

© 1981 Optical Society of America

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References

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  1. A. E. Siegman, Proc. IEEE 53, 277 (1965).
    [CrossRef]
  2. Yu. A. Ananev, Sov. J. Quantum Electron. 1, 565 (1972).
    [CrossRef]
  3. A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
    [CrossRef]
  4. A. E. Siegman, Appl. Opt. 13, 353 (1974).
    [CrossRef] [PubMed]
  5. R. A. Chodzko, H. Mirels, F. Roehrs, R. Pederson, IEEE J. Quantum Electron. QE-9, 523 (1973).
    [CrossRef]
  6. W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
    [CrossRef]
  7. A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).
  8. P. Horwitz, J. Opt. Soc. Am. 63, 1528 (1973).
    [CrossRef]
  9. P. Horwitz, Appl. Opt. 15, 167 (1976).
    [CrossRef] [PubMed]
  10. R. R. Butts, P. V. Avizonis, J. Opt. Soc. Am. 68, 1072 (1978).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 463.
  12. J. B. Shellan, D. A. Holmes, M. L. Bernabe, A. M. Simonoff, Appl. Opt. 19, 610 (1980).
    [CrossRef] [PubMed]
  13. G. Zeiders, “A Study of Wave Characteristics Influence on Laser Selection for Applications: Propagation Analysis,” WJSA-TR-74-18 (August1974), p. 16.

1980 (1)

1978 (1)

1976 (1)

1974 (1)

1973 (2)

R. A. Chodzko, H. Mirels, F. Roehrs, R. Pederson, IEEE J. Quantum Electron. QE-9, 523 (1973).
[CrossRef]

P. Horwitz, J. Opt. Soc. Am. 63, 1528 (1973).
[CrossRef]

1972 (1)

Yu. A. Ananev, Sov. J. Quantum Electron. 1, 565 (1972).
[CrossRef]

1969 (1)

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

1967 (1)

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

1965 (1)

A. E. Siegman, Proc. IEEE 53, 277 (1965).
[CrossRef]

1961 (1)

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Ananev, Yu. A.

Yu. A. Ananev, Sov. J. Quantum Electron. 1, 565 (1972).
[CrossRef]

Arrathoon, R.

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

Avizonis, P. V.

Bernabe, M. L.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 463.

Butts, R. R.

Chodzko, R. A.

R. A. Chodzko, H. Mirels, F. Roehrs, R. Pederson, IEEE J. Quantum Electron. QE-9, 523 (1973).
[CrossRef]

Fox, A. G.

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Holmes, D. A.

Horwitz, P.

Krupke, W. F.

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Li, T.

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Mirels, H.

R. A. Chodzko, H. Mirels, F. Roehrs, R. Pederson, IEEE J. Quantum Electron. QE-9, 523 (1973).
[CrossRef]

Pederson, R.

R. A. Chodzko, H. Mirels, F. Roehrs, R. Pederson, IEEE J. Quantum Electron. QE-9, 523 (1973).
[CrossRef]

Roehrs, F.

R. A. Chodzko, H. Mirels, F. Roehrs, R. Pederson, IEEE J. Quantum Electron. QE-9, 523 (1973).
[CrossRef]

Shellan, J. B.

Siegman, A. E.

A. E. Siegman, Appl. Opt. 13, 353 (1974).
[CrossRef] [PubMed]

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

A. E. Siegman, Proc. IEEE 53, 277 (1965).
[CrossRef]

Simonoff, A. M.

Sooy, W. R.

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 463.

Zeiders, G.

G. Zeiders, “A Study of Wave Characteristics Influence on Laser Selection for Applications: Propagation Analysis,” WJSA-TR-74-18 (August1974), p. 16.

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

IEEE J. Quantum Electron. (3)

R. A. Chodzko, H. Mirels, F. Roehrs, R. Pederson, IEEE J. Quantum Electron. QE-9, 523 (1973).
[CrossRef]

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

A. E. Siegman, R. Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

Proc. IEEE (1)

A. E. Siegman, Proc. IEEE 53, 277 (1965).
[CrossRef]

Sov. J. Quantum Electron. (1)

Yu. A. Ananev, Sov. J. Quantum Electron. 1, 565 (1972).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 463.

G. Zeiders, “A Study of Wave Characteristics Influence on Laser Selection for Applications: Propagation Analysis,” WJSA-TR-74-18 (August1974), p. 16.

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Figures (4)

Fig. 1
Fig. 1

Confocal positive branch unstable resonator.

Fig. 2
Fig. 2

Confocal negative branch unstable resonator.

Fig. 3
Fig. 3

Strehl ratio as a function of k(Mw)4/R3 for spherical aberration.

Fig. 4
Fig. 4

Strehl ratio as a function of rear cone distortion λ/N cos2ϕ.

Equations (24)

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SR = 1 - ( ψ 2 - ψ 2 ) ,
t = 1 π ( M 2 - 1 ) a 2 0 2 π a M a t ( r , ϕ ) r d r d ϕ
ψ ( r , ϕ ) - ψ ( r / M , ϕ ) = C n p r n exp ( i p ϕ )
ψ ( r / M , ϕ ) - ψ ( r / M 2 , ϕ ) = C n p r n M n exp ( i p ϕ )
ψ ( r , ϕ ) - ψ ( r , M q , ϕ ) = C n p exp ( i p ϕ ) r n [ 1 + 1 M n + 1 M 2 n + + 1 M n ( q - 1 ) ] = M n M n - 1 C n p r n exp ( i p ϕ ) [ 1 - 1 M n q ] .
r M Q = r 0             Q = ln ( r / r 0 ) ln M .
ψ ( r , ϕ ) = M n M n - 1 C n p r n exp ( i p ϕ ) ( 1 - 1 M n Q ) | ,
ψ ( r , ϕ ) = M n M n - 1 C n p r n exp ( i p ϕ ) .
ψ ( r , ϕ ) = limit n 0 C n p M n r n M n - 1 [ 1 - 1 M n Q ] exp ( i p ϕ ) = limit n 0 C o p exp ( i p ϕ ) [ exp ( n ln M ) - 1 ] [ 1 - exp ( - n Q ln M ) ] = C o p Q exp ( i p ϕ ) .
ψ ( r , ϕ ) = C o p ln M ln ( r r 0 ) exp ( i p ϕ )             for n = 0.
ψ ( r , ϕ ) = C 00 ln ( r / r 0 ) ln M .
L = ( N λ ) / 2 , N = an integer .
ψ ( r , ϕ ) - ψ ( r / M , ϕ + π ) = C n p r n exp ( i p ϕ ) .
ψ ( r , ϕ ) = C n p M n ( - 1 ) P r n exp ( i p ϕ ) ( - 1 ) P M n - 1
ψ ( r , ϕ ) = C o p ln M ln ( r r 0 ) exp ( i p ϕ )
ψ ( r , ϕ ) = 2 M M - 1 k χ r cos ϕ ,
Φ 0 = 2 M M - 1 χ .
ψ ( r , ϕ ) = M 4 M 4 - 1 k 4 R 3 r 4 .
ψ f ( r , ϕ ) = ψ ( r , ϕ ) - A r cos ϕ - B r sin ϕ - C r 2 .
A = ψ r cos ϕ / r 2 cos 2 ϕ ,
B = ψ r sin ϕ / r 2 sin 2 ϕ ,
C = [ r 2 ψ - r 2 ψ ] / [ r 4 - r 2 2 ] .
δ ψ 2 = 32 π 2 N 2 ( M 2 - 1 ) ln 2 M [ M 2 2 ln 2 M a r 0 - M 2 2 ln M a r o + M 2 4 - ½ ln 2 a r 0 + ½ ln a r 0 - ¼ ] .
SR = 1 1 + δ ψ 2 .

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