Abstract

Computer studies have shown that azimuthal static mirror misfigures as small as λ/20 can lead to severe degradation in the far field on axis intensity for resonators with an annular gain region. This poor far-field pattern can, however, be dramatically improved by the use of adaptive elements within the resonator. A rear cone in the resonator had a static misfigure applied to it, and an adaptive ring axicon located in the front of the resonator was deformed in such a way as to compensate for the misfigure of the rear element of the resonator.

© 1980 Optical Society of America

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References

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1979 (2)

1978 (2)

1976 (1)

1975 (2)

1974 (1)

1973 (5)

L. W. Casperson, J. Opt. Soc. Am. 63, 25 (1973).
[Crossref]

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

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

D. Milam, H. Schlossberg, J. Appl. Phys. 44, 2297 (1973).
[Crossref]

C. Chi, Opt. Acta 20, 979 (1973).
[Crossref]

1972 (1)

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

1971 (1)

R. K. Garnsworthy, L. E. S. Mathias, C. H. N. Carmichael, Appl. Phys. Lett. 19, 506 (1971).
[Crossref]

1970 (1)

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, 227 (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]

Bernabe, M. L.

Burlamacchi, P.

Carmichael, C. H. N.

R. K. Garnsworthy, L. E. S. Mathias, C. H. N. Carmichael, Appl. Phys. Lett. 19, 506 (1971).
[Crossref]

Casperson, L. W.

Chi, C.

C. Chi, Opt. Acta 20, 979 (1973).
[Crossref]

Chodzko, R. A.

R. A. Chodzko, S. B. Mason, E. F. Cross, Appl. Opt. 15, 2137 (1976).
[Crossref] [PubMed]

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

Cross, E. F.

Fink, D.

Fox, A. G.

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

Garnsworthy, R. K.

R. K. Garnsworthy, L. E. S. Mathias, C. H. N. Carmichael, Appl. Phys. Lett. 19, 506 (1971).
[Crossref]

Horwitz, P.

Kreuzer, J. L.

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).

Mason, S. B.

Mathias, L. E. S.

R. K. Garnsworthy, L. E. S. Mathias, C. H. N. Carmichael, Appl. Phys. Lett. 19, 506 (1971).
[Crossref]

McCullough, A. W.

Milam, D.

D. Milam, H. Schlossberg, J. Appl. Phys. 44, 2297 (1973).
[Crossref]

Miller, H. Y.

Mirels, H.

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

Mumola, P. B.

Murphy, W. D.

Pederson, R.

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

Pratesi, R.

Robertson, H. J.

Roehrs, F.

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

Ronchi, L.

Schlossberg, H.

D. Milam, H. Schlossberg, J. Appl. Phys. 44, 2297 (1973).
[Crossref]

Shabbir Shekhani, M.

Siegman, A.

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, 227 (1965).
[Crossref]

Sooy, W. R.

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

Southwell, W. H.

Steinberg, G. N.

Appl. Opt. (9)

Appl. Phys. Lett. (1)

R. K. Garnsworthy, L. E. S. Mathias, C. H. N. Carmichael, Appl. Phys. Lett. 19, 506 (1971).
[Crossref]

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. Appl. Phys. (1)

D. Milam, H. Schlossberg, J. Appl. Phys. 44, 2297 (1973).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

C. Chi, Opt. Acta 20, 979 (1973).
[Crossref]

Proc. IEEE (1)

A. E. Siegman, Proc. IEEE 53, 227 (1965).
[Crossref]

Sov. J. Quantum Electron. (1)

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

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Figures (10)

Fig. 1
Fig. 1

Common pass annular resonator. The beam compactor consists of two toric parabolas with a common ring focus. The focal length ratio is m.

Fig. 2
Fig. 2

Rear cone with a static misfigure of the form (λ/N) cosϕ. Dotted surface and ray represent an ideal mirror surface and ray path. Solid surface and ray represent the distorted surface and ray path. Ray path lengths are the same for the two cases. (Diagram applies for ϕ = 0 plane.)

Fig. 3
Fig. 3

Rear cone with a static misfigure of the form (λ/N) cos2ϕ. Distorted and ideal ray paths are no longer the same length. (Diagram applied for ϕ = 0 plane.)

Fig. 4
Fig. 4

Resonator with a rear cone with a static misfigure of the form (λ/N) cos2ϕ but with a compensating outer axicon. (Diagram applies for ϕ = 0 plane.)

Fig. 5
Fig. 5

Figure used to predict ideal compensatory misfigure for a distorted resonator [see Eq. (1)].

Fig. 6
Fig. 6

Placement of actuators on the outer axicon.

Fig. 7
Fig. 7

Far-field intensity pattern for a perfect resonator or a resonator with ideal compensation.

Fig. 8
Fig. 8

Far-field intensity pattern for a (λ/40) cos4ϕ distortion on the rear cone—uncompensated.

Fig. 9
Fig. 9

Far-field intensity pattern for a (λ/20) cos2ϕ distortion on the rear cone—uncompensated.

Fig. 10
Fig. 10

Far-field pattern for a (λ/10) cos2ϕ distortion on the rear cone—uncompensated.

Tables (3)

Tables Icon

Table I Computer Results for Distortions of the Form (λ/N) cos2ϕ Applied to the Rear Cone

Tables Icon

Table II Computer Results for Distortions of the Form (λ/40) cos Applied to the Rear Cone

Tables Icon

Table III Computer Results for a Distortion of (c0 + c1r + c2r2) cos6ϕ Applied to the Outer Axicon

Equations (4)

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E ( r , ϕ ) = E ( r , ϕ ) exp [ i Φ ( r , ϕ ) ] .
cos ( θ / 2 ) f 0 ( a + λ 1 r , ϕ ) + ( 2 ) 1 / 2 2 f r ( a + λ 2 r , ϕ ) + ( 2 ) 1 / 2 2 f r ( a + λ 3 r , ϕ + π ) + cos ( θ / 2 ) f 0 ( a + λ 4 r , ϕ + π ) = 0.
f 0 ( R , ϕ ) = - C ( 2 ) 1 / 2 2 cos θ / 2 cos p ϕ { q = 0 n ( n q ) a n - q ( R - a ) q [ λ 3 q + ( - 1 ) p λ 2 q λ 4 q + ( - 1 ) p λ 1 q ] } ,
( n q ) n ! ( n - q ) ! q ! .

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