Abstract

This paper reviews the current level of theoretical understanding and experimental confirmation of the properties of unstable optical resonators for laser oscillators. A primary conclusion is that for any laser system characterized by a moderate gain per pass and a Fresnel number greater than a few times unity the unstable resonator provides the best practical resonator design for obtaining a high-quality near-diffraction-limited output laser beam combined with efficient energy extraction from the laser medium.

© 1974 Optical Society of America

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1973 (18)

D. B. Rensch, A. N. Chester, Appl. Opt. 12, 997 (1973).
[CrossRef] [PubMed]

G. L. McAllister, D. K. Rice, W. H. Steier, J. Opt. Soc. Am. 63, 502 (1973).

D. L. Bullock, R. J. Wagner, J. Opt. Soc. Am. 63, 502 (1973).

L. W. Chen, L. B. Felsen, IEEE J. Quantum Electron. QE-9, 1102 (1973).
[CrossRef]

A. N. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973).
[CrossRef]

W. K. Kahn, Appl. Optics 12, 2026 (1973).
[CrossRef]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, Appl. Opt. 12, 1140 (1973).
[CrossRef] [PubMed]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

G. R. Wisner, M. C. Foster, P. R. Blaszuk, Appl. Phys. Lett. 22, 14 (1973).
[CrossRef]

J. Davit, C. Charles, Appl. Phys. Lett. 22, 248 (1973).
[CrossRef]

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

H. Granek, A. J. Morency, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

R. G. Buser, R. S. Rhode, F. G. Gebhardt, D. C. Smith, IEEE J. Quantum Electron. QE-9, 717 (1973).
[CrossRef]

D. B. Rensch, A. N. Chester, J. Opt. Soc. Am. 63, 502 (1973).

C. J. Buczek, R. J. Freiberg, M. L. Skolnik, Proc. IEEE 61, 1411 (1973).
[CrossRef]

L. V. Koval-chuk, N. A. Sventsitskaya, Sov. J. Quant. Elect. 2, 450 (1973).
[CrossRef]

A. N. Chester, Appl. Optics 12, 2353 (1973).
[CrossRef]

P. dal Pozzo et al.IEEE J. Quantum Electron. QE-91061 (1973).
[CrossRef]

1972 (15)

E. V. Locke, E. D. Hoag, R. A. Hella, IEEE J. Quantum Electron. QE-8, 132 (1972).
[CrossRef]

J. P. Reilly, IEEE J. Quantum Electron. QE-8, 136 (1972).
[CrossRef]

P. E. Dyer, D. J. James, S. A. Ramsden, Opt. Commun. 5, 236 (1972).
[CrossRef]

R. J. Freiberg, P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-8, 882 (1972).
[CrossRef]

Yu. A. Ananev et al., Sov. J. Quant. Elect. 2, 157 (1972).
[CrossRef]

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quant. Elect. 2, 224 (1972).
[CrossRef]

H. Mirels, S. B. Batdorf, Appl. Opt. 11, 2384 (1972).
[CrossRef] [PubMed]

M. P. Vanyukov, V. A. Serebryakov, V. N. Sizov, A. D. Starikov, O. A. Shorokhov, Sov. J. Opt. Technol. 39, 51 (1972).

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (Jan./Feb. 1972).
[CrossRef]

A. V. Gorlanov, V. V. Lyubimov, V. F. Petrov, Sov. J. Quantum Electron. 1, 408 (Jan./Feb. 1972).
[CrossRef]

M. P. Vanyukov et al., Sov. J. Quantum Electron. 1, 410 (Jan./Feb. 1972).
[CrossRef]

V. V. Lyubimov, I. B. Orlova, Opt. Spectrosc. 33, 74 (1972).

M. Lax, W. H. Louisell, C. Greninger, W. B. McKnight, IEEE J. Quantum Electron. QE-8, 554 (1972).
[CrossRef]

A. N. Chester, Appl. Opt. 11, 2584 (1972).
[CrossRef] [PubMed]

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

1971 (5)

Yu. A. Ananev, V. E. Sherstobitov, O. A. Shorokhov, Sov. J. Quantum Electron. 1, 65 (July/Aug. 1971).
[CrossRef]

Yu. A. Ananev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (Nov./Dec. 1971).
[CrossRef]

G. R. Bisio, L. Ronchi, V. Tognetti, IEEE Trans. Microwave Theory Tech. MTT-19, 490 (1971).
[CrossRef]

D. N. Mansell, J. A. Love, W. L. Snell, IEEE J. Quantum Electron. QE-7, 177 (1971).
[CrossRef]

E. V. Locke, R. Hella, L. Westra, IEEE J. Quantum Electron. QE-7, 581 (1971).
[CrossRef]

1970 (5)

A. E. Siegman, H. Y. Miller, Appl. Opt. 9, 2729 (1970).
[CrossRef] [PubMed]

H. Zucker, Bell Syst. Tech. J. 49, 2349 (1970).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Tech. Phys. 14, 997 (1970).

Yu. A. Ananev, G. N. Vinokurov, Sov. Phys. Tech. Phys. 14, 1000 (1970).

Yu. A. Ananev, G. N. Vinokurov, L. V. Kovalchuk, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. JETP 31, 420 (1970).

1969 (4)

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

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Shorstobitov, Sov. Phys. JETP 28, 69 (1969).

R. L. Sanderson, W. Streifer, Appl. Opt. 8, 2129 (1969).
[CrossRef] [PubMed]

R. L. Sanderson, W. Streifer, Appl. Opt. 8, 2241 (1969).
[CrossRef] [PubMed]

1968 (3)

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Dokl. 13, 351 (1968).

L. Bergstein, Appl. Opt. 7, 495 (1968).
[CrossRef] [PubMed]

W. Streifer, IEEE J. Quantum Electron. QE-4, 229 (1968).
[CrossRef]

1967 (3)

1966 (2)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966); Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

W. K. Kahn, Appl. Opt. 5, 407 (1966).
[CrossRef] [PubMed]

1965 (1)

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

1964 (1)

1963 (1)

A. Okaya, Proc. IEEE 51, 1033 (1963).
[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 (May/June 1972).
[CrossRef]

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (Jan./Feb. 1972).
[CrossRef]

Yu. A. Ananev et al., Sov. J. Quant. Elect. 2, 157 (1972).
[CrossRef]

Yu. A. Ananev, V. E. Sherstobitov, O. A. Shorokhov, Sov. J. Quantum Electron. 1, 65 (July/Aug. 1971).
[CrossRef]

Yu. A. Ananev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (Nov./Dec. 1971).
[CrossRef]

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Tech. Phys. 14, 997 (1970).

Yu. A. Ananev, G. N. Vinokurov, Sov. Phys. Tech. Phys. 14, 1000 (1970).

Yu. A. Ananev, G. N. Vinokurov, L. V. Kovalchuk, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. JETP 31, 420 (1970).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Shorstobitov, Sov. Phys. JETP 28, 69 (1969).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Dokl. 13, 351 (1968).

Arrathoon, R. W.

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

Barone, S. R.

Batdorf, S. B.

Bergstein, L.

Bisio, G. R.

G. R. Bisio, L. Ronchi, V. Tognetti, IEEE Trans. Microwave Theory Tech. MTT-19, 490 (1971).
[CrossRef]

Blaszuk, P. R.

G. R. Wisner, M. C. Foster, P. R. Blaszuk, Appl. Phys. Lett. 22, 14 (1973).
[CrossRef]

Buczek, C. J.

C. J. Buczek, R. J. Freiberg, M. L. Skolnik, Proc. IEEE 61, 1411 (1973).
[CrossRef]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, Appl. Opt. 12, 1140 (1973).
[CrossRef] [PubMed]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

R. J. Freiberg, P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-8, 882 (1972).
[CrossRef]

Bullock, D. L.

D. L. Bullock, R. J. Wagner, J. Opt. Soc. Am. 63, 502 (1973).

Buser, R. G.

R. G. Buser, R. S. Rhode, F. G. Gebhardt, D. C. Smith, IEEE J. Quantum Electron. QE-9, 717 (1973).
[CrossRef]

Charles, C.

J. Davit, C. Charles, Appl. Phys. Lett. 22, 248 (1973).
[CrossRef]

Chen, L. W.

L. W. Chen, L. B. Felsen, IEEE J. Quantum Electron. QE-9, 1102 (1973).
[CrossRef]

Chenausky, P.

R. J. Freiberg, P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-8, 882 (1972).
[CrossRef]

Chenausky, P. P.

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, Appl. Opt. 12, 1140 (1973).
[CrossRef] [PubMed]

Chernov, V. N.

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (Jan./Feb. 1972).
[CrossRef]

Chester, A. N.

D. B. Rensch, A. N. Chester, Appl. Opt. 12, 997 (1973).
[CrossRef] [PubMed]

A. N. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973).
[CrossRef]

A. N. Chester, Appl. Optics 12, 2353 (1973).
[CrossRef]

D. B. Rensch, A. N. Chester, J. Opt. Soc. Am. 63, 502 (1973).

A. N. Chester, Appl. Opt. 11, 2584 (1972).
[CrossRef] [PubMed]

Chodzko, R. A.

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

Cottrell, T. H. E.

dal Pozzo, P.

P. dal Pozzo et al.IEEE J. Quantum Electron. QE-91061 (1973).
[CrossRef]

Davit, J.

J. Davit, C. Charles, Appl. Phys. Lett. 22, 248 (1973).
[CrossRef]

Dyer, P. E.

P. E. Dyer, D. J. James, S. A. Ramsden, Opt. Commun. 5, 236 (1972).
[CrossRef]

Felsen, L. B.

L. W. Chen, L. B. Felsen, IEEE J. Quantum Electron. QE-9, 1102 (1973).
[CrossRef]

Foster, M. C.

G. R. Wisner, M. C. Foster, P. R. Blaszuk, Appl. Phys. Lett. 22, 14 (1973).
[CrossRef]

Fox, A. G.

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

A. G. Fox, T. Li, “Modes in a Maser Interferometer with Curved Mirrors,” in Quantum Electronics III, P. Grivet, N. Bloembergen, Eds. (Columbia U.P.New York, Vol. 2, p. 1263.

Freiberg, R. J.

C. J. Buczek, R. J. Freiberg, M. L. Skolnik, Proc. IEEE 61, 1411 (1973).
[CrossRef]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, Appl. Opt. 12, 1140 (1973).
[CrossRef] [PubMed]

R. J. Freiberg, P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-8, 882 (1972).
[CrossRef]

Gebhardt, F. G.

R. G. Buser, R. S. Rhode, F. G. Gebhardt, D. C. Smith, IEEE J. Quantum Electron. QE-9, 717 (1973).
[CrossRef]

Gorlanov, A. V.

A. V. Gorlanov, V. V. Lyubimov, V. F. Petrov, Sov. J. Quantum Electron. 1, 408 (Jan./Feb. 1972).
[CrossRef]

Granek, H.

H. Granek, A. J. Morency, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

Greninger, C.

M. Lax, W. H. Louisell, C. Greninger, W. B. McKnight, IEEE J. Quantum Electron. QE-8, 554 (1972).
[CrossRef]

Hella, R.

E. V. Locke, R. Hella, L. Westra, IEEE J. Quantum Electron. QE-7, 581 (1971).
[CrossRef]

Hella, R. A.

E. V. Locke, E. D. Hoag, R. A. Hella, IEEE J. Quantum Electron. QE-8, 132 (1972).
[CrossRef]

Hoag, E. D.

E. V. Locke, E. D. Hoag, R. A. Hella, IEEE J. Quantum Electron. QE-8, 132 (1972).
[CrossRef]

Horwitz, P.

P. Horwitz, J. Opt. Soc. Am. in press.

Imbusch, G. F.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, A. D. May, “The High Gain Laser as a Wavelength Standard,” in Optical Masers, J. Fox, Ed., MRI Symposium Series Vol. 13 (Polytechnic Press, Brooklyn1964), p. 51.

Jacobs, S. F.

James, D. J.

P. E. Dyer, D. J. James, S. A. Ramsden, Opt. Commun. 5, 236 (1972).
[CrossRef]

Kahn, W. K.

Kogelnik, H.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966); Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

Kovalchuk, L. V.

Yu. A. Ananev, G. N. Vinokurov, L. V. Kovalchuk, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. JETP 31, 420 (1970).

Koval-chuk, L. V.

L. V. Koval-chuk, N. A. Sventsitskaya, Sov. J. Quant. Elect. 2, 450 (1973).
[CrossRef]

Krupke, W. F.

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

LaTourette, J. T.

Lax, M.

M. Lax, W. H. Louisell, C. Greninger, W. B. McKnight, IEEE J. Quantum Electron. QE-8, 554 (1972).
[CrossRef]

Li, T.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966); Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

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

A. G. Fox, T. Li, “Modes in a Maser Interferometer with Curved Mirrors,” in Quantum Electronics III, P. Grivet, N. Bloembergen, Eds. (Columbia U.P.New York, Vol. 2, p. 1263.

Locke, E. V.

E. V. Locke, E. D. Hoag, R. A. Hella, IEEE J. Quantum Electron. QE-8, 132 (1972).
[CrossRef]

E. V. Locke, R. Hella, L. Westra, IEEE J. Quantum Electron. QE-7, 581 (1971).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, C. Greninger, W. B. McKnight, IEEE J. Quantum Electron. QE-8, 554 (1972).
[CrossRef]

Love, J. A.

D. N. Mansell, J. A. Love, W. L. Snell, IEEE J. Quantum Electron. QE-7, 177 (1971).
[CrossRef]

Lyubimov, V. V.

V. V. Lyubimov, I. B. Orlova, Opt. Spectrosc. 33, 74 (1972).

A. V. Gorlanov, V. V. Lyubimov, V. F. Petrov, Sov. J. Quantum Electron. 1, 408 (Jan./Feb. 1972).
[CrossRef]

Mansell, D. N.

D. N. Mansell, J. A. Love, W. L. Snell, IEEE J. Quantum Electron. QE-7, 177 (1971).
[CrossRef]

May, A. D.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, A. D. May, “The High Gain Laser as a Wavelength Standard,” in Optical Masers, J. Fox, Ed., MRI Symposium Series Vol. 13 (Polytechnic Press, Brooklyn1964), p. 51.

McAllister, G. L.

G. L. McAllister, D. K. Rice, W. H. Steier, J. Opt. Soc. Am. 63, 502 (1973).

McKnight, W. B.

M. Lax, W. H. Louisell, C. Greninger, W. B. McKnight, IEEE J. Quantum Electron. QE-8, 554 (1972).
[CrossRef]

Miller, H. Y.

Mirels, H.

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

H. Mirels, S. B. Batdorf, Appl. Opt. 11, 2384 (1972).
[CrossRef] [PubMed]

Mollenauer, L. F.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, A. D. May, “The High Gain Laser as a Wavelength Standard,” in Optical Masers, J. Fox, Ed., MRI Symposium Series Vol. 13 (Polytechnic Press, Brooklyn1964), p. 51.

Moos, H. W.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, A. D. May, “The High Gain Laser as a Wavelength Standard,” in Optical Masers, J. Fox, Ed., MRI Symposium Series Vol. 13 (Polytechnic Press, Brooklyn1964), p. 51.

Morency, A. J.

H. Granek, A. J. Morency, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

Okaya, A.

A. Okaya, Proc. IEEE 51, 1033 (1963).
[CrossRef]

Orlova, I. B.

V. V. Lyubimov, I. B. Orlova, Opt. Spectrosc. 33, 74 (1972).

Pedersen, R. J.

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

Petrov, V. F.

A. V. Gorlanov, V. V. Lyubimov, V. F. Petrov, Sov. J. Quantum Electron. 1, 408 (Jan./Feb. 1972).
[CrossRef]

Rabinowitz, P.

Ramsden, S. A.

P. E. Dyer, D. J. James, S. A. Ramsden, Opt. Commun. 5, 236 (1972).
[CrossRef]

Reilly, J. P.

J. P. Reilly, IEEE J. Quantum Electron. QE-8, 136 (1972).
[CrossRef]

Rensch, D. B.

D. B. Rensch, A. N. Chester, J. Opt. Soc. Am. 63, 502 (1973).

D. B. Rensch, A. N. Chester, Appl. Opt. 12, 997 (1973).
[CrossRef] [PubMed]

Rhode, R. S.

R. G. Buser, R. S. Rhode, F. G. Gebhardt, D. C. Smith, IEEE J. Quantum Electron. QE-9, 717 (1973).
[CrossRef]

Rice, D. K.

G. L. McAllister, D. K. Rice, W. H. Steier, J. Opt. Soc. Am. 63, 502 (1973).

Roehrs, F. S.

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

Ronchi, L.

G. R. Bisio, L. Ronchi, V. Tognetti, IEEE Trans. Microwave Theory Tech. MTT-19, 490 (1971).
[CrossRef]

Sanderson, R. L.

Schawlow, A. L.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, A. D. May, “The High Gain Laser as a Wavelength Standard,” in Optical Masers, J. Fox, Ed., MRI Symposium Series Vol. 13 (Polytechnic Press, Brooklyn1964), p. 51.

Serebryakov, V. A.

M. P. Vanyukov, V. A. Serebryakov, V. N. Sizov, A. D. Starikov, O. A. Shorokhov, Sov. J. Opt. Technol. 39, 51 (1972).

Sherstobitov, V. E.

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (Jan./Feb. 1972).
[CrossRef]

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quant. Elect. 2, 224 (1972).
[CrossRef]

Yu. A. Ananev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (Nov./Dec. 1971).
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Yu. A. Ananev, V. E. Sherstobitov, O. A. Shorokhov, Sov. J. Quantum Electron. 1, 65 (July/Aug. 1971).
[CrossRef]

Yu. A. Ananev, G. N. Vinokurov, L. V. Kovalchuk, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. JETP 31, 420 (1970).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Tech. Phys. 14, 997 (1970).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Dokl. 13, 351 (1968).

Shorokhov, O. A.

M. P. Vanyukov, V. A. Serebryakov, V. N. Sizov, A. D. Starikov, O. A. Shorokhov, Sov. J. Opt. Technol. 39, 51 (1972).

Yu. A. Ananev, V. E. Sherstobitov, O. A. Shorokhov, Sov. J. Quantum Electron. 1, 65 (July/Aug. 1971).
[CrossRef]

Shorstobitov, V. E.

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Shorstobitov, Sov. Phys. JETP 28, 69 (1969).

Siegman, A. E.

A. E. Siegman, H. Y. Miller, Appl. Opt. 9, 2729 (1970).
[CrossRef] [PubMed]

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

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

E. A. Sziklas, A. E. Siegman, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 2: A New Fast Fourier Transform Method for Diffraction Calculations,” (to be published).

A. E. Siegman, E. A. Sziklas, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 1: Hermite-Gaussian Mode Expansion,” (to be published in Appl. Opt.).

Sinclair, D. C.

Sizov, V. N.

M. P. Vanyukov, V. A. Serebryakov, V. N. Sizov, A. D. Starikov, O. A. Shorokhov, Sov. J. Opt. Technol. 39, 51 (1972).

Skolnik, M. L.

C. J. Buczek, R. J. Freiberg, M. L. Skolnik, Proc. IEEE 61, 1411 (1973).
[CrossRef]

Smith, D. C.

R. G. Buser, R. S. Rhode, F. G. Gebhardt, D. C. Smith, IEEE J. Quantum Electron. QE-9, 717 (1973).
[CrossRef]

Snell, W. L.

D. N. Mansell, J. A. Love, W. L. Snell, IEEE J. Quantum Electron. QE-7, 177 (1971).
[CrossRef]

Sooy, W. R.

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

Starikov, A. D.

M. P. Vanyukov, V. A. Serebryakov, V. N. Sizov, A. D. Starikov, O. A. Shorokhov, Sov. J. Opt. Technol. 39, 51 (1972).

Steier, W. H.

G. L. McAllister, D. K. Rice, W. H. Steier, J. Opt. Soc. Am. 63, 502 (1973).

Streifer, W.

Sventsitskaya, N. A.

L. V. Koval-chuk, N. A. Sventsitskaya, Sov. J. Quant. Elect. 2, 450 (1973).
[CrossRef]

Yu. A. Ananev, G. N. Vinokurov, L. V. Kovalchuk, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. JETP 31, 420 (1970).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Tech. Phys. 14, 997 (1970).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Shorstobitov, Sov. Phys. JETP 28, 69 (1969).

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Dokl. 13, 351 (1968).

Sziklas, E. A.

A. E. Siegman, E. A. Sziklas, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 1: Hermite-Gaussian Mode Expansion,” (to be published in Appl. Opt.).

E. A. Sziklas, A. E. Siegman, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 2: A New Fast Fourier Transform Method for Diffraction Calculations,” (to be published).

Tognetti, V.

G. R. Bisio, L. Ronchi, V. Tognetti, IEEE Trans. Microwave Theory Tech. MTT-19, 490 (1971).
[CrossRef]

Vanyukov, M. P.

M. P. Vanyukov et al., Sov. J. Quantum Electron. 1, 410 (Jan./Feb. 1972).
[CrossRef]

M. P. Vanyukov, V. A. Serebryakov, V. N. Sizov, A. D. Starikov, O. A. Shorokhov, Sov. J. Opt. Technol. 39, 51 (1972).

Vinokurov, G. N.

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quant. Elect. 2, 224 (1972).
[CrossRef]

Yu. A. Ananev, G. N. Vinokurov, Sov. Phys. Tech. Phys. 14, 1000 (1970).

Yu. A. Ananev, G. N. Vinokurov, L. V. Kovalchuk, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. JETP 31, 420 (1970).

Wagner, R. J.

D. L. Bullock, R. J. Wagner, J. Opt. Soc. Am. 63, 502 (1973).

Weinstein, L. A.

L. A. Weinstein, Open Resonators and Open Waveguides (Golem Press, Boulder, Colo., 1969).

Westra, L.

E. V. Locke, R. Hella, L. Westra, IEEE J. Quantum Electron. QE-7, 581 (1971).
[CrossRef]

Wisner, G. R.

G. R. Wisner, M. C. Foster, P. R. Blaszuk, Appl. Phys. Lett. 22, 14 (1973).
[CrossRef]

Zucker, H.

H. Zucker, Bell Syst. Tech. J. 49, 2349 (1970).

Appl. Opt. (12)

Appl. Optics (2)

W. K. Kahn, Appl. Optics 12, 2026 (1973).
[CrossRef]

A. N. Chester, Appl. Optics 12, 2353 (1973).
[CrossRef]

Appl. Phys. Lett. (2)

G. R. Wisner, M. C. Foster, P. R. Blaszuk, Appl. Phys. Lett. 22, 14 (1973).
[CrossRef]

J. Davit, C. Charles, Appl. Phys. Lett. 22, 248 (1973).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Zucker, Bell Syst. Tech. J. 49, 2349 (1970).

Bell. Syst. Tech. J. (1)

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

IEEE J. Quantum Electron. (16)

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

W. Streifer, IEEE J. Quantum Electron. QE-4, 229 (1968).
[CrossRef]

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

M. Lax, W. H. Louisell, C. Greninger, W. B. McKnight, IEEE J. Quantum Electron. QE-8, 554 (1972).
[CrossRef]

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

H. Granek, A. J. Morency, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

R. G. Buser, R. S. Rhode, F. G. Gebhardt, D. C. Smith, IEEE J. Quantum Electron. QE-9, 717 (1973).
[CrossRef]

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-9, 716 (1973).
[CrossRef]

A. N. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973).
[CrossRef]

L. W. Chen, L. B. Felsen, IEEE J. Quantum Electron. QE-9, 1102 (1973).
[CrossRef]

P. dal Pozzo et al.IEEE J. Quantum Electron. QE-91061 (1973).
[CrossRef]

R. J. Freiberg, P. Chenausky, C. J. Buczek, IEEE J. Quantum Electron. QE-8, 882 (1972).
[CrossRef]

D. N. Mansell, J. A. Love, W. L. Snell, IEEE J. Quantum Electron. QE-7, 177 (1971).
[CrossRef]

E. V. Locke, R. Hella, L. Westra, IEEE J. Quantum Electron. QE-7, 581 (1971).
[CrossRef]

E. V. Locke, E. D. Hoag, R. A. Hella, IEEE J. Quantum Electron. QE-8, 132 (1972).
[CrossRef]

J. P. Reilly, IEEE J. Quantum Electron. QE-8, 136 (1972).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

G. R. Bisio, L. Ronchi, V. Tognetti, IEEE Trans. Microwave Theory Tech. MTT-19, 490 (1971).
[CrossRef]

J. Opt. Soc. Am. (3)

D. L. Bullock, R. J. Wagner, J. Opt. Soc. Am. 63, 502 (1973).

D. B. Rensch, A. N. Chester, J. Opt. Soc. Am. 63, 502 (1973).

G. L. McAllister, D. K. Rice, W. H. Steier, J. Opt. Soc. Am. 63, 502 (1973).

Opt. Commun. (1)

P. E. Dyer, D. J. James, S. A. Ramsden, Opt. Commun. 5, 236 (1972).
[CrossRef]

Opt. Spectrosc. (1)

V. V. Lyubimov, I. B. Orlova, Opt. Spectrosc. 33, 74 (1972).

Proc. IEEE (4)

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

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966); Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

A. Okaya, Proc. IEEE 51, 1033 (1963).
[CrossRef]

C. J. Buczek, R. J. Freiberg, M. L. Skolnik, Proc. IEEE 61, 1411 (1973).
[CrossRef]

Sov. J. Opt. Technol. (1)

M. P. Vanyukov, V. A. Serebryakov, V. N. Sizov, A. D. Starikov, O. A. Shorokhov, Sov. J. Opt. Technol. 39, 51 (1972).

Sov. J. Quant. Elect. (3)

L. V. Koval-chuk, N. A. Sventsitskaya, Sov. J. Quant. Elect. 2, 450 (1973).
[CrossRef]

Yu. A. Ananev et al., Sov. J. Quant. Elect. 2, 157 (1972).
[CrossRef]

V. E. Sherstobitov, G. N. Vinokurov, Sov. J. Quant. Elect. 2, 224 (1972).
[CrossRef]

Sov. J. Quantum Electron. (6)

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (Jan./Feb. 1972).
[CrossRef]

A. V. Gorlanov, V. V. Lyubimov, V. F. Petrov, Sov. J. Quantum Electron. 1, 408 (Jan./Feb. 1972).
[CrossRef]

M. P. Vanyukov et al., Sov. J. Quantum Electron. 1, 410 (Jan./Feb. 1972).
[CrossRef]

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

Yu. A. Ananev, V. E. Sherstobitov, O. A. Shorokhov, Sov. J. Quantum Electron. 1, 65 (July/Aug. 1971).
[CrossRef]

Yu. A. Ananev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (Nov./Dec. 1971).
[CrossRef]

Sov. Phys. Dokl. (1)

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Dokl. 13, 351 (1968).

Sov. Phys. JETP (2)

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Shorstobitov, Sov. Phys. JETP 28, 69 (1969).

Yu. A. Ananev, G. N. Vinokurov, L. V. Kovalchuk, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. JETP 31, 420 (1970).

Sov. Phys. Tech. Phys. (2)

Yu. A. Ananev, N. A. Sventsitskaya, V. E. Sherstobitov, Sov. Phys. Tech. Phys. 14, 997 (1970).

Yu. A. Ananev, G. N. Vinokurov, Sov. Phys. Tech. Phys. 14, 1000 (1970).

Other (6)

P. Horwitz, J. Opt. Soc. Am. in press.

A. G. Fox, T. Li, “Modes in a Maser Interferometer with Curved Mirrors,” in Quantum Electronics III, P. Grivet, N. Bloembergen, Eds. (Columbia U.P.New York, Vol. 2, p. 1263.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, A. D. May, “The High Gain Laser as a Wavelength Standard,” in Optical Masers, J. Fox, Ed., MRI Symposium Series Vol. 13 (Polytechnic Press, Brooklyn1964), p. 51.

A. E. Siegman, E. A. Sziklas, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 1: Hermite-Gaussian Mode Expansion,” (to be published in Appl. Opt.).

E. A. Sziklas, A. E. Siegman, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 2: A New Fast Fourier Transform Method for Diffraction Calculations,” (to be published).

L. A. Weinstein, Open Resonators and Open Waveguides (Golem Press, Boulder, Colo., 1969).

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Figures (26)

Fig. 1
Fig. 1

Typical stable and unstable resonator configurations.

Fig. 2
Fig. 2

Some predecessors of the unstable resonator concept.

Fig. 3
Fig. 3

Development of the geometrical or spherical-wave analysis (Siegman, 1965) of the unstable resonator’s mode properties.

Fig. 4
Fig. 4

Virtual and/or real centers of the spherical waves in the geometrical analysis for different unstable mirror configurations.

Fig. 5
Fig. 5

The magnification parameter M that characterizes the geometrical properties of an unstable resonator.

Fig. 6
Fig. 6

Positive- and negative-branch confocal or telescopic unstable resonators (Ananev, 1969; Krupke and Sooy, 1969).

Fig. 7
Fig. 7

Unstable resonator output coupling methods.

Fig. 8
Fig. 8

Losses per bounce, 1 − |γn|2 vs equivalent Fresnel number Neq for a typical unstable resonator, showing the mode crossing phenomena. From Siegman and Arrathoon.2

Fig. 9
Fig. 9

Eigenvalue magnitudes and phase angles plotted vs equivalent Fresnel number Neq for all the significant axially symmetric eigenmodes (i.e., γn not ≈ 0) of a typical round-mirror unstable optical resonator. From Siegman and Miller.18

Fig. 10
Fig. 10

Exact lowest-order eigenmode characteristics for a strip unstable resonator with M = 2.5 and Neq = 0.6. (a) Variation of the field amplitude |Un(x)| across the resonator cross section; the vertical lines mark the edges of the output mirror. (b) Variation across the resonator of the difference between the exact phase angle of Un(x) and the spherical-wave phase angle predicted by the geometrical analysis. (c) Far-field angular profile of the output beam vs angle θ. (d) Integrated fractional energy within a far-field angle θ vs θ. From Rensch and Chester.19

Fig. 11
Fig. 11

Lowest-order eigenmode characteristics for a strip unstable resonator with M = 5, Neq = 4.8. See caption to Fig. 10 for details. From Rensch and Chester.19

Fig. 12
Fig. 12

Losses per bounce vs equivalent Fresnel number for a large-magnification and large-Fresnel-number strip unstable resonator, showing the mode separation phenomenon at large enough Neq. From Sanderson and Streifer.12

Fig. 13
Fig. 13

Geometrical interpretation of the equivalent Fresnel number. From Ananev and Sherstobitov.25

Fig. 14
Fig. 14

A number of different concepts for smoothing or tapering the sharp edge in the reflectivity profile of the resonator output mirror. Three of the sketches show mirror reflectivity profiles vs radius or transverse coordinate. The lower right-hand sketch shows an end view of the shape of a mirror in the transverse plane. (Zucker, 1970; Ananev, 1971, 1972; Chester, 1972; McAllister, 1973.)

Fig. 15
Fig. 15

Comparison of the theoretical mode losses vs equivalent Fresnel number for an unstable resonator using a conventional sharp-edged mirror (left-hand plot) and using an output mirror whose reflectivity tapers gradually down to zero at the outer edge (right-hand plot). From Anan’ev and Sherstobitov.25

Fig. 16
Fig. 16

A ring-type unstable resonator, showing significantly different overlap of the resonant mode with the laser medium for waves traveling in the two opposite directions around the ring (Ananev et al., 1969, 1970; Buczek, Freiberg, and Chenausky, 1972).

Fig. 17
Fig. 17

An asymmetric unstable ring resonator, giving increased flexibility in mirror design and in active mode volume (Buczek, Freiberg, and Chenausky, 1972).

Fig. 18
Fig. 18

Comparison between theory and experiment for the far-field beam pattern from a low-power CO2 unstable-resonator laser. From Krupke and Sooy.16

Fig. 19
Fig. 19

Transverse intensity distributions inside and outside an unstable resonator. From Freiberg et al.51

Fig. 20
Fig. 20

Integrated power within a given fair-field divergence angle vs the far-field divergence angle for a low-power unstable-resonator CO2 laser. From Freiberg et al.51

Fig. 21
Fig. 21

Output coupling from an unstable resonator vs equivalent Fresnel number. The coupling is measured by taking the ratio of externally coupled power to internal circulating power using observations such as Fig. 19. From Freiberg et al.51

Fig. 22
Fig. 22

Far-field beam intensity vs far-field beam angle for a TEA CO2 laser at high power and energy (3.5 J per pulse, 30 MW peak). From Dyer et al.50

Fig. 23
Fig. 23

Integrated power vs far-field beam divergence angle from another TEA laser experiment. From Davit and Charles.53

Fig. 24
Fig. 24

Results for energy extraction from a pulsed CO2 laser showing essentially the same energy extracted from a laser medium at a given coupling by using either an essentially diffraction-limited unstable resonator or a highly multimode stable resonator (with consequently much poorer beam quality). From Reilly.49

Fig. 25
Fig. 25

Integrated beam power vs far-field beam divergence angle for a 500–1500-W high-power cw CO2 laser using various unstable resonators. N = 36; M = 1.35. The anomalous results for Neq ≡ 3/2 are believed to represent an experimental flaw rather than a basic difference. From Wisner et al.52

Fig. 26
Fig. 26

A demonstration experiment employing a one-dimensional, one-sided unstable resonator in a thin (3-cm) flat glass slab. The mirror and lens are both cylindrical elements; the resonator mode is essentially planar in the plane of the figure. M = 2; N ≈ 56,000; Neq = 7000; Δθ ≃ 2 × 10−5 rad ≈ diffraction-limited (one-dimensional). From Ananev et al.27

Equations (1)

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γ n U n ( x , y ) = K ( x , y , x , y ) U n ( x , y ) d x d y

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