J. Nagel, D. Rogovin, P. Avizonis, and R. Butts, "Asymptotic Approaches to Marginally Stable Resonators," Opt. Lett. 4, 300–302 (1979).

M. Lax, G. Agrawal, and W. Louisell, "Continuous Fourier transform spline solution of unstable resonator field distribution," Opt. Lett. 4, 303–305 (1979).

G. C. Dente, "Polarization effects in resonators," Appl. Opt. 18, 2911 (1979).

P. Horwitz, "Asymptotic theory of unstable resonator modes," J. Opt. Soc. Am. 63, 1528–1543 (1973).

L. Chen and L. Felsen, "Coupled Mode Theory of Unstable Resonators," IEEE J. Quantum Electron. QE9, 1102–1113 (1973).

G. N. Vinokurov, V. V. Lyubimov, and I. B. Orlova, "Investigation of the Selective Properties of Open Unstable Cavities," Opt. Spectrosc. 34, 437–432 (1973).

A. Siegman and R. Arrathoon, "Modes in Unstable Optical Resonators and Lens Waveguides," IEEE J. Quantum Electron. QE3, 156–163 (1967).

H. Hochstadt, "Integral Equations in Laser Theory," SAIM Rev. 8, 62–65 (1966).

W. Kahn, "Unstable optical resonators," Appl. Opt. 4, 407–417 (1966).

See references in the following reviews: H. Kogelnik and T. Li, "Laser Beams and Resonators," Proc. IEEE 54, 1312–1329, (1966); A. E. Siegman, "Unstable optical resonators," Appl. Opt. 13, 353 (1974).

A. E. Siegman, "Unstable Optical Resonators for Laser Applications," Proc. IEEE 53, 277–287 (1965).

J. Cochran, "The Existence of Eigenvalues for the Integral Equations in Laser Theory," Bell Syst. Tech. J. 44, 77–88 (1965).

D. Newman and S. Morgan, "Existence of Eigenvalues of a Class of Integral Equations Arising in Laser Theory," Bell Syst. Tech. J. 43, 113–126 (1964).

S. Morgan, "On the Integral Equations of Laser Theory," IEEE Trans. Microwave Theory Tech. 8, 191–193 (1963).

G. Boyd and H. Kogelnik, "Generalized confocal resonator theory," Bell Syst. Tech. J. 41, 1347–1369 (1962).

A. G. Fox and T. Li, "Resonant Modes in a Maser Interferometer," Bell Syst. Tech. J. 40, 453–488 (1961).

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York 1964).

A. Siegman and R. Arrathoon, "Modes in Unstable Optical Resonators and Lens Waveguides," IEEE J. Quantum Electron. QE3, 156–163 (1967).

G. Boyd and H. Kogelnik, "Generalized confocal resonator theory," Bell Syst. Tech. J. 41, 1347–1369 (1962).

L. Chen and L. Felsen, "Coupled Mode Theory of Unstable Resonators," IEEE J. Quantum Electron. QE9, 1102–1113 (1973).

J. Cochran, "The Existence of Eigenvalues for the Integral Equations in Laser Theory," Bell Syst. Tech. J. 44, 77–88 (1965).

L. M. Delves and J. Walsh, Numerical Solution of Integral Equations (Claredon, Oxford, 1974).

P. Morse and H. Feshbach, Methods in Mathematical Physics (McGraw-Hill, New York, 1953).

A. G. Fox and T. Li, "Resonant Modes in a Maser Interferometer," Bell Syst. Tech. J. 40, 453–488 (1961).

H. Hochstadt, "Integral Equations in Laser Theory," SAIM Rev. 8, 62–65 (1966).

W. Kahn, "Unstable optical resonators," Appl. Opt. 4, 407–417 (1966).

See references in the following reviews: H. Kogelnik and T. Li, "Laser Beams and Resonators," Proc. IEEE 54, 1312–1329, (1966); A. E. Siegman, "Unstable optical resonators," Appl. Opt. 13, 353 (1974).

G. Boyd and H. Kogelnik, "Generalized confocal resonator theory," Bell Syst. Tech. J. 41, 1347–1369 (1962).

See references in the following reviews: H. Kogelnik and T. Li, "Laser Beams and Resonators," Proc. IEEE 54, 1312–1329, (1966); A. E. Siegman, "Unstable optical resonators," Appl. Opt. 13, 353 (1974).

A. G. Fox and T. Li, "Resonant Modes in a Maser Interferometer," Bell Syst. Tech. J. 40, 453–488 (1961).

W. H. Louisell, in Physics of Quantum Electronics, edited by S. F. Jacobs, M. O. Scully, M. Sargent, and C. D. Cantrell (Addison-Wesley, Reading, Massachusetts, 1976), Vol. 3, p. 369.

G. N. Vinokurov, V. V. Lyubimov, and I. B. Orlova, "Investigation of the Selective Properties of Open Unstable Cavities," Opt. Spectrosc. 34, 437–432 (1973).

D. Newman and S. Morgan, "Existence of Eigenvalues of a Class of Integral Equations Arising in Laser Theory," Bell Syst. Tech. J. 43, 113–126 (1964).

S. Morgan, "On the Integral Equations of Laser Theory," IEEE Trans. Microwave Theory Tech. 8, 191–193 (1963).

P. Morse and H. Feshbach, Methods in Mathematical Physics (McGraw-Hill, New York, 1953).

D. Newman and S. Morgan, "Existence of Eigenvalues of a Class of Integral Equations Arising in Laser Theory," Bell Syst. Tech. J. 43, 113–126 (1964).

G. N. Vinokurov, V. V. Lyubimov, and I. B. Orlova, "Investigation of the Selective Properties of Open Unstable Cavities," Opt. Spectrosc. 34, 437–432 (1973).

R. Butts and A. Paxton (private communication).

L. Rall, Computational Solution of Nonlinear Operator Equations (Wiley, New York, 1969).

A. Siegman and R. Arrathoon, "Modes in Unstable Optical Resonators and Lens Waveguides," IEEE J. Quantum Electron. QE3, 156–163 (1967).

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York 1964).

G. N. Vinokurov, V. V. Lyubimov, and I. B. Orlova, "Investigation of the Selective Properties of Open Unstable Cavities," Opt. Spectrosc. 34, 437–432 (1973).

L. M. Delves and J. Walsh, Numerical Solution of Integral Equations (Claredon, Oxford, 1974).

G. Watson, Theory of Bessel Functions (Cambridge University, Cambridge, 1966).

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

W. Kahn, "Unstable optical resonators," Appl. Opt. 4, 407–417 (1966).

L. Bergstein, "Modes of stable and unstable optical resonators," Appl. Opt. 7, 495–504 (1968).

R. L. Sanderson and W. Streifer, "Comparison of laser mode calculations," Appl. Opt. 8, 131–140 (1969).

R. Sanderson and W. Streifer, "Unstable laser resonator modes," Appl. Opt. 8, 2129–2136 (1969).

A. E. Siegman and H. Y. Miller, "Unstable optical resonator loss calculations using the Prony method," Appl. Opt. 9, 2729–2736 (1970).

D. Rensch and A. Chester, "Iterative diffraction calculations of transverse mode distributions in confocal unstable laser resonators," Appl. Opt. 12, 997–1010 (1972).

C. Santana and L. Felsen, "Unstable open resonators: Two dimensional and three-dimensional losses by a waveguide analysis," Appl. Opt. 15, 1470–1478 (1976).

W. Murphy and M. L. Bernabe, "Numerical procedures for solving nonsymmetric eigenvalue problems associated with optical resonators," Appl. Opt. 15, 2358–2365 (1978).

G. C. Dente, "Polarization effects in resonators," Appl. Opt. 18, 2911 (1979).

G. Boyd and H. Kogelnik, "Generalized confocal resonator theory," Bell Syst. Tech. J. 41, 1347–1369 (1962).

A. G. Fox and T. Li, "Resonant Modes in a Maser Interferometer," Bell Syst. Tech. J. 40, 453–488 (1961).

D. Newman and S. Morgan, "Existence of Eigenvalues of a Class of Integral Equations Arising in Laser Theory," Bell Syst. Tech. J. 43, 113–126 (1964).

J. Cochran, "The Existence of Eigenvalues for the Integral Equations in Laser Theory," Bell Syst. Tech. J. 44, 77–88 (1965).

L. Chen and L. Felsen, "Coupled Mode Theory of Unstable Resonators," IEEE J. Quantum Electron. QE9, 1102–1113 (1973).

A. Siegman and R. Arrathoon, "Modes in Unstable Optical Resonators and Lens Waveguides," IEEE J. Quantum Electron. QE3, 156–163 (1967).

S. Morgan, "On the Integral Equations of Laser Theory," IEEE Trans. Microwave Theory Tech. 8, 191–193 (1963).

J. Nagel, D. Rogovin, P. Avizonis, and R. Butts, "Asymptotic Approaches to Marginally Stable Resonators," Opt. Lett. 4, 300–302 (1979).

M. Lax, G. Agrawal, and W. Louisell, "Continuous Fourier transform spline solution of unstable resonator field distribution," Opt. Lett. 4, 303–305 (1979).

G. N. Vinokurov, V. V. Lyubimov, and I. B. Orlova, "Investigation of the Selective Properties of Open Unstable Cavities," Opt. Spectrosc. 34, 437–432 (1973).

H. Hochstadt, "Integral Equations in Laser Theory," SAIM Rev. 8, 62–65 (1966).

W. H. Louisell, in Physics of Quantum Electronics, edited by S. F. Jacobs, M. O. Scully, M. Sargent, and C. D. Cantrell (Addison-Wesley, Reading, Massachusetts, 1976), Vol. 3, p. 369.

P. Morse and H. Feshbach, Methods in Mathematical Physics (McGraw-Hill, New York, 1953).

L. M. Delves and J. Walsh, Numerical Solution of Integral Equations (Claredon, Oxford, 1974).

L. Rall, Computational Solution of Nonlinear Operator Equations (Wiley, New York, 1969).

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York 1964).

G. Watson, Theory of Bessel Functions (Cambridge University, Cambridge, 1966).

See references in the following reviews: H. Kogelnik and T. Li, "Laser Beams and Resonators," Proc. IEEE 54, 1312–1329, (1966); A. E. Siegman, "Unstable optical resonators," Appl. Opt. 13, 353 (1974).

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

A. E. Siegman, "Unstable Optical Resonators for Laser Applications," Proc. IEEE 53, 277–287 (1965).

R. Butts and A. Paxton (private communication).

The condition is *M* > 1 + *N*^{-1}. and not *M* > 1 + N^{-½}. as stated in Ref. 29.