J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high
energy laser beams through the atmosphere,”
Appl. Phys. 10, 129–160
(1976).

[CrossRef]

R. C. Le Bail, “Use of fast Fourier transform for
solving partial differential equations,” J.
Comput. Phys. 9, 440–465
(1972).

[CrossRef]

R. C. Singleton, “An algorithm for computing the mixed
radix fast Fourier transform,” IEEE Trans.
Audio Electroacoust. AE-17, 93–103
(1969).

[CrossRef]

R. W. Hockney, “A fast direct solution of
Poisson’s equation using Fourier analysis,”
J. Assoc. Comput. Mach. 17, 95–113
(1965).

[CrossRef]

J. W. Cooley, J. W. Tukey, “An algorithm for the machine
calculation of complex Fourier series,”
Math. Comput. 19, 297–301
(1965).

[CrossRef]

The exponential transformation
r =
r0eαx
is attributed to Gardner by Siegman in Ref. 9: D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of
multi-component exponential decays,” J.
Chem. Phys. 31, 987 (1959). However, its usefulness in connection
with the solution of the radial Sehrödinger equation was recognized much
earlier by Langer: see R. E. Langer, “On the connection formulas and the
solution of the wave equation,” Phys.
Rev. 51, 669–676
(1937).

[CrossRef]

M. Lax, G. P. Agrawal, W. H. Louisell, “Continuous Fourier-transform spline
solution of unstable resonator field-distribution,”
Opt. Lett. 4, 303–305
(1979).

[CrossRef]
[PubMed]

M. Lax, J. H. Batteh, G. P. Agrawal, “Channeling of intense electromagnetic
beams,” J. Appl. Phys. (in press); G. P. Agrawal, M. Lax, J. H. Batteh, “Laser-induced channel for atmospheric
transmission,” Opt. News 6(3), 37 (1980); G. P. Agrawal, M. Lax, J. H. Batteh, presented at the Optical Society of America Annual
Meeting, October 1980.

M. Lax, J. H. Batteh, G. P. Agrawal, “Channeling of intense electromagnetic
beams,” J. Appl. Phys. (in press); G. P. Agrawal, M. Lax, J. H. Batteh, “Laser-induced channel for atmospheric
transmission,” Opt. News 6(3), 37 (1980); G. P. Agrawal, M. Lax, J. H. Batteh, presented at the Optical Society of America Annual
Meeting, October 1980.

J. W. Cooley, J. W. Tukey, “An algorithm for the machine
calculation of complex Fourier series,”
Math. Comput. 19, 297–301
(1965).

[CrossRef]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high
energy laser beams through the atmosphere,”
Appl. Phys. 10, 129–160
(1976).

[CrossRef]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high
energy laser beams through the atmosphere,”
Appl. Phys. 10, 129–160
(1976).

[CrossRef]

The exponential transformation
r =
r0eαx
is attributed to Gardner by Siegman in Ref. 9: D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of
multi-component exponential decays,” J.
Chem. Phys. 31, 987 (1959). However, its usefulness in connection
with the solution of the radial Sehrödinger equation was recognized much
earlier by Langer: see R. E. Langer, “On the connection formulas and the
solution of the wave equation,” Phys.
Rev. 51, 669–676
(1937).

[CrossRef]

The exponential transformation
r =
r0eαx
is attributed to Gardner by Siegman in Ref. 9: D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of
multi-component exponential decays,” J.
Chem. Phys. 31, 987 (1959). However, its usefulness in connection
with the solution of the radial Sehrödinger equation was recognized much
earlier by Langer: see R. E. Langer, “On the connection formulas and the
solution of the wave equation,” Phys.
Rev. 51, 669–676
(1937).

[CrossRef]

R. W. Hockney, “A fast direct solution of
Poisson’s equation using Fourier analysis,”
J. Assoc. Comput. Mach. 17, 95–113
(1965).

[CrossRef]

The exponential transformation
r =
r0eαx
is attributed to Gardner by Siegman in Ref. 9: D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of
multi-component exponential decays,” J.
Chem. Phys. 31, 987 (1959). However, its usefulness in connection
with the solution of the radial Sehrödinger equation was recognized much
earlier by Langer: see R. E. Langer, “On the connection formulas and the
solution of the wave equation,” Phys.
Rev. 51, 669–676
(1937).

[CrossRef]

M. Lax, G. P. Agrawal, W. H. Louisell, “Continuous Fourier-transform spline
solution of unstable resonator field-distribution,”
Opt. Lett. 4, 303–305
(1979).

[CrossRef]
[PubMed]

M. Lax, J. H. Batteh, G. P. Agrawal, “Channeling of intense electromagnetic
beams,” J. Appl. Phys. (in press); G. P. Agrawal, M. Lax, J. H. Batteh, “Laser-induced channel for atmospheric
transmission,” Opt. News 6(3), 37 (1980); G. P. Agrawal, M. Lax, J. H. Batteh, presented at the Optical Society of America Annual
Meeting, October 1980.

R. C. Le Bail, “Use of fast Fourier transform for
solving partial differential equations,” J.
Comput. Phys. 9, 440–465
(1972).

[CrossRef]

The exponential transformation
r =
r0eαx
is attributed to Gardner by Siegman in Ref. 9: D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of
multi-component exponential decays,” J.
Chem. Phys. 31, 987 (1959). However, its usefulness in connection
with the solution of the radial Sehrödinger equation was recognized much
earlier by Langer: see R. E. Langer, “On the connection formulas and the
solution of the wave equation,” Phys.
Rev. 51, 669–676
(1937).

[CrossRef]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high
energy laser beams through the atmosphere,”
Appl. Phys. 10, 129–160
(1976).

[CrossRef]

R. C. Singleton, “An algorithm for computing the mixed
radix fast Fourier transform,” IEEE Trans.
Audio Electroacoust. AE-17, 93–103
(1969).

[CrossRef]

J. W. Cooley, J. W. Tukey, “An algorithm for the machine
calculation of complex Fourier series,”
Math. Comput. 19, 297–301
(1965).

[CrossRef]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high
energy laser beams through the atmosphere,”
Appl. Phys. 10, 129–160
(1976).

[CrossRef]

R. C. Singleton, “An algorithm for computing the mixed
radix fast Fourier transform,” IEEE Trans.
Audio Electroacoust. AE-17, 93–103
(1969).

[CrossRef]

The exponential transformation
r =
r0eαx
is attributed to Gardner by Siegman in Ref. 9: D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of
multi-component exponential decays,” J.
Chem. Phys. 31, 987 (1959). However, its usefulness in connection
with the solution of the radial Sehrödinger equation was recognized much
earlier by Langer: see R. E. Langer, “On the connection formulas and the
solution of the wave equation,” Phys.
Rev. 51, 669–676
(1937).

[CrossRef]

R. C. Le Bail, “Use of fast Fourier transform for
solving partial differential equations,” J.
Comput. Phys. 9, 440–465
(1972).

[CrossRef]

R. W. Hockney, “A fast direct solution of
Poisson’s equation using Fourier analysis,”
J. Assoc. Comput. Mach. 17, 95–113
(1965).

[CrossRef]

J. W. Cooley, J. W. Tukey, “An algorithm for the machine
calculation of complex Fourier series,”
Math. Comput. 19, 297–301
(1965).

[CrossRef]

A. E. Siegman, “Quasi-fast Hankel
transform,” Opt. Lett. 1, 13–15
(1977).

[CrossRef]
[PubMed]

M. Lax, G. P. Agrawal, W. H. Louisell, “Continuous Fourier-transform spline
solution of unstable resonator field-distribution,”
Opt. Lett. 4, 303–305
(1979).

[CrossRef]
[PubMed]

W. P. Latham, T. C. Salvi, “Resonator studies with the
Gardner–Fresnel–Kirchhoff
propagator,” Opt. Lett. 5, 219–221
(1980).

[CrossRef]
[PubMed]

M. Lax, J. H. Batteh, G. P. Agrawal, “Channeling of intense electromagnetic
beams,” J. Appl. Phys. (in press); G. P. Agrawal, M. Lax, J. H. Batteh, “Laser-induced channel for atmospheric
transmission,” Opt. News 6(3), 37 (1980); G. P. Agrawal, M. Lax, J. H. Batteh, presented at the Optical Society of America Annual
Meeting, October 1980.