N. Mukunda, R. Simon, E. C. G. Sudarshan, “Fourier optics for the Maxwell field:
formalism and applications,” J. Opt. Soc.
Am. A 2, 416–426
(1985).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial Maxwell beams: transformation
by general linear optical systems,” J. Opt.
Soc. Am. A 2, 1291–1296
(1985).

[CrossRef]

For a proof, see E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first order optical
systems using thin lenses,” Opt.
Acta 32, 855–872
(1985). Compare this assertion with the comments to
the contrary in O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics
(Academic, New
York, 1972), pp. 288,
294. See also S. Cornbleet, “Geometrical optics revisited: a new
light on an old subject,” Proc.
IEEE 71, 471–502
(1983).

[CrossRef]

R. J. Hill, “A stochastic parabolic wave equation
and field moment equations for random media having spatial variation of mean
refractive index,”J. Accoust. Soc.
Am. 77, 1742–1753
(1985).

[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first order optics:
transformation properties of Gaussian Schell-model
fields,” Phys. Rev. A 29, 3273–3279
(1984).

[CrossRef]

E. C. G. Sudarshan, R. Simon, N. Mukunda, “Paraxial wave optics and relativistic
front description. I. The scalar theory,”
Phys. Rev. A 28, 2921–2932
(1983).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial wave optics and relativistic
front description. II. The vector theory,”
Phys. Rev. A 28, 2933–2942
(1983).

[CrossRef]

M. Nazarathy, J. Shamir, “First order optics—a canonical
operator representation: lossless sytems,”J.
Opt. Soc. Am. 72, 356–364
(1982).

[CrossRef]

J. Corones, B. DeFacio, R. J. Krueger, “Parabolic approximations to the
time-independent elastic wave equation,”J.
Math. Phys. 23, 577–586
(1982).

[CrossRef]

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier
optics,” Phys. Rev. A 23, 2533–2536
(1981); D. Gloge, D. Marcuse, “Formal quantum theory of light
rays,”J. Opt. Soc. Am. 59, 1629–1631
(1969).

[CrossRef]

F. Gori, “Collett–Wolf sources and
multimode lasers,” Opt. Commun. 34, 301–305
(1980); A. Starikov, E. Wolf, “Coherent-mode representation of
Gaussian Schell-model sources and of their radiation
fields,” J. Opt. Soc. Am. 72, 923–928
(1982); F. Gori, “Mode propagation of the field generated
by Collett–Wolf Schell-model sources,”
Opt. Commun. 46, 149–154
(1983).

[CrossRef]

For a critical analysis of this
assumption, see M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave
optics,” Phys. Rev. A 11, 1365–1370
(1975).

[CrossRef]

See, for example, H. Kogelnik, T. Li, “Laser beams and
resonators,” Proc. IEEE 54, 1312–1329
(1966), where further references can be found.

[CrossRef]

H. Kogelnik, “Imaging of optical
modes—resonators with internal lenses,”
Bell. Syst. Tech. J. 44, 455–494
(1965).

The front form of dynamics was first
introduced in P. A. M. Dirac, “Forms of relativistic
dynamics,” Rev. Mod. Phys. 21, 392–399
(1949). It has been used for a systematic analysis of paraxial
wave optics, both the scalar case and the vector case, in Refs.
6 and
7.

[CrossRef]

L. Fishman, J. J. McCoy, “Factorization, path integral
representations, and the construction of direct and inverse wave propagation
theories,”IEEE Trans. Geosci. Rem.
Sen. G-22, 682–692
(1948).

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier
optics,” Phys. Rev. A 23, 2533–2536
(1981); D. Gloge, D. Marcuse, “Formal quantum theory of light
rays,”J. Opt. Soc. Am. 59, 1629–1631
(1969).

[CrossRef]

For an analysis of this rule, see
H. Bacry, “Group theory and paraxial
optics,” invited paper presented at the
XIII International Colloquium on Group Theoretical Methods in
Physics, University of Maryland,
May, 1984, where it has been called the MSS
postulate. It was postulated in Ref. 7 and subsequently proved in Ref. 3.

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier
optics,” Phys. Rev. A 23, 2533–2536
(1981); D. Gloge, D. Marcuse, “Formal quantum theory of light
rays,”J. Opt. Soc. Am. 59, 1629–1631
(1969).

[CrossRef]

J. Corones, B. DeFacio, R. J. Krueger, “Parabolic approximations to the
time-independent elastic wave equation,”J.
Math. Phys. 23, 577–586
(1982).

[CrossRef]

J. Corones, B. DeFacio, R. J. Krueger, “Parabolic approximations to the
time-independent elastic wave equation,”J.
Math. Phys. 23, 577–586
(1982).

[CrossRef]

The front form of dynamics was first
introduced in P. A. M. Dirac, “Forms of relativistic
dynamics,” Rev. Mod. Phys. 21, 392–399
(1949). It has been used for a systematic analysis of paraxial
wave optics, both the scalar case and the vector case, in Refs.
6 and
7.

[CrossRef]

L. Fishman, J. J. McCoy, “Factorization, path integral
representations, and the construction of direct and inverse wave propagation
theories,”IEEE Trans. Geosci. Rem.
Sen. G-22, 682–692
(1948).

J. W. Goodman, Introduction to Fourier Optics
(McGraw-Hill, New
York, 1968), p.
60.

F. Gori, “Collett–Wolf sources and
multimode lasers,” Opt. Commun. 34, 301–305
(1980); A. Starikov, E. Wolf, “Coherent-mode representation of
Gaussian Schell-model sources and of their radiation
fields,” J. Opt. Soc. Am. 72, 923–928
(1982); F. Gori, “Mode propagation of the field generated
by Collett–Wolf Schell-model sources,”
Opt. Commun. 46, 149–154
(1983).

[CrossRef]

R. J. Hill, “A stochastic parabolic wave equation
and field moment equations for random media having spatial variation of mean
refractive index,”J. Accoust. Soc.
Am. 77, 1742–1753
(1985).

[CrossRef]

See, for example, H. Kogelnik, T. Li, “Laser beams and
resonators,” Proc. IEEE 54, 1312–1329
(1966), where further references can be found.

[CrossRef]

H. Kogelnik, “Imaging of optical
modes—resonators with internal lenses,”
Bell. Syst. Tech. J. 44, 455–494
(1965).

J. Corones, B. DeFacio, R. J. Krueger, “Parabolic approximations to the
time-independent elastic wave equation,”J.
Math. Phys. 23, 577–586
(1982).

[CrossRef]

For a critical analysis of this
assumption, see M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave
optics,” Phys. Rev. A 11, 1365–1370
(1975).

[CrossRef]

See, for example, H. Kogelnik, T. Li, “Laser beams and
resonators,” Proc. IEEE 54, 1312–1329
(1966), where further references can be found.

[CrossRef]

For a critical analysis of this
assumption, see M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave
optics,” Phys. Rev. A 11, 1365–1370
(1975).

[CrossRef]

L. Fishman, J. J. McCoy, “Factorization, path integral
representations, and the construction of direct and inverse wave propagation
theories,”IEEE Trans. Geosci. Rem.
Sen. G-22, 682–692
(1948).

For a critical analysis of this
assumption, see M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave
optics,” Phys. Rev. A 11, 1365–1370
(1975).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Fourier optics for the Maxwell field:
formalism and applications,” J. Opt. Soc.
Am. A 2, 416–426
(1985).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial Maxwell beams: transformation
by general linear optical systems,” J. Opt.
Soc. Am. A 2, 1291–1296
(1985).

[CrossRef]

For a proof, see E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first order optical
systems using thin lenses,” Opt.
Acta 32, 855–872
(1985). Compare this assertion with the comments to
the contrary in O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics
(Academic, New
York, 1972), pp. 288,
294. See also S. Cornbleet, “Geometrical optics revisited: a new
light on an old subject,” Proc.
IEEE 71, 471–502
(1983).

[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first order optics:
transformation properties of Gaussian Schell-model
fields,” Phys. Rev. A 29, 3273–3279
(1984).

[CrossRef]

E. C. G. Sudarshan, R. Simon, N. Mukunda, “Paraxial wave optics and relativistic
front description. I. The scalar theory,”
Phys. Rev. A 28, 2921–2932
(1983).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial wave optics and relativistic
front description. II. The vector theory,”
Phys. Rev. A 28, 2933–2942
(1983).

[CrossRef]

M. Nazarathy, J. Shamir, “First order optics—a canonical
operator representation: lossless sytems,”J.
Opt. Soc. Am. 72, 356–364
(1982).

[CrossRef]

M. Nazarathy, J. Shamir, “First order optics—a canonical
operator representation: lossless sytems,”J.
Opt. Soc. Am. 72, 356–364
(1982).

[CrossRef]

A. E. Siegman, An Introduction to Lasers and Masers
(McGraw-Hill, New
York, 1971), p.
307.

For a proof, see E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first order optical
systems using thin lenses,” Opt.
Acta 32, 855–872
(1985). Compare this assertion with the comments to
the contrary in O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics
(Academic, New
York, 1972), pp. 288,
294. See also S. Cornbleet, “Geometrical optics revisited: a new
light on an old subject,” Proc.
IEEE 71, 471–502
(1983).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial Maxwell beams: transformation
by general linear optical systems,” J. Opt.
Soc. Am. A 2, 1291–1296
(1985).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Fourier optics for the Maxwell field:
formalism and applications,” J. Opt. Soc.
Am. A 2, 416–426
(1985).

[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first order optics:
transformation properties of Gaussian Schell-model
fields,” Phys. Rev. A 29, 3273–3279
(1984).

[CrossRef]

E. C. G. Sudarshan, R. Simon, N. Mukunda, “Paraxial wave optics and relativistic
front description. I. The scalar theory,”
Phys. Rev. A 28, 2921–2932
(1983).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial wave optics and relativistic
front description. II. The vector theory,”
Phys. Rev. A 28, 2933–2942
(1983).

[CrossRef]

For a proof, see E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first order optical
systems using thin lenses,” Opt.
Acta 32, 855–872
(1985). Compare this assertion with the comments to
the contrary in O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics
(Academic, New
York, 1972), pp. 288,
294. See also S. Cornbleet, “Geometrical optics revisited: a new
light on an old subject,” Proc.
IEEE 71, 471–502
(1983).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Fourier optics for the Maxwell field:
formalism and applications,” J. Opt. Soc.
Am. A 2, 416–426
(1985).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial Maxwell beams: transformation
by general linear optical systems,” J. Opt.
Soc. Am. A 2, 1291–1296
(1985).

[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first order optics:
transformation properties of Gaussian Schell-model
fields,” Phys. Rev. A 29, 3273–3279
(1984).

[CrossRef]

E. C. G. Sudarshan, R. Simon, N. Mukunda, “Paraxial wave optics and relativistic
front description. I. The scalar theory,”
Phys. Rev. A 28, 2921–2932
(1983).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial wave optics and relativistic
front description. II. The vector theory,”
Phys. Rev. A 28, 2933–2942
(1983).

[CrossRef]

H. Kogelnik, “Imaging of optical
modes—resonators with internal lenses,”
Bell. Syst. Tech. J. 44, 455–494
(1965).

L. Fishman, J. J. McCoy, “Factorization, path integral
representations, and the construction of direct and inverse wave propagation
theories,”IEEE Trans. Geosci. Rem.
Sen. G-22, 682–692
(1948).

J. Corones, B. DeFacio, R. J. Krueger, “Parabolic approximations to the
time-independent elastic wave equation,”J.
Math. Phys. 23, 577–586
(1982).

[CrossRef]

M. Nazarathy, J. Shamir, “First order optics—a canonical
operator representation: lossless sytems,”J.
Opt. Soc. Am. 72, 356–364
(1982).

[CrossRef]

R. J. Hill, “A stochastic parabolic wave equation
and field moment equations for random media having spatial variation of mean
refractive index,”J. Accoust. Soc.
Am. 77, 1742–1753
(1985).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial Maxwell beams: transformation
by general linear optical systems,” J. Opt.
Soc. Am. A 2, 1291–1296
(1985).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Fourier optics for the Maxwell field:
formalism and applications,” J. Opt. Soc.
Am. A 2, 416–426
(1985).

[CrossRef]

For a proof, see E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first order optical
systems using thin lenses,” Opt.
Acta 32, 855–872
(1985). Compare this assertion with the comments to
the contrary in O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics
(Academic, New
York, 1972), pp. 288,
294. See also S. Cornbleet, “Geometrical optics revisited: a new
light on an old subject,” Proc.
IEEE 71, 471–502
(1983).

[CrossRef]

F. Gori, “Collett–Wolf sources and
multimode lasers,” Opt. Commun. 34, 301–305
(1980); A. Starikov, E. Wolf, “Coherent-mode representation of
Gaussian Schell-model sources and of their radiation
fields,” J. Opt. Soc. Am. 72, 923–928
(1982); F. Gori, “Mode propagation of the field generated
by Collett–Wolf Schell-model sources,”
Opt. Commun. 46, 149–154
(1983).

[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first order optics:
transformation properties of Gaussian Schell-model
fields,” Phys. Rev. A 29, 3273–3279
(1984).

[CrossRef]

For a critical analysis of this
assumption, see M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave
optics,” Phys. Rev. A 11, 1365–1370
(1975).

[CrossRef]

E. C. G. Sudarshan, R. Simon, N. Mukunda, “Paraxial wave optics and relativistic
front description. I. The scalar theory,”
Phys. Rev. A 28, 2921–2932
(1983).

[CrossRef]

N. Mukunda, R. Simon, E. C. G. Sudarshan, “Paraxial wave optics and relativistic
front description. II. The vector theory,”
Phys. Rev. A 28, 2933–2942
(1983).

[CrossRef]

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier
optics,” Phys. Rev. A 23, 2533–2536
(1981); D. Gloge, D. Marcuse, “Formal quantum theory of light
rays,”J. Opt. Soc. Am. 59, 1629–1631
(1969).

[CrossRef]

See, for example, H. Kogelnik, T. Li, “Laser beams and
resonators,” Proc. IEEE 54, 1312–1329
(1966), where further references can be found.

[CrossRef]

The front form of dynamics was first
introduced in P. A. M. Dirac, “Forms of relativistic
dynamics,” Rev. Mod. Phys. 21, 392–399
(1949). It has been used for a systematic analysis of paraxial
wave optics, both the scalar case and the vector case, in Refs.
6 and
7.

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics
(McGraw-Hill, New
York, 1968), p.
60.

For an analysis of this rule, see
H. Bacry, “Group theory and paraxial
optics,” invited paper presented at the
XIII International Colloquium on Group Theoretical Methods in
Physics, University of Maryland,
May, 1984, where it has been called the MSS
postulate. It was postulated in Ref. 7 and subsequently proved in Ref. 3.

A. E. Siegman, An Introduction to Lasers and Masers
(McGraw-Hill, New
York, 1971), p.
307.