Abstract

The relationship between Maxwell’s equations and radiative-transport theory is studied for isotropic, nondispersive media that have arbitrary permittivity variations. It is demonstrated that the postulates of transport theory are consistent with Maxwell’s equations if the characteristics of the medium and the fields are such that the field-correlation tensor possesses certain properties and if the relative permittivity fluctuations in the medium are small in comparison with unity and have correlation lengths that satisfy appropriate requirements.

© 1981 Optical Society of America

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  1. A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65, 1030–1061 (1977).
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  3. L. S. Dolin, Radiats. Fiz. 7, 380–391 (1964).
  4. V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Spring-field, Va., 1971).
  5. Y. N. Barabanenkovet al., "Application of the theory of multiple scattering of waves to the derivation of the radiation transfer equation for a statistically inhomogeneous medium," Radiophys. Quantum Electron. 15, 1852–1860 (1972).
  6. K. M. Watson, "Multiple scattering of electromagnetic waves in an underdense plasma," J. Math. Phys. 10, 688–702 (1969).
  7. D. Bugnolo, "Radio star scintillation and multiple scattering in the ionosphere," IRE Trans. Antennas Propag. AP-9, 89–96 (1961).
  8. P. Stott, "A transport theory for multiple scattering of electro-magnetic waves by a turbulent plasma," J. Phys. A 1, 675–689 (1968).
  9. R. Fante, "Propagation of electromagnetic waves through a turbulent plasma using transport theory," IEEE Trans. Antennas Propag. AP-21, 750–755 (1973).
  10. A. Walther, "Radiometry and coherence," J. Opt. Soc. Am. 58, 1256–1259 (1968).
  11. A. Friberg, in Proceedings of the Fourth Rochester Conference on Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1978).
  12. E. Collett, J. Foley, and E. Wolf, "On an investigation of Tatarskii into the relationship between coherence new theory of radiative energy transfer in free electromagnetic fields," J. Opt. Soc. Am. 67, 465–467 (1977).
  13. E. Wolf, "New theory of radiative energy transfer in free electromagnetic fields," Phys. Rev. D 13, 869–886 (1976).
  14. E. Wolf, "Coherence and radiometry," J. Opt. Soc. Am. 68, 6–17 (1978).
  15. M. Zubairy and E. Wolf, "Exact equations for radiative transfer for energy and momentum in free electromagnetic fields," Opt. Commun. 20, 321–324 (1977).
  16. J. Startton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  17. The condition in Eq. (25) places a restriction on the size and rate of variance of the permittivity. For further discussion see Appendix 3 and J. Strohbehn and S. Clifford, "Polarization and angle of arrival fluctuations for a plane wave propagated through a turbulent medium," IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).
  18. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  19. E. Novikov, "Functionals and the method of random forces in the theory of turbulence," Sov. Phys. JETP 20, 1290–1294 (1965).
  20. K. Furutsu, "On the statistical theory of electromagnetic waves in a fluctuating medium," J. Res. Nat. Bur. Stand. 67D, 303–310 (1963).
  21. V. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Spring-field, Va., 1971), Sec. 60.
  22. The proof holds also for media in which B(r,ŕ″) is a slowly varying function of R1 = (ŕ + ŕ″)/2 but depends arbitrarily on ρ = (ŕ - ŕ″).

1978 (1)

1977 (2)

M. Zubairy and E. Wolf, "Exact equations for radiative transfer for energy and momentum in free electromagnetic fields," Opt. Commun. 20, 321–324 (1977).

E. Collett, J. Foley, and E. Wolf, "On an investigation of Tatarskii into the relationship between coherence new theory of radiative energy transfer in free electromagnetic fields," J. Opt. Soc. Am. 67, 465–467 (1977).

1976 (1)

E. Wolf, "New theory of radiative energy transfer in free electromagnetic fields," Phys. Rev. D 13, 869–886 (1976).

1973 (1)

R. Fante, "Propagation of electromagnetic waves through a turbulent plasma using transport theory," IEEE Trans. Antennas Propag. AP-21, 750–755 (1973).

1972 (1)

Y. N. Barabanenkovet al., "Application of the theory of multiple scattering of waves to the derivation of the radiation transfer equation for a statistically inhomogeneous medium," Radiophys. Quantum Electron. 15, 1852–1860 (1972).

1969 (1)

K. M. Watson, "Multiple scattering of electromagnetic waves in an underdense plasma," J. Math. Phys. 10, 688–702 (1969).

1968 (2)

A. Walther, "Radiometry and coherence," J. Opt. Soc. Am. 58, 1256–1259 (1968).

P. Stott, "A transport theory for multiple scattering of electro-magnetic waves by a turbulent plasma," J. Phys. A 1, 675–689 (1968).

1967 (1)

The condition in Eq. (25) places a restriction on the size and rate of variance of the permittivity. For further discussion see Appendix 3 and J. Strohbehn and S. Clifford, "Polarization and angle of arrival fluctuations for a plane wave propagated through a turbulent medium," IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).

1965 (1)

E. Novikov, "Functionals and the method of random forces in the theory of turbulence," Sov. Phys. JETP 20, 1290–1294 (1965).

1963 (1)

K. Furutsu, "On the statistical theory of electromagnetic waves in a fluctuating medium," J. Res. Nat. Bur. Stand. 67D, 303–310 (1963).

1961 (1)

D. Bugnolo, "Radio star scintillation and multiple scattering in the ionosphere," IRE Trans. Antennas Propag. AP-9, 89–96 (1961).

Barabanenkov, Y. N.

Y. N. Barabanenkovet al., "Application of the theory of multiple scattering of waves to the derivation of the radiation transfer equation for a statistically inhomogeneous medium," Radiophys. Quantum Electron. 15, 1852–1860 (1972).

Bugnolo, D.

D. Bugnolo, "Radio star scintillation and multiple scattering in the ionosphere," IRE Trans. Antennas Propag. AP-9, 89–96 (1961).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Clifford, S.

The condition in Eq. (25) places a restriction on the size and rate of variance of the permittivity. For further discussion see Appendix 3 and J. Strohbehn and S. Clifford, "Polarization and angle of arrival fluctuations for a plane wave propagated through a turbulent medium," IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).

Collett, E.

Dolin, L. S.

L. S. Dolin, Radiats. Fiz. 7, 380–391 (1964).

Fante, R.

R. Fante, "Propagation of electromagnetic waves through a turbulent plasma using transport theory," IEEE Trans. Antennas Propag. AP-21, 750–755 (1973).

Foley, J.

Friberg, A.

A. Friberg, in Proceedings of the Fourth Rochester Conference on Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1978).

Furutsu, K.

K. Furutsu, "On the statistical theory of electromagnetic waves in a fluctuating medium," J. Res. Nat. Bur. Stand. 67D, 303–310 (1963).

Ishimaru, A.

A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65, 1030–1061 (1977).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Novikov, E.

E. Novikov, "Functionals and the method of random forces in the theory of turbulence," Sov. Phys. JETP 20, 1290–1294 (1965).

Startton, J.

J. Startton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Stott, P.

P. Stott, "A transport theory for multiple scattering of electro-magnetic waves by a turbulent plasma," J. Phys. A 1, 675–689 (1968).

Strohbehn, J.

The condition in Eq. (25) places a restriction on the size and rate of variance of the permittivity. For further discussion see Appendix 3 and J. Strohbehn and S. Clifford, "Polarization and angle of arrival fluctuations for a plane wave propagated through a turbulent medium," IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).

Tatarskii, V.

V. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Spring-field, Va., 1971), Sec. 60.

Tatarskii, V. I.

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Spring-field, Va., 1971).

Walther, A.

Watson, K. M.

K. M. Watson, "Multiple scattering of electromagnetic waves in an underdense plasma," J. Math. Phys. 10, 688–702 (1969).

Wolf, E.

E. Wolf, "Coherence and radiometry," J. Opt. Soc. Am. 68, 6–17 (1978).

E. Collett, J. Foley, and E. Wolf, "On an investigation of Tatarskii into the relationship between coherence new theory of radiative energy transfer in free electromagnetic fields," J. Opt. Soc. Am. 67, 465–467 (1977).

M. Zubairy and E. Wolf, "Exact equations for radiative transfer for energy and momentum in free electromagnetic fields," Opt. Commun. 20, 321–324 (1977).

E. Wolf, "New theory of radiative energy transfer in free electromagnetic fields," Phys. Rev. D 13, 869–886 (1976).

Zubairy, M.

M. Zubairy and E. Wolf, "Exact equations for radiative transfer for energy and momentum in free electromagnetic fields," Opt. Commun. 20, 321–324 (1977).

IEEE Trans. Antennas Propag. (2)

R. Fante, "Propagation of electromagnetic waves through a turbulent plasma using transport theory," IEEE Trans. Antennas Propag. AP-21, 750–755 (1973).

The condition in Eq. (25) places a restriction on the size and rate of variance of the permittivity. For further discussion see Appendix 3 and J. Strohbehn and S. Clifford, "Polarization and angle of arrival fluctuations for a plane wave propagated through a turbulent medium," IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).

IRE Trans. Antennas Propag. (1)

D. Bugnolo, "Radio star scintillation and multiple scattering in the ionosphere," IRE Trans. Antennas Propag. AP-9, 89–96 (1961).

J. Math. Phys. (1)

K. M. Watson, "Multiple scattering of electromagnetic waves in an underdense plasma," J. Math. Phys. 10, 688–702 (1969).

J. Opt. Soc. Am. (3)

J. Phys. A (1)

P. Stott, "A transport theory for multiple scattering of electro-magnetic waves by a turbulent plasma," J. Phys. A 1, 675–689 (1968).

J. Res. Nat. Bur. Stand. (1)

K. Furutsu, "On the statistical theory of electromagnetic waves in a fluctuating medium," J. Res. Nat. Bur. Stand. 67D, 303–310 (1963).

Opt. Commun. (1)

M. Zubairy and E. Wolf, "Exact equations for radiative transfer for energy and momentum in free electromagnetic fields," Opt. Commun. 20, 321–324 (1977).

Phys. Rev. D (1)

E. Wolf, "New theory of radiative energy transfer in free electromagnetic fields," Phys. Rev. D 13, 869–886 (1976).

Radiophys. Quantum Electron. (1)

Y. N. Barabanenkovet al., "Application of the theory of multiple scattering of waves to the derivation of the radiation transfer equation for a statistically inhomogeneous medium," Radiophys. Quantum Electron. 15, 1852–1860 (1972).

Sov. Phys. (1)

E. Novikov, "Functionals and the method of random forces in the theory of turbulence," Sov. Phys. JETP 20, 1290–1294 (1965).

Other (9)

V. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Spring-field, Va., 1971), Sec. 60.

The proof holds also for media in which B(r,ŕ″) is a slowly varying function of R1 = (ŕ + ŕ″)/2 but depends arbitrarily on ρ = (ŕ - ŕ″).

A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65, 1030–1061 (1977).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

L. S. Dolin, Radiats. Fiz. 7, 380–391 (1964).

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Spring-field, Va., 1971).

A. Friberg, in Proceedings of the Fourth Rochester Conference on Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1978).

J. Startton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

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