Interaction of a moving charged particle with a spatially dispersive medium. I. Structure of the electromagnetic field

B. J. Hoenders; D. N. Pattanayak

doi:10.1103/PhysRevD.13.282

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Interaction of a moving charged particle with a spatially dispersive medium. I. Structure of the electromagnetic field

B. J. Hoenders^* and D. N. Pattanayak^†

Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627

^*Present address: Technical Physical Laboratories, State University at Groningen, Nÿenborgh 18, Groningen 8002, The Netherlands.
^†Present address: Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7.

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Phys. Rev. D 13, 282 – Published 15 January, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.282

Abstract

The general structure of the electromagnetic field is determined which is generated by a uniformly moving point charge interacting with a spatially dispersive medium forming a plane parallel slab. The direction of the point charge is taken to be at right angles to the faces of the slab, and the dielectric constant of the medium in the wave-vector frequency space is assumed to be of the form $ε_{ij} (\vec{k}, ω) = δ_{ij} {ε_{0} (ω) + \frac{χ}{[{\vec{k}}^{2} - μ^{2} (ω)]}}$ , Expressions for Čerenkov and transition radiation fields associated with a uniformly moving point charge passing from a vacuum into such a medium, forming a half space, are also obtained.

References (11)

P. A. Čerenkov, Dokl. Akad. Nauk S. S. S. R. 2, 451 (1934) I. E. Tamm and I. M. Frank, ibid. 14, 107 (1937) B. M. Bolotovsky, Usp. Fiz. Nauk 62, 201 (1957) [Sov. Phys.-Usp. 62, 372 (1957)]
V. L. Ginzburg and J. M. Frank, Zh. Eksp. Teor. Fiz. 16, 1 (1946) I. M. Frank, Usp. Fiz. Nauk 87, 189 (1965) [Sov. Phys.-Usp. 8, 729 (1966)]
F. G. Bass and V. M. Yakovenko, Usp. Fiz. Nauk 86, 189 (1965) [Sov. Phys.-Usp. 8, 420 (1965)]
S. I. Pekar, Zh. Eksp. Teor. Fiz. 33, 1022 (1957) [Sov. Phys.-JETP 6, 785 (1958)] J. J. Hopfield and D. G. Thomas, Phys. Rev. 132, 563 (1963)
V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, New York, 1966)
J. Heinrichs, Phys. Rev. B 5, 4775 (1972)
J. J. Hopfield and D. G. Thomas, Phys. Rev. 132, 563 (1963)
(a) J. J. Sein, Ph.D. dissertation, New York University, 1969 (unpublished) (b) J. L. Birman and J. J. Sein, Phys. Rev. B 6, 2482 (1972) (c) A. A. Maradudin and D. L. Mills, ibid. 7, 2787 (1973) (d) G. S. Agarwal, D. N. Pattanayak, and E. Wolf, 10, 1447 (1974) (e) 11, 1342 (1975)
Eq. (3.3) of [8]
C. J. Bouwkamp, Rep. Prog. Phys. 17, 41 (1954) J. R. Shewell and E. Wolf, J. Opt. Soc. Am. 58, 1596 (1968)
R. Asby and E. Wolf, J. Opt. Soc. Am. 61, 52 (1971)

[c1] P. A. Čerenkov, Dokl. Akad. Nauk S. S. S. R. 2, 451 (1934) I. E. Tamm and I. M. Frank, ibid. 14, 107 (1937) B. M. Bolotovsky, Usp. Fiz. Nauk 62, 201 (1957) [Sov. Phys.-Usp. 62, 372 (1957)]

[c2] V. L. Ginzburg and J. M. Frank, Zh. Eksp. Teor. Fiz. 16, 1 (1946) I. M. Frank, Usp. Fiz. Nauk 87, 189 (1965) [Sov. Phys.-Usp. 8, 729 (1966)]

[c3] F. G. Bass and V. M. Yakovenko, Usp. Fiz. Nauk 86, 189 (1965) [Sov. Phys.-Usp. 8, 420 (1965)]

[c4] S. I. Pekar, Zh. Eksp. Teor. Fiz. 33, 1022 (1957) [Sov. Phys.-JETP 6, 785 (1958)] J. J. Hopfield and D. G. Thomas, Phys. Rev. 132, 563 (1963)

[c5] V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, New York, 1966)

[c6] J. Heinrichs, Phys. Rev. B 5, 4775 (1972)

[c7] J. J. Hopfield and D. G. Thomas, Phys. Rev. 132, 563 (1963)

[c8] (a) J. J. Sein, Ph.D. dissertation, New York University, 1969 (unpublished) (b) J. L. Birman and J. J. Sein, Phys. Rev. B 6, 2482 (1972) (c) A. A. Maradudin and D. L. Mills, ibid. 7, 2787 (1973) (d) G. S. Agarwal, D. N. Pattanayak, and E. Wolf, 10, 1447 (1974) (e) 11, 1342 (1975)

[c9] Eq. (3.3) of [8]

[c10] C. J. Bouwkamp, Rep. Prog. Phys. 17, 41 (1954) J. R. Shewell and E. Wolf, J. Opt. Soc. Am. 58, 1596 (1968)

[c11] R. Asby and E. Wolf, J. Opt. Soc. Am. 61, 52 (1971)

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Interaction of a moving charged particle with a spatially dispersive medium. I. Structure of the electromagnetic field

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Interaction of a moving charged particle with a spatially dispersive medium. II. Čerenkov and transition radiation

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