Abstract
The theoretical investigation of electromagnetic transients in media has been an ongoing topic of interest since (at least) the classic work of Sommerfeld and Brillouin [1] on precursor theory. The prototypical problem is the analysis of the amplitude f(z, t) of the electromagnetic field at point z, time t in a material dielectric when a wave with sharp front (for example, a sharply truncated laser) impinges on the surface of a bounded medium. Coming into play in this analysis are: the model of the medium, (which in the classical theory is taken as a “Lorentz model” dielectric); the coupling of field and medium via some dielectric response function; and the propagation of the field, described by Maxwell equations. All these aspects of radiation and matter theory can be explored by analysing the time evolution of the amplitude f(z, t), which in effect samples the dynamics of the system in a time-resolved succession of stages, each such stage referring to a different frequency regime.
Supported in part by the National Science Foundation, DMR76-20641, Army Research Office, DAHC04-75-G-0052, and FRAP-CUNY 11453.
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References
See L. Brillouin Wave Propagation and Group Velocity (Academic Press, New York, 1960); papers of Sommerfeld and Brillouin are given there along with references. Also see Transient Electromagnetic Fields, ed. L.B. Felsen ( Springer-Verlag, New York, 1976 ).
E.G. Skrotskaya et al., Sov. Phys. JETP 29,123 (1969)
M.J. Frankel and J.L. Birman, Phys. Rev. A 15, 2000 (1977); J.L. Birman and M.J. Frankel, Opt. Comm. 3, 303 (1975).
See J.J. Sein, Ph.D. Thesis, New York University (1969); J.J. Sein and J.L. Birman, Phys. Rev. B 6, 2482 (1972); G.S. Agarwal, D.N. Pattanayak, E. Wolf, Phys. Rev. Lett. 27, 1022 (1971); Phys. Rev. B 10, 1477 (1972); A.A. Maradudin and D.L. Mills, Phys. Rev. B 7, 2787 (1973); R. Zeyher, J.L. Birman, W. Brenig, Phys. Rev. A 6, 4613 and 4617 (1972).
See E. Gitterman and M. Gitterman, Phys. Rev. A 13,763 (1976), who discuss the integral for the local case, extending Sommerfeld’s work in several ways.
See Ref. 3 and M.J. Frankel, Ph.D. Thesis, New York University (1975).
D.N. Pattanayak and E. Wolf, Opt. Comm. 6, 217 (1972).
D.N. Pattanayak and J.L. Birman, to be published.
P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Co., New York, 1953 ) Vol. I, p. 856.
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Birman, J.L., Frankel, M.J., Pattanayak, D.N. (1978). Theory of Electromagnetic Transients in Spatially Dispersive Media and a New Approach to Precursor Theory. In: Mandel, L., Wolf, E. (eds) Coherence and Quantum Optics IV. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0665-9_24
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DOI: https://doi.org/10.1007/978-1-4757-0665-9_24
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