Modal analysis of wave propagation in dispersive media

M. Ismail Abdelrahman and B. Gralak
Phys. Rev. A 97, 013824 – Published 17 January 2018

Abstract

Surveys on wave propagation in dispersive media have been limited since the pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914)] by the presence of branches in the integral expression of the wave function. In this article a method is proposed to eliminate these critical branches and hence to establish a modal expansion of the time-dependent wave function. The different components of the transient waves are physically interpreted as the contributions of distinct sets of modes and characterized accordingly. Then, the modal expansion is used to derive a modified analytical expression of the Sommerfeld precursor improving significantly the description of the amplitude and the oscillating period up to the arrival of the Brillouin precursor. The proposed method and results apply to all waves governed by the Helmholtz equations.

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  • Received 19 June 2017

DOI:https://doi.org/10.1103/PhysRevA.97.013824

©2018 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsAtomic, Molecular & OpticalGeneral PhysicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Ismail Abdelrahman* and B. Gralak

  • Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France

  • *m.abdelrahman@fresnel.fr

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Vol. 97, Iss. 1 — January 2018

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