Variational principles derived for discontinuous electromagnetic fields

Abstract

A unified procedure based on a general principle of physics (e.g., Hamilton’s principle) together with Legendre’s (or Friedrichs’s) transformation is proposed to systematically derive certain variational principles for discontinuous electromagnetic fields which are useful to treat electromagnetic waves and vibrations in dielectrics. The integral and differential types of variational principles generate Maxwell’s equations and the associated natural boundary and jump conditions as well as the initial conditions, as their Euler–Lagrange equations, for a regular finite and bounded dielectric region with or without a fixed, internal surface of discontinuity. Special cases of the variational principles, including a reciprocal one, are recorded which have those for time-harmonic motions and a dielectric region within a vacuum or a perfect conductor, and they are shown to agree with and to recover some of earlier variational principles [e.g., M. C. Dökmeci, IEEE Trans. UFFC UFFC-35, 775–787 (1988); UFFC-37, 369–385 (1990) and G. A. Aşkar, 3007 (1994) and references therein]. [Work supported in part by The Scientific and Technical Research Council of Turkey.]