Notation using six-vectors and six-dyadics appears very applicable for describing electromagnetic problems in general bi-anisotropic media, because with normal threevector notation analytic expressions often tend to be very complicated. Introducing some operations, recourse to the three-vector and three-dyadic notation during the analysis can be avoided. A number of theorems and concepts of electromagnetic fields in bi-anisotropic media are given as examples.
For lossless media, Hamilton's equations of geometrical optics can be derived from the dispersion equation either by the method of characteristics or by its combination with Sommerfeld-Runge's refraction law, Whitham's conservation law, and the expression 0to/0k for the group velocity. The formal generalization to media with absorption leads to characteristics with complex space-time coordinates due to the now complex coefficients of the dispersion equation. For media with moderate absorption a real-valued generalization of Hamilton's equations is proposed. It is based on a dispersion equation with complex coefficients, on Sommerfeld-Runge's and Whitham's laws for the real parts of k, to, on Connor and Felsen's condition for the imaginary part of k, and on the expressionRe (0to/0k) for the velocity of a wave packet. These real-valued equations have been shown to hold in homogeneous media with moderate absorption.
The field of a pulsed beam (a ‘wave packet’), travelling through a medium with moderate absorption, is calculated by the saddle-point method. The packet velocity (i.e. the velocity of the spatial amplitude maximum) has the same direction as the velocity Re (∂ω/∂k), a generalization of the group velocity ∂ω/∂k in non-absorbing media. It differs from the absolute value of this velocity by a correction factor depending on the absorption, beam width and pulse duration. This factor is unity for vanishing absorption and infinite beam width. The velocity Im (∂ω/∂k) has no apparent physical meaning.
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