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Real Hamilton equations of geometric optics for media with moderate absorption
Author(s) -
Suchy Kurt
Publication year - 1981
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs016i006p01179
Subject(s) - geometrical optics , refraction , snell's law , generalization , dispersion (optics) , mathematical analysis , mathematics , conservation law , dispersion relation , absorption (acoustics) , physics , group velocity , classical mechanics , optics
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 ∂ω / ∂ k 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 , ω, on Connor and Felsen's condition for the imaginary part of k , and on the expression Re (∂ ω/∂ k ) for the velocity of a wave packet. These real‐valued equations have been shown to hold in homogeneous media with moderate absorption.