Energy-velocity description of pulse propagation in absorbing, dispersive dielectrics
نویسندگان
چکیده
The evolution of an electromagnetic pulse propagating through a linear, dispersive, and absorbing dielectric (as predicted by the modern asymptotic extension of the classic theory of Sommerfeld and Brillouin) is described in physical terms. The description is similar to the group-velocity description known for plane-wave pulses propagating through lossless, gainless, dispersive media but with two modifications: (1) the group velocity is replaced by the velocity of energy in time-harmonic waves, and (2) a nonoscillatory component is added that consists of a wave that grows exponentially with time with a time-dependent growth rate. In the nonoscillatory component the growth rate at each space–time point is determined by the velocity of energy in exponentially growing waves in the medium. The new description provides, for the first time to our knowledge, a physical explanation of the localized details of pulse dynamics in dispersive and absorbing dielectric media and a simple mathematical algorithm for quantitative predictions. Numerical comparisons of the results of the algorithm with the exact integral solution are presented for a highly transparent dielectric and for a highly absorbing dielectric. In both cases the agreement is excellent.
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