Abstract
We consider the propagation of arbitrary electromagnetic pulses in anomalously dispersive dielectrics characterized by M relaxation processes. A partial differential equation for the electric field in the dielectric is derived and analyzed. This single equation describes a hierarchy of M + 1 wave types, each type characterized by an attenuation coefficient and a wave speed. Our analysis identifies a "skin-depth" where the pulse response is described by a telegrapher's equation with smoothing terms, travels with the wavefront speed, and decays exponentially. Past this shallow depth we show that the pulse response is described by a weakly dispersive advection-diffusion equation, travels with the sub-characteristic advection speed equal to the zero-frequency phase velocity in the dielectric, and decays algebraically. The analysis is verified with a numerical simulation. The relevance of our results to the development of numerical methods for such problems is discussed.
Original language | English (US) |
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Pages (from-to) | 253-262 |
Number of pages | 10 |
Journal | Wave Motion |
Volume | 21 |
Issue number | 3 |
DOIs | |
State | Published - May 1995 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- General Physics and Astronomy
- Computational Mathematics
- Applied Mathematics