Multi-Scale Complexity in Linear Dispersive Pulse Propagation Phenomena
Abstract
The classical asymptotic description of dispersive pulse propagation, initiated by Arnold Sommerfeld [1] and Leon Brillouin [2, 3] in 1914 using the then newly developed method of steepest descent due to Debye [4], and more recently completed by Oughstun & Sherman [5, 6, 7], Oughstun [8, 9], and Cartwright & Oughstun [10] using modern, uniform asymptotic expansion techniques, has provided an accurate mathematical description of ultrawideband pulse propagation in causally dispersive dielectrics and conducting media. The accuracy of this asymptotic description increases monotonically as the propagation distance z increases above some characteristic distance zd set by the material dispersion, typically given by the e 1 penetration depth at some oscillation frequency characteristic of the input pulse. This asymptotic description has also resulted in a simple physical description of dispersive pulse dynamics [11, 12] based upon the energy transport velocity [8, 13] and attenuation of a time-harmonic electromagnetic plane wave in the dispersive medium that reduces to the approximate group velocity description in a specific limit of vanishing loss (the limit in which the group velocity approximation is valid). What remains to be done in order to complete this mathematically rigorous theory of dispersive pulse propagation is the development of a physical description of the precursor field formation at the molecular level, as it is there that the origin of the material dispersion occurs and the precursor field formation first appears. Associated with this problem is the correct physical description of dispersive pulse propagation in the immature dispersion regime where the precursor formation occurs. Although it has been asserted that the group velocity description would provide this near-field description, the research conducted in this grant has shown that this is is not necessarily true. These two related problems formed the focus of this research grant.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 2011
- Accession Number
- ADA563848
Entities
People
- Kurt E. Oughstun
Organizations
- University of Vermont