The dispersive properties of dielectric materials in both the time and the frequency domains are discussed. Special emphasis is placed on the treatment of heterogeneous materials, particularly two-phase mixtures. A time-domain Maxwell–Garnett rule is derived that differs from the corresponding frequency-domain formula in that it is expressed in terms of convolutions and inverse operators of the susceptibility kernels of the materials. Much of the analysis deals with the question of how the temporal dispersion of the dielectric responses of various physical materials is affected by the mixing process. Debye, Lorentz, Drude, and modified Debye susceptibility models are treated in detail.
© 1998 Optical Society of America
Original Manuscript: July 3, 1997
Revised Manuscript: January 16, 1998
Manuscript Accepted: December 17, 1997
Published: May 1, 1998
Gerhard Kristensson, Sten Rikte, and Ari Sihvola, "Mixing formulas in the time domain," J. Opt. Soc. Am. A 15, 1411-1422 (1998)