A Specific Wave of Electromagnetic Energy Accumulation in a Random Medium of Small Spherical Particles with Magnetic Dipole Mie Resonance

The properties of artificial optical materials of modern optoelectronics, such as photonic crystals and metamaterials, are given by the effects of multiple scattering of electromagnetic (EM) waves in inhomogeneous media. Numerous analytical investigations consider stationary problems and only rare of them deal with more subtle effects of nonstationary processes. To study the dynamics of the spatio-temporal energy redistribution of a pulse in a random medium composed of small spherical particles tuned to the magnetic dipole Mie resonance by pulse carrier frequency, solutions of the modified radiative transfer equation (MRTE) with delay which describes a quasimonochromatic pulse multiple scattering in a discrete resonant random medium, are derived in the diffusion regime, when the pulse source is located in the infinite resonant random medium, and in the ballistic regime, when a pulse is incident on a slab of such a medium. In a diffusion regime, the part a/(a + 2) of a short pulse energy accumulates inside resonant scatterers during a time t of the order of 2akav/(a + 2) of the time t/t0 given in optical units, while the part 2/(a + 2) remains in the environment of the scatterers. Here a is the resonance efficiency factor, which accounts for the accumulation of electromagnetic energy inside the scatterers due to their resonance polarization by the pulse wave field, akav = tdelay/t0, t0 is a radiation extinction mean free time between scattering events, tdelay is a single scattering time delay. Redistributing the pulse energy is much more complicated when a pulse is incident on a random medium slab. In a ballistic regime, the incident short pulse energy is redistributed in the above ratio during pulse transmission through the slab if the slab thickness is on the order of or greater than the energy transport velocity multiplied by a single scattering delay tdelay. The accumulated energy then gradually escapes from the slab. Thus, the parameter a of the energy accumulation inside the scatterers defines the final result of the pulse energy redistribution, while the parameter akav of the single scattering delay defines the temporal rate of the energy redistribution.