Localization and absorption of waves in a weakly dissipative disordered medium

Abstract

The effect of a small imaginary part ${\ensuremath{\epsilon}}_{2}$ to the dielectric constant on the propagation of waves in a disordered medium near the Anderson localization transition is considered. The n\ensuremath{\rightarrow}0 replica-field representation of the averaged Green's function leads to a nonlinear \ensuremath{\sigma} model with a symmetry-breaking perturbation proportional to ${\ensuremath{\epsilon}}_{2}$. In d=2+\ensuremath{\epsilon}, the renormalized energy absorption coefficient is shown to increase anomalously with frequency \ensuremath{\omega} near the mobility edge ${\ensuremath{\omega}}^{\mathrm{*}}$ as \ensuremath{\alpha}\ensuremath{\sim}(${\ensuremath{\omega}}^{\mathrm{*}}$-\ensuremath{\omega}${)}^{\mathrm{\ensuremath{-}}(d\mathrm{\ensuremath{-}}2)\ensuremath{\nu}/2}$, \ensuremath{\nu}=1/\ensuremath{\epsilon}. It is shown that the wavelength ${\ensuremath{\lambda}}^{\mathrm{*}}$ below which localization occurs is related to the elastic mean free path l by (l/${\ensuremath{\lambda}}^{\mathrm{*}}$${)}^{d\mathrm{\ensuremath{-}}1}$\ensuremath{\sim}1/\ensuremath{\epsilon} (d>2). This may occur near the limit of attainable disorder from a quenched random array of small dielectric or metallic spheres.

Keywords

Affiliated Institutions

• Harvard University US

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