Coherent Random Lasing and `Almost Localized' Photon Modes

Abstract

There exists a formal analogy between the Schrödinger equation describing electron motion in a random potential, and the scalar wave equation for light propagation in a medium with fluctuating dielectric constant. Consider, for concreteness, a two-dimensional geometry (quantum well for an electron and a thin film for light). Then both equations can be presented in the form

$$\Delta _\rho \psi + [k^2 - U(\rho )]\psi = 0,$$

((1))

where ρ is the in-plane coordinate. For an electron with mass m and energy E, moving in a random potential V(ρ), the parameters k ² and U(ρ) are For a light wave with frequency ω, traveling in a medium with dielectric constant ε, corresponding expressions for k ² and U(ρ) take the form

$$k^2 = 2mE, U(\rho ) = 2mV(\rho ).$$

((2))

where δ∈(ρ) is the fluctuating part of the dielectric constant.