This is a theoretical study of the interplay of optical phase conjugation and multiple scattering. We calculate the intensity of light reflected by a phase-conjugating mirror when it is placed behind a disordered medium. We compare the results of a fully phase-coherent theory with those from the theory of radiative transfer. Both methods are equivalent if the dwell time ${\ensuremath{\tau}}_{\mathrm{dwell}}$ of a photon in the disordered medium is much larger than the inverse of the frequency shift $2\ensuremath{\Delta}\ensuremath{\omega}$ acquired at the phase-conjugating mirror. When ${\ensuremath{\tau}}_{\mathrm{dwell}}\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\lesssim}1$, in contrast, phase coherence drastically affects the reflected intensity. In particular, a minimum in the dependence of the reflectance on the disorder strength disappears when $\ensuremath{\Delta}\ensuremath{\omega}$ is reduced below $1/{\ensuremath{\tau}}_{\mathrm{dwell}}.$ The analogies and differences with Andreev reflection of electrons at the interface between a normal metal and a superconductor are discussed.
We present an analytical approach to random lasing in a one-dimensional medium, consistent with transfer matrix numerical simulations. It is demonstrated that the lasing threshold is defined by transmission through the passive medium and thus depends exponentially on the size of the system. Lasing in the most efficient regime of strong three-dimensional localization of light is discussed. We argue that the lasing threshold should have anomalously strong fluctuations from probe to probe, in agreement with recent measurements.
We develop an analytic approach to evaluating the density
ρ(E,Γ) of complex resonance poles with real energies
E and widths
Γ in the pure reflection problem from a one-dimensional disordered sample with white-noise random potential. We start with establishing a general link between the density of resonances and the distribution of the reflection coefficient
r=∣R(E,L)∣2, where
R(E,L) is the reflection amplitude, at {\it complex} energies
E=E+iη, identifying the parameter
η>0 with the uniform rate of absorption within the disordered medium. We show that leveraging this link allows for a detailed analysis of the resonance density in the weak disorder limit. In particular, for a (semi)infinite sample, it yields an explicit formula for
ρ(E,Γ), describing the crossover from narrow to broad resonances in a unified way. Similarly, our approach yields a limiting formula for
ρ(E,Γ) in the opposite case of a short disordered sample, with size much smaller than the localization length. This regime seems to have not been systematically addressed in the literature before, with the corresponding analysis requiring an accurate and rather non-trivial implementation of WKB-like asymptotics in the scattering problem. Finally, we study the resonance statistics numerically for the one-dimensional Anderson tight-binding model and compare the results with our analytic expressions.
We consider the phase coherent transport of a quasi-one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length
L. Among the possible different types of flow we identified [T. Paul, P. Schlagheck, P. Leboeuf, and N. Pavloff, Phys. Rev. Lett. 98, 210602 (2007)], we focus here on the supersonic stationary regime where Anderson localization exists. We generalize the diffusion formalism of Dorokhov-Mello-Pereyra-Kumar to include interaction effects. It is shown that interactions modify the localization length and also introduce a length scale ${L}^{\ensuremath{\ast}}$ for the disordered region, above which most of the realizations of the random potential lead to time-dependent flows. A Fokker-Planck equation for the probability density of the transmission coefficient that takes this effect into account is introduced and solved. The theoretical predictions are verified numerically for different types of disordered potentials. Experimental scenarios for observing our predictions are discussed.
We study the evolution of a system performing a one-dimensional quantum walk in the presence of static phase disorder. The same model also describes the propagation of classical light pulses in photonic mesh lattices. We study the interplay between the coupling (i.e. the bias of the "quantum coin") and disorder. We provide an exact analytical expression for the localization length for two limiting cases of strong and weak phase disorder. In all the cases of interest we supply numerical simulations for participation ratio, Lyapunov exponent and the return probability as functions of the coupling parameter.