Light scattering from an amplifying medium bounded by a randomly rough surface: A numerical study

We study by numerical simulations the scattering of $s$-polarized light from a rough dielectric film deposited on the planar surface of a semi-infinite perfect conductor. The dielectric film is allowed to be either active or passive, situations that we model by assigning negative and positive values, respectively, to the imaginary part $\epsilon_2$ of the dielectric constant of the film. We study the reflectance ${\cal R}$ and the total scattered energy ${\cal U}$ for the system as functions of both $\epsilon_2$ and the angle of incidence of the light. Furthermore, the positions and widths of the enhanced backscattering and satellite peaks are discussed. It is found that these peaks become narrower and higher when the amplification of the system is increased, and that their widths scale linearly with $\epsilon_2$. The positions of the backscattering peaks are found to be independent of $\epsilon_2$, while we find a weak dependence on this quantity in the positions of the satellite peaks.Comment: Revtex, 9 pages, 9 figure

Theory for the photon statistics of random lasers

A theory for the photon statistics of a random laser is presented. Noise is described by Langevin operators, where both fluctuations of the electromagnetic field and of the medium are included. The theory is valid for all lasers with small outcoupling when the laser cavity is large compared to the wavelength of the radiation. The theory is applied to a chaotic laser cavity with a small opening. It is known that a large number of modes can be above threshold simultaneously in such a cavity. It is shown the amount of fluctuations is increased compared to the Poissonian value by an amount that depends on that number

Activated Transport in the individual Layers that form the νT\nu_T=1 Exciton Condensate

We observe the total filling factor $\nu_{T}$=1 quantum Hall state in a bilayer two-dimensional electron system with virtually no tunnelling. We find thermally activated transport in the balanced system with a monotonic increase of the activation energy with decreasing $d/\ell_B$ below 1.65. In the imbalanced system we find activated transport in each of the layers separately, yet the activation energies show a striking asymmetry around the balance point. This implies that the gap to charge-excitations in the {\em individual} layers is substantially different for positive and negative imbalance.Comment: 4 pages. 4 figure

Time Dependent Theory for Random Lasers

A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field pattern and the spectra of localized lasing modes inside the system. A critical pumping rate $P_{r}^{c}$ exists for the appearance of the lasing peaks. The number of lasing modes increase with the pumping rate and the length of the system. There is a lasing mode repulsion. This property leads to a saturation of the number of modes for a given size system and a relation between the localization length $\xi$ and average mode length $L_m$.Comment: 8 pages. Send to PR

Super-reflection of light from a random amplifying medium with disorder in the complex refractive index : Statistics of fluctuations

The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with {\it cross-correlated} spatial disorder in the real and the imaginary parts of the refractive index is derived using the method of invariant imbedding. The statistics of fluctuations have been obtained for both the correlated telegraph noise and the Gaussian white-noise models for the disorder. In both cases, an enhanced backscattering (super-reflection with reflection coefficient greater than unity) results because of coherent feedback due to Anderson localization and coherent amplification in the medium. The results show that the effect of randomness in the imaginary part of the refractive index on localization and super-reflection is qualitatively different.Comment: RevTex 6 pages, 3 figures in ps file

Statistical regimes of random laser fluctuations

Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations depending on external control parameters. In the Levy regime, the output pulse is highly irregular leading to huge deviations from a mean--field description. Monte Carlo simulations of a simplified model which includes the population of the medium, demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.Comment: Revised version, resubmitted to Physical Review

Determination of the diffusion constant using phase-sensitive measurements

We apply a pulsed-light interferometer to measure both the intensity and the phase of light that is transmitted through a strongly scattering disordered material. From a single set of measurements we obtain the time-resolved intensity, frequency correlations and statistical phase information simultaneously. We compare several independent techniques of measuring the diffusion constant for diffuse propagation of light. By comparing these independent measurements, we obtain experimental proof of the consistency of the diffusion model and corroborate phase statistics theory.Comment: 9 pages, 8 figures, submitted to Phys. Rev.

Random Resonators and Prelocalized Modes in Disordered Dielectric Films

Areal density of disorder-induced resonators with a high quality factor, $Q\gg 1$, in a film with fluctuating refraction index is calculated theoretically. We demonstrate that for a given $kl>1$, where $k$ is the light wave vector, and $l$ is the transport mean free path, when {\em on average} the light propagation is diffusive, the likelihood for finding a random resonator increases dramatically with increasing the correlation radius of the disorder. Parameters of {\em most probable} resonators as functions of $Q$ and $kl$ are found.Comment: 6 pages including 2 figure