Andreas Lubatsch

Theory of strong localization effects of light in disordered loss or gain media

We present a systematical theory for the interplay of strong localization effects and absorption or gain of classical waves in three-dimensional, disordered dielectrics. The theory is based on the self-consistent Cooperon resummation, implementing the effects of energy conservation and its absorptive or emissive corrections by an exact, generalized Ward identity. Substantial renormalizations are found, depending on whether the absorption or gain occurs in the scatterers or in the background medium. We find a finite, gain-induced correlation volume which may be significantly smaller than the scale set by the scattering mean-free path, even if there are no truly localized modes. Possible consequences for coherent feedback in random lasers as well as the possibility of oscillatory in time behavior induced by sufficiently strong gain are discussed.

Theory of light diffusion in disordered media with linear absorption or gain

We present a detailed, microscopic transport theory for light in strongly scattering disordered systems whose constituent materials exhibit linear absorption or gain. Starting from Maxwells equations, we derive general expressions for transport quantities such as energy transport velocity, transport mean free path, diffusion coefficient, and absorption/gain length. The approach is based on a fully vectorial treatment of the generalized kinetic equation and utilizes an exact Ward identity (WI). While for loss- and gainless media the WI reflects local energy conservation, the effects of absorption or coherent gain are implemented exactly by novel, additional terms in the WI. As a result of resonant (Mie) scattering from the individual scatterers, all transport quantities acquire strong, frequency-dependent renormalizations, which are, in addition, characteristically modified by absorption or gain. We illustrate the influence of various experimentally accessible parameters on these quanitities for dilute systems. The transport theory presented here may set the stage for a theory of Random Lasing in three-dimensional disordered media.

Inelastic scattering puts in question recent claims of Anderson localization of light

The interplay between nonlinear effects and Anderson localization in disordered optical fibres1 has recently attracted great interest, and it is important in the action of random lasers in which closed multiple scattering loops have enhanced intensity. As optical nonlinearities in TiO2 can give valuable information on the nature of light transport in strongly scattering powders, we studied these effects in an extended experimental and theoretical investigation (to be published). Now, Scheffold and Wiersma have ...

Coherent transport and symmetry breaking?laser dynamics of constrained granular matter

We present diagrammatic transport theory including self-consistent nonlinear enhancement and dissipation in the multiple scattering regime. Our model of Vollhardt–Wolfle transport of photons is fit-parameter-free and raises the claim that the results hold up to the closest packed volume of randomly arranged ZnO Mie scatterers. We find that a symmetry breaking caused by dissipative effects through the lossy underlying silicon (SI) substrate leads to qualitatively different physics of coherence and lasing in granular amplifying media. According to our results, confined and extended random laser modes and their laser thresholds can be clearly attributed to unbroken and broken spatial symmetry. The diameters and emission profiles of the modes, as well as their thresholds and the positional-dependent degree of coherence, can be checked experimentally.

Light Propagation in Anisotropic Disordered Media

We present a semi‐analytical theory for light propagation in three dimensional, strongly scattering, disordered, anisotropic dielectrics. The anisotropy of the system is incorporated by a tensor dielectric function. By starting at Maxwell’s equations, we derive a general transport theory for light including transport quantities such as energy transport velocity, transport mean free path and diffusion coefficient. This approach is based on a fully vectorial treatment of the generalized kinetic equation and also incorporated a generalized Ward identity for these systems. Furthermore, self‐interference contributions to the transport are included by means of a generalized localization theory based on a cooperon resummation first derived for electrons by Vollhardt and Wolfie [1]. Numerical evaluations will be presented.

Theoretical Approach to Random Lasing in thin Systems on reflecting Substrates

We develop a theory for random laser systems especially for different experimentally relevant setups [1]. A systematical semi‐analytical transport theory for amplifying random media is presented. The optical gain is described self‐consistently by coupling the transport theory to the semiclassical rate equations and solving this system. In order to stabilize a stationary lasing mode, we include necessarily a loss of photons through the surface of the sample. In experiments [1, 2] the disordered laser active material is placed on a substrate and then optically pumped. The free surface on the one side of the sample and the substrate on the other side of the sample yield different conditions for the lasing mode, which we include by considering asymmetric boundary conditions by means of loss through the free surface and reflection on the substrate side, respectively. We calculate all relevant quantities such as the mean photon number and the correlation length for these systems, and compare these results with ...

Tuning the Quantum Efficiency of Random Lasers - Intrinsic Stokes-Shift and Gain

We report the theoretical analysis for tuning the quantum efficiency of solid state random lasers. Vollhardt-Wölfle theory of photonic transport in disordered non-conserving and open random media, is coupled to lasing dynamics and solved positionally dependent. The interplay of non-linearity and homogeneous non-radiative frequency conversion by means of a Stokes-shift leads to a reduction of the quantum efficiency of the random laser. At the threshold a strong decrease of the spot-size in the stationary state is found due to the increase of non-radiative losses. The coherently emitted photon number per unit of modal surface is also strongly reduced. This result allows for the conclusion that Stokes-shifts are not sufficient to explain confined and extended mode regimes.

Bi-functional nonlinearities in monodisperse ZnO nano-grains – Self-consistent transport and random lasing

We report a quantum field theoretical description of light transport and random lasing. The Bethe-Salpeter equation is solved including maximally crossed diagrams and non-elastic scattering. This is the first theoretical framework that combines so called off-shell scattering and lasing in random media. We present results for the self-consistent scattering mean free path that varies over the width of the sample. Further we discuss the density dependent correlation length of self-consistent transport in disordered media composed of semi-conductor Mie scatterers.

Random lasing in disordered arrays of ZnO nanorods

A diffusive theory of random lasing is derived for finite systems comprised of disordered arrays of laser active ZnO nanopillars. The diffusive transport of the light intensity is coupled to the semiclassical laser rate equations, therefore incorporating nonlinear optical gain in this effectively two dimensional system. We solve the resulting boundary condition problem to obtain the full spatial intensity profile of lasing spots in dependence of the pumprate and other system parameters. Our theory predicts two different types of random laser modes in effectively two dimensional systems in general. A surface mode with a large size extending over the entire sample width, and a bulk mode, with small laser spot sizes. We discuss their origin and characteristics.

Selfconsistent Theory for Random Lasers in Disordered 3-D Media of Finite Size

We develop a semianalytical theory for random lasers. Within this nonlinear self-consistent approach we combine a diagrammatic transport-theory with semiclassical laser-rate-equations. Optical gain is calculated self-consistently, boundary conditions and spatially varying pump strength are respected.