Path-length dependent flux from random walk theory

Calculation of the flux Ψ(R, s) due to a point isotropic source in an infinite medium, as a function of the distance R and actual pathlength s is treated as a random walk problem. In the case of isotropic scattering, this method is shown to lead to a standard transport-theoretical result, for the integrated flux. However, for Ψ(R, s) far from the source, the random walk theory predicts a modified maxwellian form.     

Time dependent canonical perturbation theory I: General theory

In this communication, we reanalyze the causes of the singularities of canonical perturbation theory and show that some of these singularities can be removed by using time-dependent canonical perturbation theory. A study of the local and global properties (in terms of the perturbation parameter) is also undertaken.     

Correlations for parameter— dependent random matrices

Correlations for parameter-dependent Gaussian random matrices, intermediate between symmetric and Hermitian and antisymmetric Hermitian and Hermitian, are calculated. The (dynamical) density-density correlation between eigenvalues at different values of the parameter is calculated for the symmetric to Hermitian transition and the scaledN→∞ limit is computed. For the antisymmetric Hermitian to Hermitian transition the equal-parametern-point distribution function is calculated and the scaled limit computed. A circular version of the antisymmetric Hermitian to Hermitian transition is formulated. In the thermodynamic limit the equal-parameter distribution function is shown to coincide with the scaled-limit expression of this distribution for the Gaussian antisymmetric Hermitian to Hermitian transition. Furthermore, the thermodynamic limit of the corresponding density-density correlation is computed. The results for the correlations are illustrated by comparison with empirical correlations calculated from numerical data obtained from computer-generated Gaussian random matrices.     

Two-photon pumping of random lasers by picosecond and nanosecond lasers

We experimentally demonstrated two-photon pumping of random lasers using picosecond and nanosecond pump lasers. The picosecond laser pumping experiment was performed with 400 ps laser pulses at 770 nm, and the gain media was a Coumarin 480D dye solution doped with TiO₂ nanoparticles. Onset of laser action was observed at a pump laser pulse energy below 500 μJ. The nanosecond laser pumping experiment was performed with 7 ns laser pulses at 1064 nm, and the gain media was a Rhodamine 640 dye solution doped with TiO₂ nanoparticles. Onset of laser action was observed at a pump laser energy ∼18 mJ. Our results suggest that there exists an optimal pulse duration of the pumping laser in two-photon pumped random lasing that leads to minimum photodamage of the gain media and still keeps a high pumping efficiency. PACS 33.50.Dq; 42.55.Mv; 42.55.Zz     

Time dependent canonical perturbation theory II: Application to the Henon-Heiles system

In this communication, we report the results of the application of time-dependent perturbation theory to the Henon-Heiles system. We show that the predictions of the perturbation theory hold good for short times, and try to explain the increase of error in the predicted results with the increase in energy.     

Amplified extended modes in random lasers

We report on a new random laser phenomenon that gives rise to narrow emission modes without requiring optical cavities. Sharp emission peaks are observed experimentally over a broad range of scattering strengths and analyzed in numerical calculations. We find that the introduction of exponential gain in a multiple light scattering process strongly increases the importance of very long light paths. Such long paths are rare and often neglected in passive disordered materials but we show that they can dominate the emission spectrum from an amplifying disordered system.     

Time varyingM 2 inQ-switched lasers

Numerical simulations of the pulse build up in aQ-switched laser reveal a considerable change in the beam spatial profile during the pulse evolution, on a nanosecond time scale. Such changes were measured experimentally, and the measured temporal evolution of the beam profile is shown to be in good agreement with the theoretical results. The time evolution of the spatial profile translates into an evolution of the beam quality parameterM ²; for typical experimental conditions, in a Nd:YAG laser utilizing a variable-reflectivity mirror resonator,M ² is very close to a value of 1 at the beginning of the pulse, and increases smoothly throughout the pulse to reach a value of approximately 2 at the pulse trailing edge.     

Unification of perturbation theory, random matrix theory, and semiclassical considerations in the study of parametrically dependent eigenstates

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where x is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where x controls a deformation of the boundary or the position of a "piston." The quantum eigenstates of the system are |n(x)>. We describe how the parametric kernel P(nmid R:m) = ||(2) evolves as a function of deltax = x-x(0). We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.     

Quantum theory of dye lasers

A quantum model of dye laser is given. To account for triplet losses a six levels model for the molecular system is assumed. The solution of generalized von Neumann equation in thermodynamical limit leads to a system of kinetic equations. Stationary solutions of this system are discussed. There are two distinct types of dependence of photon number versus pumping parameter. Beside a usual one, a new dependence characteristic for dye lasers only is present. In this case the definition of threshold should be revised.     

Single-site theory for the random Hubbard alloy

A new theory for the random system with electron correlation is presented, which is an extension of the Hubbard's theory for the random system and also an extension of the CPA for the interacting electron system. The equation of motion for the Green function is solved by the same decoupling method used by Hubbard. The self-consistent relations for the Green function, the self-energy and the effective occupation number are derived. It is predicted in the binary alloy system that tails or satellites of the state density are produced by the combined effect of the randomness and electron correlation. The origin of the tail is the inelastic scattering of the electron byA — B atomic pairs, whose electronic configuration is changed during the scattering. Numerical calculations are reported for a simple model.     

Inverse spectral theory for random Jacobi matrices

We give necessary and sufficient conditions for a Herglotz function to be thew-function of a random stationary Jacobi matrix.This paper is dedicated to the memory of Mark Kac.     

Photon statistics of random lasers with resonant feedback

We have measured the photon statistics of random lasers with resonant feedback. With an increase of the pump intensity, the photon number distribution in a single mode changes continuously from Bose-Einstein distribution at the threshold to Poisson distribution well above the threshold. The second-order correlation coefficient drops gradually from 2 to 1. By comparing the photon statistics of a random laser with resonant feedback and that of a random laser with nonresonant feedback, we illustrate very different lasing mechanisms for the two types of random lasers.     

Time dependent Ginzburg-Landau equations for strong coupling superconductors

We derive time dependent Ginzburg-Landau equations for strong coupling superconductors. It is shown that due to a certain separability of the order parameter the equation for it’s time dependent fluctuations is again of diffusion type. Strong coupling effects show up only in the numerical coefficients of the diffusion equation. We apply our findings to the problem of electrical resistivity in strong coupling superconducting materials above the transition temperatureT _c.     

Semiclassical theory of three-level gas lasers

We present numerical solutions of the density matrix equations for a three-level gas laser gain medium with a single resonator mode at each of the two transition frequencies. Population pulsations and interference effects between the two transition amplitudes are included. Comparison with solutions obtained neglecting the interference terms shows these effects to be significant in low-pressure lasers at moderate intensities. Population pulsations also change results for resonator modes tuned near line center.