The spatial and spectral evolution of emission from gain media with homogeneously distributed scatterers is modeled using a Monte Carlo simulation of the random walk of pump and emitted photons. We find a sharp transition to ultrafast, narrow-linewidth emission for a 10-ps incident pump pulse and a rapid approach to steady state for longer pulses. The threshold for this transition is raised significantly when the transverse diffusion of photons out of the excited region is substantial. The quantitative agreement of the results with recent observations of emission from random gain media lends further support to the interpretation of ``random lasers'' in terms of amplified spontaneous emission within a multiply-scattering medium.
The spatial and spectral evolution of emission from gain media with homogeneously distributed scatterers is modeled using a Monte Carlo simulation of the random walk of pump and emitted photons. We find a sharp transition to ultrafast, narrow-linewidth emission for a 10-ps incident pump pulse and a rapid approach to steady state for longer pulses. The threshold for this transition is raised significantly when the transverse diffusion of photons out of the excited region is substantial. The quantitative agreement of the results with recent observations of emission from random gain media lends further support to the interpretation of ``random lasers'' in terms of amplified spontaneous emission within a multiply-scattering medium.
We simulate the transition from amplified spontaneous emission (ASE) to lasing in random systems with varying degrees of mode overlap. This is accomplished by solving the stochastic Maxwell-Bloch equations with the finite-difference time-domain method. Below lasing threshold, the continuous emission spectra are narrowed by frequency-dependent amplification. Our simulations reproduce the stochastic emission spikes in the spectra. Well-defined peaks, corresponding to the system resonances, emerge at higher pumping and are narrowed by stimulated emission before lasing takes place. Noise tends to distribute pump energy over many modes, resulting in multimode operation. Well above the lasing threshold, the effects of noise lessen and results become similar to those without noise. By comparing systems of different scattering strength, we find that weaker scattering extends the transition region from ASE to lasing, where the effects of noise are most significant.
We study the dynamics of lasing from photonic paints excited by short, localized, optical pulses, using a time-dependent diffusion model for light propagating in the medium containing active atoms. The full time-dependent, nonadiabatic nonlinear response of the atomic system to the local optical field intensity is described using the Einstein rate equations for absorption and emission of light. Solving the time-dependent diffusion equation for the light intensity in the medium with nonlinear gain and loss, we derive detailed information on the spectral, spatial, and temporal properties of the emitted laser light. Our model recaptures the effects of scatterers to narrow the emission spectral linewidth and to narrow the emitted pulse duration, at a specific threshold pump intensity. Our model also describes how this threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results.
In two recent works, the authors have investigated the spectro-temporal properties of the random laser emission from solid state dye-doped powders in picosecond pumping regime. Each emission pulse consists, both above and below threshold, in a collection of narrow peaks of a spectro-temporal width at the theoretical limit (ΔωΔt≅1). The distribution of path lengths traveled inside the diffusive active medium by photons that can be amplified by stimulated emission explains this behavior, as demonstrated by a simple theoretical model developed by the authors. The aim of the present work is, first, to develop an implemented model that does not depend on fitting parameters, and which is compatible with the energetic and spectro-temporal properties of the material; and second, to get knowledge about the spatial properties of the emission. The transverse coherence size of each emitted photon packet has been measured; and in addition, we have shown the existence of spatial fluctuations of the emission of these materials, as our model predicts.
The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to constrain light propagation by L\'evy walks, i.e., with a ``heavy-tailed'' distribution of steps, has opened the opportunity to investigate the behavior of a superdiffusive optical gain medium that can lead to a ``superdiffusive random laser.'' Here, we present a theoretical investigation, based on Monte Carlo simulations, on such a kind of medium, focusing on the widespread presence of fluctuation regimes, that, in contrast to a diffusive random laser, appears very hard to switch off by changing the gain and scattering strength. Hence, the superdiffusion appears as a condition that increases the value of the threshold energy and promotes the presence of fluctuations in the emission spectrum.
In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.
We investigated random scattering of light in a disorder gain medium of ZnO powder using the pump-probe technique. Using a probe beam at (lambda) =390nm, the width ((theta) ) of the coherent backscattering peak from the ZnO powder is measured to be ~7.5 degree(s), thus the coherent scattering length l is approximately 1.2(lambda) ((theta) =(lambda) /2(pi) l) which is close to the strong scattering regime. When a pump beam ((lambda) =267nm) exceeds a certain excitation threshold, supernarrow emission peaks (bandwidth less than 1nm) emerged from the ZnO broad photoluminescence background. Concurrently, we also observed enhancement and sharpening of the coherent backscattering cone. Since light from the center of the backscatter cone experience the largest number of scatterings (i.e. longest gain length), this result is thus consistent with the random laser model that the supernarrow peak is due to amplification and stimulated emission of photon in the random gain medium. The time-resolved pump-probe measurement shows that the lifetime of the emission state above the lasing threshold is only a few picoseconds which is consistent with the interpretation that the supernarrow peaks are due to stimulated emission.