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arXiv:1008.3993 · Physical Review A

Numerical study of amplified spontaneous emission and lasing in random media

Jonathan Andreasen, Hui W. Cao

Published Dec 29, 2010• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.82.063835

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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.
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 have studied the quantum-statistical properties of superfluorescence (SF) and amplified spontaneous emission (ASE) for dense media (media of densities corresponding to many atoms, on the average, within a cubic resonance wavelength). We use the Langevin equations of motion, obtained from a fully quantized model that takes into account induced near dipole-dipole interactions associated with dense media, together with the coupled Maxwell equation, to formulate a stochastic calculation ensemble. Quantum Monte Carlo methods are used in conjunction with the stochastic model, to conduct a statistical analysis of phase waves for this system. Results are presented for the phase-wave density, delay time, and peak-intensity fluctuations. The transition from SF to ASE is treated using the stochastic model.
The coupling of forward and backward propagating waves is studied theoretically in the transition region between superfluorescence (SF) and amplified spontaneous emission (ASE). To accomplish this a computer code has been written that solves Maxwell's equations in time and two spatial dimensions and accounts for counter-propagation, diffraction, and temporal coherence in the Bloch equations. Diffraction is ignored in the present calculations. In the SF regime the coupling is generally weak, as found by others; however, I have found a randomly occurring shot-to-shot coupling that is quite significant in cases where one wave, forward or backward, becomes established from quantum noise first in the amplified rod. In this case the wave that arises second is strongly coupled to the first. In the ASE regime the propagation shows strong forward-backward coupling and the characteristic spatial profile of the inversion that tends to zero at either end and to the small signal value of one in the middle of the amplifier. In the transion region the propagation shows mixed SF and ASE behavior.
A model of random laser with semi-classical theory is presented.It couples Maxwell's equations with density matrix of excited atom in a disordered system.So Maxwell-Bloch equations for random laser are obtained.A finite-difference time-domain method is used to solve Maxwell-Bloch equations directly.We studied the pattern of field and localized modes of random laser.A critical pumping rate W~c_p exists for the appearance of the lasing peaks in random system.The number of lasing modes increases with the pumping rate and it is saturated finally.
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.