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Physical review. B, Condensed matter

Stochastic wave growth in scattering media

Peter A. Robinson

Published May 1, 1997• 6 citations
Publisher

Abstract

Stochastic growth of waves is studied in a scattering medium in which the wave propagation is diffusive. This analysis generalizes previous work on randomly growing waves in nonscattering media and on constant growth in scattering media. New results are obtained for the stochastic laser threshold, the distribution of photons in the medium, the impulse response of the medium, and the transmission and reflection coefficients of a slab of random amplifying medium.

DOI
10.1103/physrevb.55.12175

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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Oct 1, 1996•457 citations
Stochastic growth of waves is studied in a scattering medium in which the wave propagation is diffusive. This analysis generalizes previous work on randomly growing waves in nonscattering media and on constant growth in scattering media. New results are obtained for the stochastic laser threshold, the distribution of photons in the medium, the impulse response of the medium, and the transmission and reflection coefficients of a slab of random amplifying medium.
We demonstrate enhanced wavelike character of diffuse photon density waves (DPDW) in an amplifying random medium. The amplifying nature makes it necessary to choose the wave solution that grows inside the amplifying medium, and has a propagation vector pointing opposite to the growth direction. This results in negative refraction of the DPDW at an absorbing-amplifying random medium interface as well as the possibility of supporting ``anti''-surface-like modes at the interface. A slab of an amplifying random medium sandwiched between two absorbing random media supports waveguide resonances that can be utilized to extend the imaging capabilities of DPDW.
Enhancing light transmission through scattering media is of much interest in many fields. Here, numerical simulations are performed to study the impact of gain on the value of reflection of the minimum reflection channel in a random medium. Surprisingly, in some random configurations, the reflection falls when gain is added even through the intensity inside the medium presumably increases once gain is introduced. This unexpected behavior is explained based on a decomposition of quasinormal modes.
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.
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.
Amplification in random media is investigated from the perspective of diffuse photon density waves (DPDWs). These exponentially decaying waves, typical in absorbing media, exhibit significantly enhanced propagation characteristics in random amplifying media. Consequently, finite amplifying regions, embedded in an absorbing random medium, exhibit specific resonant features governed by the geometry of the amplifying region. For a spheroidal amplifying region, the scattered waves are dominated by the characteristic multipolar resonances, and the monopolar as well as the dipolar resonances are closely related to random lasing thresholds. The levels of amplification at which the resonance (or lasing) occurs can be used to identify the size, shape, and orientation of the amplifying region. These resonant modes are quite robust and survive, even as the modulation frequency of the DPDW is varied from about 100 MHz to zero, thereby indicating a deeper connection between random lasing path distributions and the appropriate gain profiles resulting in the associated intensity distribution of the DPDW modes.
In this paper we present calculations on light diffusion with amplification that can explain previous experiments on the spontaneous emission from such a medium. Also we discuss the experimental considerations on realizing a medium that both multiply scatters and amplifies light. In an amplifying random medium different processes can occur. We argue that one can distinguish three regimes depending on the amount of scattering, and discuss these regimes in the context of random laser action. \textcopyright{} 1996 The American Physical Society.