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AIP conference proceedings

Estimation of first-passage lengths and Levy exponents in nanophotonic amplifying random media

Ravitej Uppu, Sushil A. Mujumdar

Published Jan 1, 2012• 0 citations
Publisher

Abstract

We estimate the parameters of intensity fluctuations in amplifying nanophotonic random media, based on analytical and numerical methods. The statistics of such media belong to the Levy domain due to underlying power-law distributions. The power-law exponent is determined by the gain length and the mean first-passage length of the photon in the system. We employ a Monte-Carlo simulation to accurately estimate the excitation region of the medium, which yields the gain length and the geometric features of this region. The aspect ratio of this pumped region allows to further analytically calculate the mean first-passage length of a photon diffusing out of the amplifying region. Our calculations are in excellent agreement with experimental trends regarding the Gaussian to Levy transition.

DOI
10.1063/1.4750104

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The statistical behavior of spectral intensity fluctuations in a Raman gain random fiber laser is investigated for the first time, to the best of our knowledge. Through a fiber Fabry–Perot tunable filter, the intensity of the filtered single wavelength from random laser (RL) spectra is measured at different pump powers. The probability density function (PDF) of spectral intensity values is analyzed. Well below the lasing threshold, the intensity of a single wavelength is stable in the time domain, and the PDF exhibits a typical Gaussian behavior. However, around the threshold, strong fluctuations in intensity emerge. In this case, the statistical distribution is characterized by a power-law-tailed function consistent with a Lévy α-stable distribution. We identify the statistical evolution as the injected pump power increases, from a Gaussian to a Lévy and then back to a Gaussian distribution, which is similar to the case of RLs with a strong disorder due to the presence of photon scatterers and gain related to electronic transitions in the active medium, indicating the universal existence of such statistical properties in random lasing systems.
We report the studies of emission from a novel random amplifying medium that we term a ``Levy Laser'' due to the non-Gaussian statistical nature of its emission over the ensemble of random realizations. It is observed that the amplification is dominated by certain improbable events that are ``larger than rare'', which give the intensity statistics a Levy like ``fat tail''. This, to the best of our knowledge, provides the first experimental realization of Levy flight in optics in a random amplifying medium.
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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.
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.