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Physical Review Letters

Random Laser in One Dimension

Alexander L. Burin, Mark A. Ratner, Hui Cao, Shih‐Hui Chang

Published Feb 14, 2002• 79 citations
Publisher

Abstract

We present an analytical approach to random lasing in a one-dimensional medium, consistent with transfer matrix numerical simulations. It is demonstrated that the lasing threshold is defined by transmission through the passive medium and thus depends exponentially on the size of the system. Lasing in the most efficient regime of strong three-dimensional localization of light is discussed. We argue that the lasing threshold should have anomalously strong fluctuations from probe to probe, in agreement with recent measurements.

DOI
10.1103/physrevlett.88.093904

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We investigated several types of random lasing modes against frequency and the excitation of active medium. Random lasing occurring from multiple light scatterings and the interference effect of the scattered light has various complex lasing states in disordered structures, in which light waves are localized in various forms. Modes of random lasing are generally classified into localized, extended and transition modes based on their localization types. Numerical methods are used for analysing such complex phenomena. In this paper, a finite-element method is used to investigate the relationship among lasing modes, frequency and population inversion density of active medium for random lasing. Light amplification defined as the ratio of radiative powers between excited and non-excited states of the active medium is computed by changing both the frequency and the population inversion density of the active medium, which is modelled by the negative imaginary part of relative permittivity. The distributions of random lasing modes is strongly influenced by the lasing frequency. We also found that the localized modes that are strongly confined lasing modes in disordered structures do not appear in the frequency ranges in which mean free paths are approximately equal to the half-wavelength.
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We theoretically study reflection and transmission of light in a one-dimensional disordered phase-conjugating medium. Using an invariant imbedding approach a Fokker-Planck equation for the distribution of the probe light reflectance and expressions for the average probabilities of reflection and transmission are derived. A new crossover length scale for localization of light is found, which depends on the competition between phase conjugation and disorder. For weak disorder, our analytical results are in good agreement with numerical simulations.
We address the problem of achieving an optical random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. The lasing threshold can be defined using the on-resonance optical thickness b0 as a single critical parameter. We predict the threshold quantitatively, as well as power and frequency of the emitted light, using two different light transport models and the atomic polarizability of a strongly pumped two-level atom. We find a critical b0 on the order of 300, which is within reach of state-of-the-art cold-atom experiments. Interestingly, we find that random lasing can already occur in a regime of relatively low scattering.