Statistical Properties of One-Dimensional Random Lasers

Zaitsev, Oleg; Shuvayev, Vladimir

doi:10.1103/physrevlett.102.043906

Cited by 20 publications

(25 citation statements)

References 17 publications

(34 reference statements)

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“…Both these methods reduce noticeably the lasing threshold as compared to 3D random lasing systems. Because the frequencies of the modes and the locations of the effective cavities vary from sample to sample randomly, in the most cases they are described statistically [20][21][22][23][24] . However, usually we deal with a specific random sample, and it is important to know how many modes and at which frequencies can be excited in a given frequency range; where these modes are localized inside this sample, etc 11 .…”

Section: B Random Lasersmentioning

confidence: 99%

Disorder-induced cavities, resonances, and lasing in randomly layered media

et al. 2012

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We study, theoretically and experimentally, disorder-induced resonances in randomly-layered samples,and develop an algorithm for the detection and characterization of the effective cavities that give rise to these resonances. This algorithm enables us to find the eigen-frequencies and pinpoint the locations of the resonant cavities that appear in individual realizations of random samples, for arbitrary distributions of the widths and refractive indices of the layers. Each cavity is formed in a region whose size is a few localization lengths. Its eigen-frequency is independent of the location inside the sample, and does not change if the total length of the sample is increased by, for example, adding more scatterers on the sides. We show that the total number of cavities, Ncav, and resonances, Nres, per unit frequency interval is uniquely determined by the size of the disordered system and is independent of the strength of the disorder. In an active, amplifying medium, part of the cavities may host lasing modes whose number is less than Nres. The ensemble of lasing cavities behaves as distributed feedback lasers, provided that the gain of the medium exceeds the lasing threshold, which is specific for each cavity. We present the results of experiments carried out with single-mode optical fibers with gain and randomly-located resonant Bragg reflectors (periodic gratings). When the fiber was illuminated by a pumping laser with an intensity high enough to overcome the lasing threshold, the resonances revealed themselves by peaks in the emission spectrum. Our experimental results are in a good agreement with the theory presented here.

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Section: B Random Lasersmentioning

confidence: 99%

Disorder-induced cavities, resonances, and lasing in randomly layered media

et al. 2012

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“…We also analyze separate contributions from three different types of interactions, namely from quadruplets (all four modes are different), triplets (only three of four modes are different) and pairs (only two different modes participate in the interaction). For quadruplets all indices in (21) should be different, i.e. µ 1 = ν, µ 2 = ν, µ 3 = ν, µ 1 = µ 2 , µ 1 = ν, µ 1 = µ 3 , µ 2 = µ 3 .…”

Section: Resonancesmentioning

confidence: 99%

Statistics of wave interactions in nonlinear disordered systems

Krimer

Flach

2010

Phys. Rev. E

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We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on (i) the localization volume of a mode which defines the number of interacting partner modes, (ii) the overlap integrals which determine the interaction strength, (iii) the average spacing between eigenvalues of interacting modes, which sets a scale for the nonlinearity strength, and (iv) resonance probabilities of interacting modes. Our results are discussed in the light of recent studies on spreading of wave packets in disordered nonlinear systems and are related to the quantum many-body problem in a random chain.

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“…This mechanism is of pure statistical origin and does not require localization or interference [17]. It was also proposed that such systems can exhibit Lévy-type statistics in the distribution of intensities [18][19][20], and crossovers among different statistics have been predicted [21].…”

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confidence: 98%

Fluctuations in a Diffusive Medium with Gain

Lepri

2013

Phys. Rev. Lett.

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We present a stochastic model for amplifying, diffusive media such as, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field which contains a multiplicative random-advection term yielding intermittency and power-law distributions of the field itself. A dimensional analysis indicates that such features are more likely to be observed for small enough samples and in lower spatial dimensions.

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Statistical Properties of One-Dimensional Random Lasers

Cited by 20 publications

References 17 publications

Disorder-induced cavities, resonances, and lasing in randomly layered media

Disorder-induced cavities, resonances, and lasing in randomly layered media

Statistics of wave interactions in nonlinear disordered systems

Fluctuations in a Diffusive Medium with Gain

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