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arXiv:1111.1906

Coherent feedback from dissipation: the lasing mode volume of random lasers

Regine Frank, Andreas Lubatsch, Johann Kroha

Published Nov 8, 2011• 0 citations
arXivHTMLPDF

Abstract

In any quantum or wave system dissipation leads to decoherence. Therefore, it was surprising in first instance when experiments on strongly lossy random lasers showed unambiguously by measurements of the photon statistics and of the lasing mode volume that coherent feedback is possible in such systems3-5,8. In coherent-feedback lasers the photons form a far-from-equilibrium condensate in the sense that a single quantum state is occupied by a macroscopic number of photons15. We demonstrate that the lossy dynamics of random lasers alone imply a three dimensional finite lasing mode extent, thus resolving the puzzle about coherent feedback without resonator. Our theory of random lasing including nonlinear gain and gain saturation predicts a characteristic dependence of this lasing mode volume on the pump intensity, which can be tested experimentally.

DOI
10.48550/arxiv.1111.1906

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In any quantum or wave system dissipation leads to decoherence. Therefore, it was surprising in first instance when experiments on strongly lossy random lasers showed unambiguously by measurements of the photon statistics and of the lasing mode volume that coherent feedback is possible in such systems3-5,8. In coherent-feedback lasers the photons form a far-from-equilibrium condensate in the sense that a single quantum state is occupied by a macroscopic number of photons15. We demonstrate that the lossy dynamics of random lasers alone imply a three dimensional finite lasing mode extent, thus resolving the puzzle about coherent feedback without resonator. Our theory of random lasing including nonlinear gain and gain saturation predicts a characteristic dependence of this lasing mode volume on the pump intensity, which can be tested experimentally.
The spatial formation of coherent random laser modes in strongly scattering disordered random media is a central feature in the understanding of the physics of random lasers. We derive a quantum field theoretical method for random lasing in disordered samples of complex amplifying Mie resonators which is able to provide self-consistently and free of any fit parameter the full set of transport characteristics at and above the laser phase transition. The coherence length and the correlation volume respectively is derived as an experimentally measurable scale of the phase transition at the laser threshold. We find that the process of stimulated emission in extended disordered arrangements of active Mie resonators is ultimately connected to time-reversal symmetric multiple scattering in the sense of photonic transport while the diffusion coefficient is finite. A power law is found for the random laser mode diameters in stationary state with increasing pump intensity.
The dynamics of stimulated emission in random lasers is studied using the system of rate equations for population inversion and density of emitted photons. In order to model the behavior of random lasers with nonresonant feedback, no coherence effects are intentionally taken into account. It has been shown that the feedback in the system is necessary for the realization of the regime of relaxation oscillations and spatial confinement of the stimulated emission to the interior regions of the pumped volume. The model also predicts the possibility of localization of stimulated emission in several spatially separated subvolumes of the random laser medium. Finally, it has been demonstrated that two adjacent random laser volumes can strongly enhance the stimulated emission in each other (the ``critical mass'' effect in random lasers).
The paper puts forward that there are two kinds of light localizations at same time in random laser with coherent feedback: the one is that the recurrent light scattering loop restricts photons in the loop,the another is that the scattering particles restrict photons in the entire gain medium,and on the base,it expatiates the work principle of the random laser with coherent feedback.For the first localization,it puts forward that it is easier to lasing in the loop with less particles,for the second localization,it gets the average life of the laser photon when gain region is cube.On the above base,it explains the new phenomenon which was reported by Sushil Mujumdar et al.
We report the theoretical analysis for tuning the quantum efficiency of solid state random lasers. Vollhardt-Wölfle theory of photonic transport in disordered non-conserving and open random media, is coupled to lasing dynamics and solved positionally dependent. The interplay of non-linearity and homogeneous non-radiative frequency conversion by means of a Stokes-shift leads to a reduction of the quantum efficiency of the random laser. At the threshold a strong decrease of the spot-size in the stationary state is found due to the increase of non-radiative losses. The coherently emitted photon number per unit of modal surface is also strongly reduced. This result allows for the conclusion that Stokes-shifts are not sufficient to explain confined and extended mode regimes.
We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.
A numerical study is presented of random lasers as a function of the pumping rate above the threshold for lasing. Depending on the leakiness of the system resonances, which is typically larger in random lasers compared to conventional lasers, we observe that the stationary lasing regime becomes unstable above a second threshold. Coherent instabilities are observed as self pulsation at a single frequency of the output intensity, population inversion, as well as the atomic polarization. We find these Rabi oscillations have the same frequency everywhere in the random laser despite the fact that the field intensity strongly depends on the spatial location.