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Applied Optics

Lasing in active, sub-mean-free path-sized systems with dense, random, weak scatterers

B. Raghavendra Prasad, Hema Ramachandran, Ajay Kumar Sood, Chinnia Subramanian, Narendra Kumar

Published Oct 20, 1997• 39 citations
Publisher

Abstract

We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent with experimentally observed features.

DOI
10.1364/ao.36.007718

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We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent with experimentally observed features.
In several recent experiments, isotropic lasing action was observed in paints that contain rhodamine 640 dye molecules in methanol solution as gain media and titania particles as optical scatterers. These so-called paint-on laser systems are extraordinary because they are highly disordered systems. The microscopic mechanism for laser activity and the coherence properties of light emission in this multiple-light-scattering medium have not yet been elucidated. In this paper we derive the emission intensity properties of a model dye system with excited singlet and triplet electronic energy levels, which is immersed in a multiple-scattering medium with transport mean free path l*. Using physically reasonable estimates for the absorption and emission cross section for the singlet and triplet manifolds, and the singlet-triplet intersystem crossing rate, we solve the nonlinear laser rate equations for the dye molecules. This leads to a diffusion equation for the light intensity in the medium with a nonlinear intensity-dependent gain coefficient. Using this model we are able to account for nearly all of the experimentally observed properties of laser paint reported so far when l*\ensuremath{\gg}${\ensuremath{\lambda}}_{0}$, the emission wavelength. This includes the dependence of the peak intensity of amplified emission on the mean free path l*, the dye concentration \ensuremath{\rho}, and the pump intensity characteristics. Our model recaptures the collapse of the emission linewidth at a specific threshold pump intensity and describes how this threshold intensity varies with l*. In addition, our model predicts a dramatic increase in the peak intensity and a further lowering of the lasing threshold for the strong scattering limit l*\ensuremath{\rightarrow}${\ensuremath{\lambda}}_{0}$. This suggests a striking enhancement of the characteristics of laser paint near the photon localization threshold in a disordered medium. \textcopyright{} 1996 The American Physical Society.
A coherently amplifying medium containing dense random weak scatterers can exhibit mirror-less lasing beyond a threshold of optical pumping even when the active medium has linear dimensions much smaller than the estimated transport mean free path. The threshold pump power decreases with decreasing mean free path. This mirror-less lasing can be understood in terms of the sub-mean free path scatterings which are normally statistically rare, but are now made effective by the coherent amplification that more than offsets their otherwise low probability of occurrence.
Regular and random lasing properties in a multiphoton active and highly scattering dye solution containing polystyrene microspheres of 366-nm diameter have been experimentally studied. Using 100-fs laser pulses of wavelength 790 nm and 1300 nm as the two- and three-photon excitation sources, the frequency-upconversion regular lasing of ~610 nm wavelength can be generated along both the forward and backward directions, characterized by high directionality, higher spectral intensity, and remarkable spectral narrowing. In the meantime, the random lasing can also be observed along all other directions, characterized by only spectral narrowing but with much lower spectral brightness. The spectral brightness ratio between the forward regular lasing and the random lasing is (10410^{4}104-10510^{5}105):1. Comparing to the input pump beam of ~3 mm diameter and divergence angle ofθ0 ≈ 0.9\theta _{0}~\approx ~0.9θ0​ ≈ 0.9mrad, the forward lasing beam size and divergence angle were ~7 mm and ~(3-4)θ0\theta _{0}θ0​, whereas the corresponding parameters were ~5 mm and∼1.5 θ0\sim 1.5~\theta _{0}∼1.5 θ0​for the backward lasing beam, indicating the phase-conjugation property of the latter.
The spectral properties of the emission of a colloidal suspension of titanium dioxide particles in Rhodamine 640 perchlorate were studied systematically. The particle density rho, the dye concentration c, and the energy of the pump pulse were varied over several orders of magnitude; the dependence of the spectra on these three parameters is discussed. We discovered a strong correlation between the particle density and the dye concentration. The amplification by stimulated emission was found to be strongest when the absorption length l(a) and the mean-free-path length l(*) had approximately the same magnitude. The respective l(*) values were determined by a pulsed transmission experiment.
We experimentally examined the threshold of the spectral collapse in dye embedded in a strongly scattering medium as a function of the excitation beam diameter and the transport mean free path in order to find a condition to minimize the threshold. We found a critical transport mean free path, below which the threshold pulse energy is almost independent of the mean free path. Experimental observations are well explained by a theoretical model based on the rate and diffusion equations, which shows that the luminescence spectra are also dependent on the position in the medium.