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Journal of Applied Physics

Amplification and diffusion of spontaneous emission in strongly scattering medium

Kouki Totsuka, Gijs van Soest, Tetsu Ito, Ad Lagendijk, Makoto Tomita

Published Jun 1, 2000• 34 citations
Publisher

Abstract

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.

DOI
10.1063/1.373432

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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.
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.
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.
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We report on a medium exhibiting extremely efficient light scattering properties: a liquid network formed in a porous matrix. Liquid fragments confined in the solid matrix result in a random fluctuation of the dielectric function and act as scattering objects for photons. The optical scattering efficiency is defined by the filling factor of the liquid in the pores and its dielectric constant. The spectral dependence of the scattering length of photons indicates that the phenomenon is governed by a Mie-type scattering mechanism. The degree of the dielectric disorder of the medium, i.e. the level of opacity is tunable by the ambient vapor pressure of the dielectric substance. In the strongest scattering regime the scattering length of photons is found to be in the micrometer range. By incorporation of dye molecules in the voids of the porous layer a system exhibiting optical gain is realized. In the multiple scattering regime the optical path of diffusively propagating photons is enhanced and light amplification through stimulated emission occurs: a strong intensity enhancement of the dye emission accompanied by significant spectral narrowing is observed above the excitation threshold for a layer being in the opalescence state.
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.
We report on a medium exhibiting extremely efficient light scattering properties: a liquid network formed in a porous matrix. Liquid fragments confined in the solid matrix result in a random fluctuation of the dielectric function and act as scattering objects for photons. The optical scattering efficiency is defined by the filling factor of the liquid in the pores and its dielectric constant. The spectral dependence of the scattering length of photons indicates that the phenomenon is governed by a Mie-type scattering mechanism. The degree of the dielectric disorder of the medium, i.e. the level of opacity is tunable by the ambient vapor pressure of the dielectric substance. In the strongest scattering regime the scattering length of photons is found to be in the micrometer range. By incorporation of dye molecules in the voids of the porous layer a system exhibiting optical gain is realized. In the multiple scattering regime the optical path of diffusively propagating photons is enhanced and light amplification through stimulated emission occurs: a strong intensity enhancement of the dye emission accompanied by significant spectral narrowing is observed above the excitation threshold for a layer being in the opalescence state. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)