PHYSICAL REVIEW E 83, 041711 (2011) Blue-shifted random-laser-mode selection in gain-assisted anisotropic complex fluids Alessandro Veltri, 1,2,* Melissa Infusino, 1 Sameh Ferjani, 1,3 Antonio De Luca, 1 and Giuseppe Strangi 1 1 LICRYL (Liquid Crystal Laboratory), National Institute for the Physics of Matter (INFM-CNR), Center of Excellence CEMIF.CAL and Department of Physics, University of Calabria, I-87036 Arcavacata di Rende (CS), Italy 2 Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115 Avenue du Dr Schweitzer, F-33600 Pessac, France 3 Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079, USA (Received 24 June 2009; revised manuscript received 7 February 2011; published 29 April 2011; corrected 3 May 2011) Random laser action in organic materials is of great topical interest that is fueled by the rapid development of active compounds and new dye molecules. We propose a pure-diffusive model to describe the strong connection established between a dye-host interaction and the scattering when considering an anisotropic complex fluid. The model considers multiple scattering induced by dielectric tensor fluctuations and a suitable quantistic description for light amplification in order to explain the generation of the narrow-band blue-shifted lasing mode experimentally observed in such systems. We also find that the introduction of a strong intermolecular force field provides the condition to enhance diffusive processes. The agreement between experimental observations and simulations advances the understanding of the physical mechanism behind mode selection in these systems. DOI: 10.1103/PhysRevE.83.041711 PACS number(s): 42.70.Df, 42.25.Dd, 07.05.Tp, 42.55.Zz I. INTRODUCTION The diffusive transport of light waves in complex dielectric structures has spurred wide interest in the past decade and has become a particularly challenging and exciting scientific subject. As suggested by Letokhov in 1968 [1], diffusive processes inside active media can realize a mechanism of mode selection. Actually, the interference of light in random dielectric systems influences the transport of light in a way that is similar to the interference that occurs for electrons when they propagate in disordered conducting materials (Anderson localization [2–5]). The interplay between the localization of light and amplification can thus lead to so-called random laser action. The occurrence of laser action in random isotropic media has been observed in the last 20 years in a number of different physical systems. (The first demonstration was given in 1986 [6].) For the mechanism of mode selection through localization to be effective, it is required that kℓ t  1, k being the light wave vector and ℓ t the transport mean free path, i.e., the length over which light loses its coherence due to random collisions. The transport mean free path ℓ t can be expressed as [7] ℓ t = ℓ s 1 −〈cos θ 〉 , (1) where ℓ s is the mean free path, i.e., the average distance between two light scattering events, θ is the angle of deflection of light in a scattering event, and the brackets represent an average over a large number of scattering events. Recently it was observed that under suitable optical excita- tion an anisotropic gain-assisted material such as a dye-doped liquid crystal is able to generate amplified stimulated emission characterized by a spatial intermittent speckle-like pattern of granular aspect and a spectral blue shift of the main peak [8–11]. These experimental evidences pose some important theoretical problems: indeed, in these media the diffusion is characterized by small deflection angles [12,13], so from * alessandro.veltri@fis.unical.it; veltri@crpp-bordeaux.cnrs.fr Eq. (1) ℓ t turns out to be much larger than ℓ s and this gives rise to a very strict condition for wave interference, i.e., ℓ s ≪ λ (where λ is the light wavelength). On the other hand, in an anisotropic liquid crystal, ℓ s is larger for visible light by many orders of magnitude than the wavelength [12]. As a consequence any mode selection picture that needs to invoke a strong localization mechanism can hardly be justified. Even when ℓ s ≪ λ is not satisfied in the presence of multiple scattering, a mode selection can still be invoked associated to the interference of two light beams counterpropagating on the same closed path (weak localization of light [14,15]). In any case, when the mode selection is related to randomly generated interference mechanisms, we expect the emitted laser spectra to be characterized by many thin peaks changing position from one pump pulse to the other [7]. When dealing with a single spectral peak emission, a laser mechanism based only on incoherent light intensity amplification could be invoked; in such a case, however, the peak in the spectrum is generally found in correspondence with the maximum of the fluorescence spectrum obtained for lower values of the pump intensity. On the contrary, just above some threshold of pump power, the amplified stimulated emission measured in the anisotropic media under consideration displays a single peak spectrum whose position is blue shifted with respect to the maximum of the fluorescence curve, whereas the typical peak distribution of the randomly generated interference mechanisms appears only at higher values of the pump intensity. The above considerations as well as the peculiar depen- dence of the mean free path on the light wavelength (ℓ s is proportional to λ 2 [12]) prompted us to consider and analyze a different mechanism of frequency selection. This mechanism does not require any light coherence and works as soon as the mean free path is sufficiently smaller than the typical dimension D of the scattering region: ℓ s ≪ D. (2) It is worth noting that the verification of this hypothesis furnishes a way to predict a priori which will be the more 041711-1 1539-3755/2011/83(4)/041711(6) ©2011 American Physical Society