Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Non Equilibrium Dynamics and ComplexityLight and ComplexityIn a nutshell, a random laser is a disorderedamplifying optical cavity emitting coherent radiation.The system can be realized by artificial nanostructuredoptical devices, or can be a self-organizeddispersion of particles in the multi-scattering regime.In both cases, optical gain can be obtained with theaddition of some active materials, like dyes orquantum dots. Random laser emission is stronglyaffected by the structure and the history of thematerial, hence it is an original and multidisciplinaryapproach for the investigation of soft-matter.Additionally, this kind of lasers strikingly displaysthose ingredients which are typical of the physics ofcomplexity: randomness and nonlinearity.In Refs. [1], it has been shown that theory ofrandom laser can be reformulated as mean field spinglass theory and a series of new physical processes,including for example a “glassy behaviour of light,”have been predicted. Such an approach open newopportunities for testing the modern theory ofcomplexity, and conceiving new experiments on theglass transition which should enable to investigatenew previously un-accessible regimes, due to theintrinsically fast dynamics of a “photon glass.”Specifically, a random optical cavity is characterizedby N resonant modes with angular frequencies ω nand complex amplitudes a n, (n=1…N); such that theenergy stored into each mode is ω n|a n| 2 . Laser theorysays that the moduli of the a n are slowly varying withrespect to the phases ϕ n, hence the former can betaken as quenched variables while the latter are therelevant dynamic variables and take the role ofspherical spins. The Hamiltonian is:∑H = cos( ϕ + ϕ −ϕ−ϕ)J spqrspqwhere the random coupling constants J aredetermined by the spatial overlap of the resonantmodes. The replica method is applied for determiningthe energy landscape of the model and the existenceof a one-step replica symmetry breaking (1RSB), orglass-transition. The role of the inverse temperatureis played by the ratio between the squared averageenergy stored into each mode and the amount ofnoise due to spontaneous emission. There exist acritical value of this effective temperature for theexistence of an exponentially large number of metastablestates, each corresponding to a differentrFig. 2: Ab initio 3D+1 computation of specklepatterns at 532nm obtained when light propagatesin high concentration colloidal materials, whosestructure is determined by molecular dynamicsimulations. These numerical techniques providenew opportunities for the investigation of softmaterialproperties, as they may enrich theinformation that can be extracted by experiments inthe multiple-scattering regime.mode-locking process of the random laser. In thisway the complexity (i.e. the configurational entropy)of light in random lasers can be calculated, and thecritical temperature is expressed in term ofexperimentally accessible quantities.Complex dynamics of light is also found, theoreticallyand experimentally, when focused laser beamspropagated in soft-matter like liquid crystals. [2] Inthis case, disorder and nonlinearity contribute to thegeneration of multiple light filaments whosedynamics can be described by the same paradigmsof the physics of soft-matter. Understanding theseprocesses is relevant for various applications, fromall optical digital devices to laser surgery.Photonics in disordered or structured systems,(“complex photonics”) is a very active andmultidisciplinary research field, to which we are alsocontributing by developing new computationalapproaches (figure 1), and designing novel opticaldevices [3] (as e.g. “photonic crystals”) which can beinfiltrated by soft-materials, and provideopportunities for femtoliter substance analysis.References[1] L. Angelani, C. Conti, G. Ruocco, F. Zamponi,Phys. Rev. Lett. 96, 065702 (2006); Condmat/0511427;L. Angelani, C. Conti, G. Ruocco, F.Zamponi, cond-mat/0604242, submitted to Phys.Rev. B[2] C. Conti, Phys. Rev. 72, 066620 (2005); C.Conti, M. Peccianti, G. Assanto, Opt. Lett. (2006),submitted.[3] A. Di Falco, C. Conti, G. Assanto, Appl. Phys. B81, 415 (2005); A. Di Falco C. Conti, G. Assanto,Opt. Lett. 31, 250 (2006); A. Di Falco C. Conti, G.Assanto, Opt. Lett. (2006), submittedFig. 1: Relevant overlap of the spin glass theoryof random lasers and complexity Vs the effectivetemperature (from Ref. 1)AuthorsL. Angelani (a), C. Conti (b,c), G. Ruocco (c) , F.Zamponi (d), G. Assanto (e), M. Peccianti (e)(a) SMC INFM-CNR (b) Research Center EnricoFermi (c) SOFT INFM-CNR (d) Ecole NormalSuperiore (e) University Roma Tre.SOFT Scientific Report 2004-0650