Nonlinear Optics in <strong>Soft</strong>-MatterLight propagation in soft-matter such as colloidalsystems can be affected via a feedback mechanismby light induced structural changes, owing to theirhigh responsivity to external stimuli. In spite of suchattractive feature and the low powers needed toobserve nonlinear phenomena, the optical nonlinearresponse of soft matter was generally overlookedwith the exception of metal colloids (whosenonlinearity is me<strong>di</strong>ated by surface polaritons) andliquid crystals that <strong>di</strong>splay a giant reorientationalnonlinearity. We have considered the case of acolloidal suspension of <strong>di</strong>electric particles <strong>di</strong>sperse<strong>di</strong>n a solvent, characterized by tunable interactionsthat can be responsible for long range correlationsand even phase transitions such as gelation. The roleof the structure of these materials in nonlinearoptical processes is essentially unexplored.Large scale ordered structures can indeed affectorientational, electrostrictive, and thermophoreticmechanisms. For isotropic particles and negligiblethermal gra<strong>di</strong>ents due to light absorption, thelea<strong>di</strong>ng optical nonlinear mechanism is expected tobe electrostriction: the particles are subject to forcesinduced by light intensity gra<strong>di</strong>ents, thus moving inthe region with higher or lower intensity depen<strong>di</strong>ngon the <strong>di</strong>fference between their refractive index andthat of the host me<strong>di</strong>um. In both cases, the opticalbeam experiences self-focusing, a process which hasbeen described by a local Kerr law or intensitydependentrefractive index variation. Recently,however, we have shown that the nonlinear responseof such materials is me<strong>di</strong>ated by the static structurefactor S(q) of the material, turning out to be stronglynonlocal. While the strength of the nonlinearity ispredominantly affected by the materialcompressibility, S(q) is strongly affected by thewhole structure of the soft-material phase, e.g. bythe presence of fractal aggregates which has impacton the nonlinear susceptibilities. [1]Thus, we have shown that specific nonlinear opticalprocesses, and in particular we have pre<strong>di</strong>cted theexistence of self-trapped optical beams, or “spatialsolutions” (SS). [1] These are light filaments whichcan propagate without <strong>di</strong>ffraction, due to nonlinearresponse of the material. We have found a strictFig. 2: Numerical simulations of laser beampropagation in a soft material in the presence ofaggregates with fractal <strong>di</strong>mensions D=1.3 (a) andD=2.3 (b). The laser intensity <strong>di</strong>stribution at theoutput plane of a soft-matter sample with lengthcomparable to the Rayleigh length of a beam withwaist w 0 profile is shown in a pseudo-color plot. Thenumber and the <strong>di</strong>stribution of the laser filamentsgenerated from a Gaussian beam is strongly affectedby the fractal <strong>di</strong>mension.relation between the SS features, like the existencecurve relating the beam waist and power, withspecific structural quantities, like the cluster spatialextension, or their fractal <strong>di</strong>mensions. We have alsopre<strong>di</strong>cted the existence of sub-wavelength ultra-thinSS than can propagate without <strong>di</strong>ffraction, and thatcan have relevant applications for opticalcommunication devices or laser surgery (figure 1).We have also considered the role of <strong>di</strong>sorder, e.g.due to density material fluctuactions, in thepropagation of a laser beam in a soft-material,inclu<strong>di</strong>ng nonlinear effects. Specifically, we haveinvestigated the con<strong>di</strong>tion for the beam breakup intoa multitude of filaments, which propagate an<strong>di</strong>nteract in due to the non local nonlinear response ofthe materials. A strong link with the materialstructure factor and these laser filamentation processcan be estabilished. (figure 2).[2]For what concern the experimental activity, weimplemented the z-scan techniques to measure thestatic and dynamic properties of the nonlinear opticalsusceptibility. We have reported specific evidences ofthe aging of the nonlinear susceptibility in Laponite,whose nonlinear optical response was augmented byad<strong>di</strong>ng a dye to the solution. [3]References[1] C. Conti, G. Ruocco, S. Trillo, Phys. Rev. Lett.96, 065702 (2006);[2] C. Conti, N. Ghofraniha, G. Ruocco, S. Trillo,submitted;[3] N. Ghofraniha, C. Conti, G. Ruocco, submitted.See the related chapter in this book.Fig. 1: Numerical simulation of the propagation of aself-trapped Gaussian beam in a soft-material withfractal <strong>di</strong>mension D=2.5, for two <strong>di</strong>fferent inputpowers in the paraxial regime (a and b) and beyond(c and d), z 0 and w 0 are the <strong>di</strong>ffraction length and thebeam waist respectively; z is the propagation<strong>di</strong>stance and r the transverse coor<strong>di</strong>nate. [1].AuthorsC. Conti (a,b), N. Ghofraniha (c), G. Ruocco (b,d), S.Trillo (b,e).(a) Research Center “Enrico Fermi”, Rome, Italy.(b) CRS SOFT-INFM-CNR, Rome, Italy.(c) CRS SMC-INFM-CNR, Rome, Italy.(d) Universita’ <strong>di</strong> Roma, Rome, Italy.(e) Universita’ <strong>di</strong> Ferrara, Ferrara, Italy.67SOFT Scientific <strong>Report</strong> 2004-06
Scientific <strong>Report</strong> – Non Equilibrium Dynamics and ComplexityColloidal Suspensions Under ShearResearch activities in the field of colloidalsuspensions have recently exhibited rapid growth,for their relevance in both technical applications andfundamental science. On one hand, they areessential in many industrial application ranging frompaints to lubrificants, or in pharmaceuticalapplications such as drug delivery. On the otherhand, they play a preminent role as model systemsfor the principles of phase transitions in condensedmatter. One of the most peculiar behavoir of softcolloidal matter is the strong sensitivity of its flowproperties to external deformation. A systematicscientific comprehension about this topic is stillimmature.In the last few years we investigated the physicalmechanism governing the interaction between agingdynamics and shear flow in a Laponite suspension,which represents a prototype of a soft glassymeterial [2]. Dynamic light scattering has been usedto probe the relaxation of the interme<strong>di</strong>ate scatteringfunction of the aging sample and the effect of shearon the non-equilibrium structural dynamics has beeninvestigated during various protocols of appliedshear. The shear flow influences significantly theaging dynamics as soon as structural relaxationenters the timescale set by the inverse shear rate(Fig. 1). Aging is strongly reduced in this sheardominated region, while for a fixed waiting time theaverage structural relaxation scales as the inverseshear rate.Fig. 2: Velocity profile of the Laponite sample putunder shear in a cone-plate cell, as a function ofthe <strong>di</strong>stance along the gap of width H. Shearlocalization shows up next to the rotating cone wall.Shear rejuvenation of gelled samples has also beeninvestigated and we observed a substantially<strong>di</strong>fferent aging regime characterized by a fasterrelaxation dynamics. In particular, the slowrelaxation time shows a power law dependence onthe waiting time after shear cessation.Another aspect of the soft glassy sample weinvestigated is the shear ban<strong>di</strong>ng phenomena,characterizing yield stress fluids at low applied shearrates. Shear localization [4] has been observed inthe Laponite sample through heterodyne dynamiclight scattering technique (Fig. 2). The velocityprofile has been stu<strong>di</strong>ed as a function of both thewaiting time and the applied shear rate. Theevolution of both the flow curve and the yield stressvalue is reflected locally in the evolution of the shearban<strong>di</strong>ng velocity profile as the system ages. Finally,a perio<strong>di</strong>c oscillation between two <strong>di</strong>fferent velocityprofiles has also been observed, showing a stick-slipbehavior in the flow.Fig. 1 Slow relaxation time as a function of waitingtime during aging under <strong>di</strong>fferent shear rates. Frombottom to top the shear rate value is: 446, 223, 67,22 s -1 . Solid symbols refer to aging without shear.Arrows in top frame in<strong>di</strong>cate the inverse shear ratevalue correspon<strong>di</strong>ng to each curve. Deviation fromthe aging evolution is evident as soon as the slowrelaxation time reaches the timescale of the inverseshear rate.References[1] D. Bonn, S. Tanase, B. Abou, H. Tanaka, J.Meunier, Phys. Rev. Lett., 89, 015701 (2002).[2] P. Sollich, F. Lequeux, P. Hèbraud, M.E. Cates,Phys. Rev. Lett., 78, 2020 (1997).[3] R. Di Leonardo, F. Ianni, G. Ruocco, Phys. Rev.E, 71, 011505 (2005)[4] F. Varnik, L. Bocquet, J.-L. Barrat, L. Berthier,Phys. Rev. Lett. 90, 095702 (2003).AuthorsR. Di Leonardo, S. Gentilini, F. Ianni and G. Ruocco.SOFT CNR-INFM – <strong>Dipartimento</strong> <strong>di</strong> <strong>Fisica</strong> Universita’Roma ‘‘La <strong>Sapienza</strong>’’ – 00185 Roma – ItalySOFT Scientific <strong>Report</strong> 2004-0668
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