Both experiment and numerical calculation were performed to study the nonlinear optical (NLO) effects in ferrofluids consisting of magnetic particles suspended in an organic solvent. We show that, in contrast to all the mechanisms responsible for NLO phenomena known so far, the novel NLO effects in ferrofluids in the zero applied field can be explained by the cross coupling between the temperature of the system and the concentration of particles through thermophoresis, which in turn leads to the spatial distribution of the refractive index. This NLO effect is enhanced by applying a moderate magnetic field whose mechanism is unclear so far

Du, Tengda

Luo, Weili

English

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University of Central Florida STARS Faculty Bibliography 1990s Faculty Bibliography 1-1-1998 Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling Tengda Du University of Central Florida Weili Luo University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib1990 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 1990s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Du, Tengda and Luo, Weili, "Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling" (1998). Faculty Bibliography 1990s. 2227. https://stars.library.ucf.edu/facultybib1990/2227 Appl. Phys. Lett. 72, 272 (1998); https://doi.org/10.1063/1.120710 72, 272© 1998 American Institute of Physics.Nonlinear optical effects in ferrofluidsinduced by temperature and concentrationcross couplingCite as: Appl. Phys. Lett. 72, 272 (1998); https://doi.org/10.1063/1.120710Submitted: 02 July 1997 . Accepted: 18 November 1997 . Published Online: 04 June 1998Tengda Du, and Weili LuoARTICLES YOU MAY BE INTERESTED INThermal lens coupled magneto-optical effect in a ferrofluidApplied Physics Letters 65, 1844 (1994); https://doi.org/10.1063/1.112861Long-Transient Effects in Lasers with Inserted Liquid SamplesJournal of Applied Physics 36, 3 (1965); https://doi.org/10.1063/1.1713919Laser self-induced thermo-optical effects in a magnetic fluidJournal of Applied Physics 96, 5930 (2004); https://doi.org/10.1063/1.1808242Nonlinear optical effects in ferrofluids induced by temperatureand concentration cross couplingTengda Du and Weili Luoa)Department of Physics, University of Central Florida, Orlando, Florida 32816~Received 2 July 1997; accepted for publication 18 November 1997!Both experiment and numerical calculation were performed to study the nonlinear optical ~NLO!effects in ferrofluids consisting of magnetic particles suspended in an organic solvent. We show that,in contrast to all the mechanisms responsible for NLO phenomena known so far, the novel NLOeffects in ferrofluids in the zero applied field can be explained by the cross coupling between thetemperature of the system and the concentration of particles through thermophoresis, which in turnleads to the spatial distribution of the refractive index. This NLO effect is enhanced by applying amoderate magnetic field whose mechanism is unclear so far. © 1998 American Institute ofPhysics. @S0003-6951~98!02003-8#The discoveries of nonlinear optical ~NLO! effects havegreatly advanced our knowledge of the interaction betweenlight and matter and, at the meantime, created a revolution inoptical technology. Searching for new mechanisms for sucheffects will not only lead to better understanding of this in-teraction but also have great economic impacts in the infor-mation age. Recently, current authors have observed NLOeffects in the diffraction patterns from a ferrofluid/magneticfluid.1 In this letter, we report new experimental and numeri-cal results that demonstrate that a new mechanism—the ther-mophoresis induced coupling between the temperature andconcentration, which leads to spatial distribution of phaseand the index of refraction—is responsible to the NLO effectin ferrofluids reported earlier. We found that this NLO effectis significantly enhanced even in a small applied magneticfield. These results will lead to a new class of optical mate-rials whose optical parameters can be easily controlled byexternal parameters such as gradient forces from tempera-ture, field, and concentration.Ferrofluid samples used in this study consist of magneticparticles suspended in kerosene.2 The mean diameter of par-ticles is 9 nm. The volume fraction of the magnetic particlesis 6%. Figure 1 is the schematic of the experimental setup.The wave length of the He–Ne laser is l50.6328 mm. Thenumber of diffraction rings appeared at the far field after thelaser is switched on, N, depends on both the thicknesses ofthe sample and the intensity of the laser. The time scale forthe ring-formation process is in the order of 1 s for the focallength of 1 cm. The details about the setup and the samplehave been published elsewhere.1Because of the large absorption coefficient of our sample~550/cm!, there is a temperature increase in the liquid. Thetemperature change follows the thermal conduction equation]T]t2xDT5sIrCp, ~1!where s is the absorption coefficient of the ferrofluid thatdepends on the concentration of particles, I the intensity ofthe laser beam, r and Cp the density and the heat capacity ofthe system, and x the thermal diffusivity. The time for ther-mal conduction can be estimated by: tcon;a2/x , a is thedistance that the heat flux travels in time tcon . For focallength of 1 cm, a;10 mm if we take the diameter of thefocused beam as a. We get tcon;0.1 ms for our ferrofluid,several orders of magnitude faster than the ring-formationtime observed in Fig. 1. Apparently, the temperature in-crease in the system originated from the thermal conductionalone cannot account for the diffraction rings observed.In order to explore the physics for the observed nonlin-ear phenomenon, we measured the time dependence of out-put power. In Fig. 2, the total transmission Pt , which isequal to the ratio of the output power to input power, plottedagainst time in zero field. The increase of Pt with time, webelieve, is due to the change in the number of particles crossthe light beam. We realize that the laser intensity has thefollowing spatial dependence: I(r ,z)5I0 f (z)exp(2r2/w2),where f (z)5exp(2sz), the temperature inside the samplewill also have a spatial distribution with the highest tempera-ture at the optical axis along the radial direction and some-where below the center of the cell along the z direction. Thistemperature gradient should lead to thermophoresis—particlemigration along the temperature gradient, which was firstdescribed by Tyndall3 in dust particles in gases. There areseveral mechanisms for thermophoresis.4 For small particles,the thermal diffusion of particles due to the temperature gra-dient in the carrier dominates. We found that, by assumingthe thermal diffusion mechanism, we could produce mainfeature of our experimental results. Taking both the thermaland mass diffusion into account, the mass flux obeys thefollowing equation:5,6]c]t5DDc1DT¹@c~12c !¹T# , ~2!a!Electronic mail: luo@pegasus.cc.ucf.eduFIG. 1. The schematics of experimental setup. The right side is the diffrac-tion rings observed in far field.272 Appl. Phys. Lett. 72 (3), 19 January 1998 0003-6951/98/72(3)/272/3/$15.00 © 1998 American Institute of Physicswhere c is the concentration of particles, T the temperature,D and DT the mass and the thermal diffusion constants, re-spectively. D5kT/6phR with h the viscosity of the solvent,R the hydrodynamics radius which is twice of the particleradius. h5331023 Pa s for our ferrofluid. We get D5731028 cm2/s. In Eq. ~2!, DT is the thermal diffusion coef-ficient with the unit of cm2/s K. From our experiment, wecould do an order of magnitude estimate for DT . The timedependence of the transmission, Pt , in Fig. 2 indicates thatthe particles migrate away from the optical axis, thus theincrease in Pt , until a maximum is reached at tmax . Thedecreasing of Pt with time for t.tmax suggests reverse flowof the particles towards the center of the light beam. Wefound that peak position tmax shortens with increasing lightintensity. For example, using a lens with a focal length of 1cm will increase the intensity from 1 W/cm2 for the unfo-cused beam to 104 W/cm2. This increase in intensity leads toa shift in the peak position in Fig. 2 towards shorter time.7The increase in the transmission with time in Fig. 2 thusshould be associated with the thermal diffusion of particlesaway from the optical axis. As time goes on, other processeswill become increasingly important that will be addressedelsewhere. Furthermore, the temperature gradient cross thelight beam will decrease. These mechanisms will reduce thethermal diffusion of particles. Therefore, we believe that it isreasonable to take the time to reach tmax as the thermal dif-fusion time t th that satisfies: DTtmax5r2/T, where r is thelength scale particle traveled within time tmax . Taking pa-rameters from data in Fig. 2, i.e., the radius of laser spot r;1.5 mm, and tmax53000 s, we found DT;231028 cm2/s K. In binary liquids, the thermal diffusion ofspecies is referred as the Ludwig–Soret effect.8Equations ~1! and ~2! are coupled through the absorptioncoefficient that is a function of the concentration c. We solvethem numerically with the following boundary conditions:~a! temperatures at the boundaries are continuous, i.e.,T~r5R !5T0 , T~z5h1L !5T~z52L !5T0 , ~3!where R is the sample size from the center of the laser beamto the edge, h and L the thicknesses of the sample layer andthat of the substrates ~glass plates!, respectively, T0 the roomtemperature. ~b! Heat fluxes at the interfaces between thesample and the substrates are continuous:k0S ]T0]z D h5k1S]T1]z D h , k0S]T0]z D 05k1S]T1]z D 0 , ~4!where k0573102 W/mK and k0150.15 W/mK are thermo-conductivities of glass and the ferrofluid, respectively; ~c! Att50, the temperature and concentration are uniform in space.We obtained temperature change T(r ,t)2T0 and relativeconcentration change Dc(r ,t)5(c2c0)/c0 as functions oftime shown in Figs. 3~a! and 3~c!. We found that, at thesteady state, the temperature change is 12 K within the laserbeam ~r50 to r/w51! and about 50 K to the boundary ofthe sample cell (r!`) in the horizontal plane. We can seethat temperature has a sudden increase at very short time(,30 ms) after the laser is switched on but percentagechange is much smaller for t.0.2 s. In contrast, the concen-tration change, Dc(r ,t) is much slower at the short time asshown in Fig. 3~c! due to the slower responses of particlemigration. Using the similar criterion for estimating the ther-mal conduction time, we found that characteristic time scalesfor both thermal and mass diffusions are in the order of 1 s.From Fig. 3~c! we can see that the concentration decreases asmuch as 70% on the optical axis when it reaches the steadystate. This change in both temperature and concentrationleads to the change in the local index of refraction dn(r ,z):dn(r ,z)5]n(r ,z)/]TdT1]n(r ,z)/]cdc . Because]n/]T,0, dT.0 and ]n/]c.0, dc,0, the results fromboth the thermal conduction and the thermal diffusion areself-defocusing. The phase change originated from dn seenby the laser beam traversing the medium of thickness h isdf~r !52pl E2h/2h/2dn~r ,z !dz ,l is the wavelength of the light. Using the number of diffrac-tion rings, N, from the experiment, we can estimate the maxi-mum of df by: df052pN52phdn/l , where h is thethickness of sample layer and dn the corresponding changein the index of refraction. For l50.6328 mm and h550 mm, we get dn5531022 for N54. The index of re-fraction is equal to: n5n01n2E2, E is the electric field anduEu2 is proportional to the intensity of the light. Then thenonlinear part of the index of refraction can be obtained:n25dn/uEu2;1021 cm3/erg. This large change in the re-fractive index is larger than that of some liquid crystals.9,10The far-field interference patterns can be obtained byusing the local phase change from the numericalcalculation.11 We plotted results in Figs. 3~b! and 3~d!. Inthese calculations, the sample thickness is 50 mm and thefocal length is 1 cm. Figure 3~b! represents diffraction at thefar field at time t51 ms. At this early stage, thermal andmass diffusions are not appreciable. Apparently, the phasechange due to temperature alone is small and the diffractionpattern is essentially invisible. Figure 3~d! shows the diffrac-tion pattern at the far field for t51 s. Within this time, par-ticle density has an obvious change as illustrated in Fig. 3~c!and reaches the saturation as time reaches the order of 1 s,agreeing with the ring-formation time in our experiment. ToFIG. 2. The transmission vs time in zero applied magnetic field without thefocal lens.273Appl. Phys. Lett., Vol. 72, No. 3, 19 January 1998 T. Du and W. Luoreproduce the number of rings observed in experiment underthe same condition, we need the thermal diffusion constant,DT;131027 cm2/s K, 5 times larger than the experimentalvalue, DT;231028 cm2/s K obtained from Fig. 2. Appar-ently, to compare with experiment quantitatively, we have totake into account other processes in the future. When thermaldissipation through the substrates is neglected, the tempera-ture increase in the sample will be around 103 K without thethermal diffusion. This huge temperature change will pro-duce ‘‘thermal rings.’’ Then the particle migration will onlychange the distribution of light intensity among the rings, butnot the number of rings.12Because particles have permanent magnetic moments,there is an interaction between the ferrofluid and an appliedmagnetic field. We found that when the external field isswitched on, the transmission has a dramatic increase in ashort time. This effect is not understood yet and will bepublished elsewhere.13In summary, NLO properties in a ferrofluid were studiedby both experiment and numerical calculations. We havedemonstrated that the cross-coupling between the concentra-tion of particles and the temperature of the system, whichoriginates from the thermophoresis, is likely the mainmechanism for the NLO effects. A magnetic field enhancesthe NLO effect dramatically. These results should lead to anew type of nonlinear optical materials for device applica-tions.The authors thank Dr. R. E. Rosensweig for providingthe sample used in this work and useful discussion with Dr.N. V. Tabiryan, Dr. S. R. Nersisyan, and Dr. Jie Huang. Thiswork is supported by NSF Young Investigator Award ~Luo!.1 T. Du, S. H. Yuan, and W. Luo, Appl. Phys. Lett. 65, 1844 ~1994!.2 For a review on ferrofluids, see R. E. Rosensweig, Ferrohydrodynamics~Cambridge University Press, Cambridge, 1985!.3 J. Tyndall, Proc. Roy. Inst. Gt. Br. 6, 3 ~1870!.4 C. N. Davies, Aerosol Science ~Academic, London, 1966!.5 K. E. Grew and T. L. Ibbs, Thermal Diffusion in Gases ~Cambridge Uni-versity Press, Cambridge, 1952!; S. R. de Groot and P. Mazur, Non-equilibrium Thermodynamics ~North-Holland, Amsterdam, 1962!.6 L. D. Landau and E. M. Lifshitz, Fluid Mechanics ~Pergamon Oxford,1987!.7 S. Nersisyan, T. Du, N. V. Tabiryan, and W. Luo ~unpublished!.8 C. Ludwig, Sitzungber, Akad. Wiss. Wien 20, 539 ~1856!; C. Soret, Arch.Sci. Phys. Nat. Geneva 2, 48 ~1879!.9 Y. R. Shen, The Principle of Nonlinear Optics ~Wiley, New York, 1984!.10 N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zeldovish, Mol. Cryst. Liq.Cryst. 136, 1 ~1986!.11 Detailed calculation will be submitted elsewhere by T. Du and W. Luo~unpublished!.12 N. V. Tabiryan and W. Luo ~unpublished!.13 T. Du and W. Luo ~unpublished!.FIG. 3. Results from numerical calculations. ~a! Temperature change as a function of radial distance, r/w , for different times, where w is the width of the laserbeam. ~b! Far field diffraction at short time, when only temperature change is appreciable. The small ring forms in less than a millisecond that is unobservablein our experiment. ~c! The change in the particle concentration as a function of reduced radial distance, r/w , for different times. ~d! For longer time, thechange in the index of refraction due to concentration decrease becomes more important. This change leads to multiple rings in far field at t51 s.274 Appl. Phys. Lett., Vol. 72, No. 3, 19 January 1998 T. Du and W. Luo

Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling

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Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling

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