The time dependent transmission is observed when a laser beam passes through a thin layer of a magnetic fluid. We found that the transmission reaches a peak at a time that depends on the intensity of the incident beam-the peak position shifts to shorter time when the input intensity is increased. The peak value of transmitted power decreases with increasing magnetic field. A simplified model is provided to explain these complex dynamics

Du, Tengda

Luo, Weili

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University of Central Florida STARS Faculty Bibliography 1990s Faculty Bibliography 1-1-1999 Intensity dependent transmission dynamics in magnetic fluids 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; Proceedings Paper 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, "Intensity dependent transmission dynamics in magnetic fluids" (1999). Faculty Bibliography 1990s. 2608. https://stars.library.ucf.edu/facultybib1990/2608 Journal of Applied Physics 85, 5953 (1999); https://doi.org/10.1063/1.370002 85, 5953© 1999 American Institute of Physics.Intensity dependent transmission dynamicsin magnetic fluidsCite as: Journal of Applied Physics 85, 5953 (1999); https://doi.org/10.1063/1.370002Published Online: 21 April 1999Tengda Du, and Weili LuoARTICLES YOU MAY BE INTERESTED INShort-time aggregation dynamics of reversible light-induced cluster formation in ferrofluidsJournal of Applied Physics 97, 034910 (2005); https://doi.org/10.1063/1.1847706Nonlinear optical effects in ferrofluids induced by temperature and concentration crosscouplingApplied Physics Letters 72, 272 (1998); https://doi.org/10.1063/1.120710Thermal lens coupled magneto-optical effect in a ferrofluidApplied Physics Letters 65, 1844 (1994); https://doi.org/10.1063/1.112861Magnetic Fluids Weili Luo, ChairmanIntensity dependent transmission dynamics in magnetic fluidsTengda Du and Weili Luoa)Department of Physics, Advanced Material Processing and Analysis Center, Center for Diagnosticsand Drug Discovery, University of Central Florida, Orlando, Florida 32826The time dependent transmission is observed when a laser beam passes through a thin layer of amagnetic fluid. We found that the transmission reaches a peak at a time that depends on the intensityof the incident beam—the peak position shifts to shorter time when the input intensity is increased.The peak value of transmitted power decreases with increasing magnetic field. A simplified modelis provided to explain these complex dynamics. © 1999 American Institute of Physics.@S0021-8979~99!79608-8#I. INTRODUCTIONThe interaction of light with binary liquids has been ofgrowing interest recently due to its broad applications.1–6However, the physical mechanisms associated with many in-teresting phenomena are still not completely understood. Inour previous works,5 we reported a new nonlinear optical~NLO! effect in magnetic fluids ~MFS! that is attributed tothe cross coupling between the temperature and concentra-tion of particles, which in turn leads to the spatial distribu-tion of the refractive index or self-phase modulation. In thisarticle, we report intensity dependent transmission dynamicsin a magnetic fluid—we found that there is a maximum inthe time dependent transmission and this peak positionchanges with incident intensity. The mechanism can be ex-plained by a simplified model. We also observed that thepeak value of transmitted power decreases while the peakposition slightly shifts to longer time in an applied magneticfield below the threshold for field induced instabilities.7II. EXPERIMENTAL SETUPThe sample used in this study is a magnetic fluid con-sisting of magnetite particles ~volume fraction 6%! sus-pended in kerosene. Each particle has a diameter of 9 nm andis coated with a surfactant layer of 2 nm in thickness. Theabsorption coefficient of the magnetic fluid, s, is measuredto be 550 cm21. The sample is confined between two parallelglass plates separated by a spacer with a thickness of 100mm. Figure 1 illustrates the schematic of the experimentsetup. A He–Ne laser ~l5633 nm! with a maximum outputof 40 mW in a single Gaussian mode is used. The laser beamis focused from an original diameter of 1.2 mm to smallersizes on the sample by different lenses. The output power isdetected by a photodiode connecting to a computer. Themagnetic field is applied normally to the sample and parallelto the laser beam.III. RESULTS AND DISCUSSIONSWe measure the output power transmitted from thesample, Pout , versus time when the laser beam is abruptlyswitched on. In Fig. 2 we plot time dependence of Pout forinput laser power P in56.6 mW and for focal length f 520,25, 40, 60, 80, and 100 mm, respectively. From the relationbetween the focal length, f, and the beam width w, w5l f /pw0 ~w0 is the original beam radius!, we know that thelonger the focal length f, the smaller the intensity because theintensity follows the relation I05Pin /pw2, I(r)5I0 exp(2r2/w2). Results in Fig. 2 show that the peak position shiftstowards longer time with decreased intensity. The time de-pendence indicates that, before the peaks appear, the mag-netic particles move away from the optical axis therefore thesample becomes more transparent, thus Pout increases. Thedecrease of Pout , after reaching the maximum, is corre-sponding to the reverse process. The concentration changeobeys thermal conduction and mass conservation equations8,9]T]t2xDT5sIrCp, ~1!a!Electronic mail: luo@pegasus.cc.ucf.edu FIG. 1. The schematic of experimental setup.JOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 8 15 APRIL 199959530021-8979/99/85(8)/5953/3/$15.00 © 1999 American Institute of Physics]c]t5DDc1DT¹@c~12c !¹T# , ~2!where I(r ,z)5I0exp(2r2/w22sz), T is temperature, c theparticle concentration, I the intensity of laser beam, w thelaser beam width, r the density of the fluid, Cp the heatcapacity, and x the thermal diffusivity. D and DT are massand thermal diffusion coefficients, respectively. For low con-centration we assume the absorption coefficient, s, is propor-tional to concentration c, or s5ac , a is a constant, so Eqs.~1! and ~2! are coupled. To solve the coupled differentialequations is not easy, but we can qualitatively describe thetemporal behavior at a fixed location, assuming that thebeam shape always follows a Gaussian profile.We rewrite c5c0(11c1) where c0 is concentration atroom temperature, c1 is the relative change of concentration;Eq. ~2! becomes]c1]t5DDc11DTDT1DT¹T¹c1 , ~3!where we assume the change of concentration c1!1 for lowc. It is reasonable to choose a location where changes of Tand c reach extremes ~such on optical axis and the first in-terface at the glass plates!. We further assume that the tem-perature and concentration in radial direction follow the dis-tribution of the intensity, i.e., the Gaussian, the onlydifference compared with the beam profile outside thesample is that the beam has a wider distribution width: w15kw , with k.1. We also assume that the temperaturechange in the sample follows a parabolic distribution in zdirection with a maximum at z50, where the laser beamenters the sample, and vanishes at z5L , where the beamexits the system, assuming that the glass plates have a perfectconductivity. The cross term in Eq. ~3! is zero at this refer-ence point ~r50, z50!. We obtainDc1~r50 !'2c1~r50 !S 4w12 12L2D ,DT~r50 !'2T~r50 !S 4w12 12L2D ,where L is the thickness of the sample. Substitute Dc1 andDT into Eqs. ~1! and ~3!, and eliminate one parameter, forexample T, and we finally get]2c1]t21x1DR2]c1]t1S DxR4 1 sDTI0R2rCpD c15g~I0!, ~4!where 1/R254/w1212/L2, g(I0) is a function of intensity.This is exactly a damping oscillation equation. To have anoscillation term, the following condition must be satisfied:S x1DR2 D224S DxR4 1 sDTI0R2rCpD,0.The oscillation frequency is equal tov5ADxR4 1sDTI0R2rCp2S x1D2R2 D2. ~5!The peak position tmax in experiments should be proportionalto 1/v, if we assume the dynamics of total transmission fol-lows the concentration change at the reference point ~r50,z50! ~the distribution shape of c does not change with time!.In our system, D/x;1023. The above expression can befurther simplified asv512R2A4sDTI0R2rCp2x2.Substituting the relation between w1 and I0 , finally we havev5S 2pI0Pin 1 1L2DA8sDTI0rCp Y S 2pI0Pin 1 1L2D2x2.Here we take k51 or w15w for simplicity. Let us look attwo extreme cases~1! w1@L , or lower intensity, then: 1/tmax2 5aI02b,where a and b are constants.~2! w1!L , or higher intensity, then: 1/tmax}I0 .This relation is qualitatively confirmed by the experimentalresults. In Fig. 3 we plot 1/tmax as a function of intensityusing experimental results. It reasonably agrees with theabove qualitative analysis.Besides the thermal diffusion and mass diffusion that areimportant mechanisms responsible for redistribution of par-ticles under the influence of laser beam, other factors such asFIG. 2. The transmitted power from the sample vs time in zero field withdifferent focusing lenses.FIG. 3. The term 1/tmax as a function of incident intensity I0 , where tmax isthe peak position.5954 J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 T. Du and W. Luoradiation pressure, which includes gradient force ~propor-tional to the gradient of intensity!, scattering force, and ab-sorption force,10 should be considered as well. For the inten-sity range we used, these effects are not key factors.Now we consider the effect of magnetic field on thecomplex dynamics. Figure 4 shows output powers versustime for different fields. The peak position slightly shifts, butmore importantly, the peak value decreases when magneticfield increases from 0 to 18 Oe. This suppression of thetransmission might be due to a magnetic body force thatresults from the spatial distribution of concentration and tem-perature, namely, the so-called Kelvin force. The force den-sity can be expressed as7f 5 m0xm2 H2~11xm!3S ¹TT 2 ¹cc D , ~6!where H is the external magnetic field, xm is the susceptibil-ity of the magnetic fluid. Because both ¹T and 2¹c aretoward the center of the system, the Kelvin force is centri-petal. The pressure from this force may resist thermal diffu-sion when the laser is switched on. To completely under-stand the effect of Kelvin force on transmission we need tosolve several coupled differential equations. Because analyti-cal solutions to these coupled equations are unlikely, numeri-cal calculations will be studied in the near future.IV. CONCLUSIONComplex behaviors are observed in the dynamics oftransmission from a magnetic fluid. We found that the trans-mission reaches a peak position that depends on incidentintensity. The observations are explained by the cross cou-pling between the temperature and particle concentration ofthe system via thermal diffusion. The intensity dependenceindicates a nonlinear optical behavior that originates fromabove novel mechanism. The influence of magnetic field onthe transmission is also discussed. Kelvin body force mightplay an important role. These results will have potential ap-plications in heat and mass transfers and optical devices.ACKNOWLEDGMENTSThe authors are grateful to Dr. R. E. Rosensweig forproviding the sample. This work is supported by the NationalScience Foundation Young Investigator Award ~Luo!.1 T. Du, S. Yuan, and W. Luo, Appl. Phys. Lett. 65, 1844 ~1994!.2 M. Kreuzer, T. Tschudi, W. H. de Jeu, and R. Eidenschink, Appl. Phys.Lett. 62, 1712 ~1993!.3 T. Du and W. Luo, Mod. Phys. Lett. B 9, 1643 ~1995!.4 P. W. Smith, P. J. Maloney, and A. Ashkin, Opt. Lett. 7, 347 ~1982!.5 T. Du and W. Luo, Appl. Phys. Lett. 72, 272 ~1998!.6 N. V. Tabiryan and W. Luo, Phys. Rev. E 57, 4431 ~1998!.7 W. Luo, T. Du, and J. Huang ~unpublished!.8 K. E. Grew and T. L. Ibbs, Thermal Diffusion in Gases ~Cambridge Uni-versity Press, Cambridge, 1952!, p. 107.9 L. D. Landau and E. M. Lifshiz, Fluid Mechanics ~Pergamon, Oxford,1987!, p. 192.10 K. Svoboda and S. M. Block, Opt. Lett. 19, 930 ~1994!.FIG. 4. The transmitted power vs time in different applied magnetic fieldswith focal length f 520 mm.5955J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 T. Du and W. Luo

Intensity dependent transmission dynamics in magnetic fluids

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Intensity dependent transmission dynamics in magnetic fluids

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