Clausius-Mossotti Approximation for Nonlinear Composites with Coated Ellipsoidal Particles
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Clausius-Mossotti Approximation for Nonlinear Composites with Coated Ellipsoidal Particles Anatoliy O. Pinchuk I. Physikalisches Institut der RWTH, D-52056 Aachen, Germany ABSRTACT An effective nonlinear dielectric permittivity of a heterogeneous composite structure consisting of coated ellipsoidal nonlinear nanoparticles embedded in a linear host medium has been theoretically studied. An expression for the effective dielectric permittivity tensor of such a system has been derived following the Clausius-Mossotti approximation. The conditions for the existence of electromagnetic bistability phenomenon in a single coated ellipsoidal particle with a nonlinear core and a metallic shell have been obtained. The numerical results show more prominent bistability phenomenon in more dense suspensions of nonlinear heterogeneous ellipsoids. INTRODUCTION Recently an intrinsic optical bistability (IOB) phenomenon has been extensively studied theoretically [1-6] as well as experimentally [7]. Kalyaniwalla et al. [3] studied IOB effect for a series of semiconductor spheroids coated with a silver shell and dispersed in a silica glass matrix. They optimised the shape of a single nonlinear coated spheroid for the particular semiconductor core and the thickness of the silver shell to obtain the lowest threshold intensity for IOB. They derived an expression for the effective dielectric permittivity of a heterogeneous system of randomly dispersed but oriented with respect to one another coated spheroids assuming that the local field, acting on a single coated spheroid, is equal to the average Maxwell field, which is valid only for low concentrations of heterogeneous nonlinear spheroids, i.e. they neglected the contribution from the dipole interaction between the heterogeneous nonlinear particles. They noticed that the effective medium approximation has to be developed for such composite structures to describe IOB in more dense nonlinear composites. Kreibig et. al [7] successfully verified experimentally IOB for a dilute suspension of CdS small spheres coated with silver shells. To describe their experimental results they used the same simple approach which suggests that the local field is equal to the average Maxwell field, which is valid only for very dilute suspensions of coated nonlinear spheres. In this paper we generalise the Clausius -Mossotti approximation for a composite structure consisting of randomly distributed but oriented with respect to one another coated ellipsoids with a nonlinear core and a metallic shell. The Clausius-Mossotti approximation for a suspension of coated spheres with the same heterogeneous structure was also generalised. We obtain the conditions to observe a so-called intrinsic optical bistability effect in a separate coated ellipsoidal particle depending on the detuning of the laser frequency. We present numerical results for the effective dielectric permittivity of the composite nonlinear structure which consists of GaAs oriented spheroids coated with a silver shell and embedded in a silica glas
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