| The higher-order nonlinear response and optical bistability of the macroscopic inhomogeneous granular composite are studied in this paper.Recent research has shown that enormous enhancements of nonlinear optical response can be achieved in such a composite material. The effective nonlinear response of the composite may be much larger than that of the nonlinear component due to the surface plasmon, and the optical bistable behavior can be found in lower external field intensity near the resonances. The speeds of the operations are extremely fast which are only limited by the intrinsic response time of the nonlinear material and the transit time through the device, therefore, this composites may have great potential applications for optical transistor and logical devices, etc.In these composites, the dielectric function depends on the applied electric field, theories which applied to linear problem are not valid to nonlinear composites, a varity of approximations have been proposed to investigate the nonlinear problem such as T-matrix approach, perturbation approach, spectral representation and Taylor-expansion method.Generally, the component possesses the electric displacement (D)-electric field (E) hasE , where x. is the (β + 1)th order nonlinearthe relation of the form Di = eiE i; response of the component i. The effective nonlinear responses of the composite for β = 2 have been discussed in many papers. For arbitrary β, an approximation based on the Maxwell-Garnett dilute limit formula was proposed for the effective higher nonlinear response including (β + 1)th order (x) and (2β + l)th order () nonlinear responses.A perturbative expansion method, based on the Clausius-Mossotti approximation was further developed to investigate the effective (β + l)th order nonlinear responsesincluding xe. The higher order effective responses xe and r/e were also numericallyIVstudied in random resister network, but the comparison of previous theoretical predictions with numerical simulations is far from satisfactory.In this paper, based on spectral representation theory and the perturbativeexpansion method, the general expressions for effective nonlinear responses (%e and rje) arederived, which are indeed valid for arbitrary (3 and for any complicated microstructures.For the dilute limit and the Maxwell-Garnett microstructures, our expressions yield the formula as those in previous work. The theoretical results for Maxwell-Garnett microstructures are compared with numerical simulations, good agreement is found. Ourstudies show that the effective nonlinear response should be considered when theapplied field is strong.When the external electric field becomes stronger, optical bistable behavior may be found near the resonance in such composite medium. The relation between the local field and the external applied field are derived to investigate the optical bistability.A general framework based on spectral representation method and self-consistent mean field theory is performed to discuss the OB in the nonlinear composite where spheroidal metallic inclusions are randomly oriented in a dielectric host, the regions of the single OB, the double OB, and the optical tristable OT are reported. The present method is shown to be in excellent agreement with the exact solution and predicts a larger threshold intensity than the variational approach.In combination with effective medium approximation, we also investigate the optical bistable behavior in a nonlinear two-phase composite in which the metal particles are embedded in the host medium. We find that the OB is dependent on the depolarizationfactor L and the volume fraction p, and for a given p, OB can be observed only whenL is larger than the critical value Lc, the upper and lower threshold intensity is foundtheoretically.Furthermore, optical bistability in three-phase composites of coated spheres withboth the core and the shell being nonlinear in no-dilute limit is studied based on self-consistent mean field appr...
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