Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior

Optical bistability in graphene-wrapped dielectric nanowires

We study the optical bistability of graphene-wrapped dielectric cylinders with Kerr-type nonlinear response within the framework of both nonlinear full-wave scattering theory and nonlinear quasistatic theory. Typical optical bistable properties are observed in both near-field and far-field spectra with the excitation of electric dipolar modes. Moreover, when high electromagnetic field is applied, nonlinear full wave theory yields new bistable region, indicating the existence of an artificial tunable magnetic dipole. The switching threshold fields are found to be tunable by changing either the size, permittivity of the nanocylinder or the chemical potential of graphene. Our results offer insight into the interaction between Kerr-type nonlinearity and graphene plasmonics, and may promise the graphene-wrapped nanowire a candidate for all-optical switching and nano-memories in terahertz region.

Nonlinear alternating current responses of dipolar fluids

The frequency-dependent nonlinear dielectric increment of dipolar fluids in nonpolar fluids is often measured by using a stationary relaxation method in which two electric fields are used: The static direct current (dc) field of high strength causing the dielectric nonlinearity, and the probing alternating current (ac) field of low strength and high frequency. When a nonlinear composite is subjected to a sinusoidal electric field, the electric response in the composite will, in general, consist of ac fields at frequencies of higher-order harmonics. Based on the Fröhlich model, we present a theory to investigate the nonlinear ac responses of dipolar fluids containing both polarizable monomers and dimers. In the case of monomers only, our theory reproduces the known results. We obtain the fundamental, second-, and third-order harmonics of the Fröhlich field by performing a perturbation expansion. The even-order harmonics are induced by the coupling between the ac and dc fields, although the system under consideration has a cubic nonlinearity only. The harmonics of the Fröhlich field can be affected by the field frequency, temperature, dispersion strength, and the characteristic frequency of the dipolar fluid, as well as the dielectric constant of the nonpolar fluid. The results are found to be in agreement with recent experimental observations.

Optical bistability and tristability in nonlinear metal/dielectric composite media of nonspherical particles

Based on a spectral representation method and a self-consistent mean field theory, we present a general framework to investigate the optical bistability in a nonlinear two-phase composite, where spheroidal metallic inclusions are randomly oriented and embedded in a dielectric host. The relation between the spatial average of the local field squared <[absolute value of E](2)>(i) (i=1,2) and the external field squared E20 is obtainable through the spectral density function which is predicted from our recently derived Maxwell-Garnett approximation. In addition to single optical bistability (OB), the appearance of double OB and optical tristability (OT) is reported, and the corresponding phase diagram is given. We find that the regions of the single OB, the double OB, and the OT are dependent on the shape and volume fraction of the metallic particles. Our method allows us to take one step forward to study some field-dependent effective optical properties, such as the refractive index, extinction coefficient as well as reflectance. The general framework is also applied to investigate exactly the solvable composites consisting of nonlinear spheroidal inclusions and linear dielectric host in the dilute limit. To this end, the present method is shown to be in excellent agreement with the exact solution. In addition, the present method predicts a larger threshold intensity than the variational approach.

Nonlinear ac response of anisotropic composites

When a suspension consisting of dielectric particles having nonlinear characteristics is subjected to a sinusoidal (ac) field, the electrical response will in general consist of ac fields at frequencies of the higher-order harmonics. These ac responses will also be anisotropic. In this work, a self-consistent formalism has been employed to compute the induced dipole moment for suspensions in which the suspended particles have nonlinear characteristics, in an attempt to investigate the anisotropy in the ac response. The results showed that the harmonics of the induced dipole moment and the local electric field are both increased as the anisotropy increases for the longitudinal field case, while the harmonics are decreased as the anisotropy increases for the transverse field case. These results are qualitatively understood with the spectral representation. Thus, by measuring the ac responses both parallel and perpendicular to the uniaxial anisotropic axis of the field-induced structures, it is possible to perform real-time monitoring of the field-induced aggregation process.

Nonlinear ac response of an electrorheological fluid

The applied electric field used in most electrorheological (ER) experiments is usually quite high, and nonlinear ER effects have been measured recently. When a nonlinear ER fluid is subjected to a sinusoidal (ac) field, the electrical response will in general consist of ac fields at frequencies of the higher-order harmonics. In this paper, a self-consistent formalism has been employed to compute the induced dipole moment for ER fluids in which the suspended particles have nonlinear characteristics, in an attempt to investigate the ac response of a nonlinear ER fluid.

Force between two spherical inclusions in a nonlinear host medium

In an attempt to investigate the effect of nonlinear characteristics on particle interactions, a self-consistent mean-field theory in combination with a multiple image method has been employed to compute the interparticle force. Taking the nonlinearity of the host medium into account, the interparticle force exhibits a nonmonotonic behavior as the applied electric field is increased. We show that the interparticle force increases initially at low fields, goes through a maximum at an optimal electric field, then decreases with increasing field, and vanishes at a critical electric field at which the effective dielectric contrast between the host and the inclusions becomes zero. The influence of a larger volume fraction of inclusions on the interparticle force is also investigated.