Nonlinear Composite Media Research Articles

Generation of multiple ultrashort temporal solitons in a third-order nonlinear composite medium with self-focusing and self-defocusing nonlinearities

Generation of multiple ultrashort temporal solitons in a third-order nonlinear composite medium with self-focusing and self-defocusing nonlinearities

Study of multilayered composites through periodic homogenization and Mori–Tanaka methods

The multilayered composite structure has been utilized frequently in the literature of periodic homogenization as a test case for developing new methodologies for linear and nonlinear composite media. The manuscript demonstrates that these composites can also be used for validating mean-field micromechanics techniques. It is shown the Mori–Tanaka method combined with the Transformation Field Analysis provides the same solution with the periodic homogenization for nonlinear multilayered composites.

Light-controlled perfect absorption of light

We study coherent perfect absorption (CPA) of light in a Kerr nonlinear metal-dielectric composite medium, illuminated from the opposite ends. Elementary symmetry considerations reveal that equality of the incident light intensities is a prerequisite to ensure CPA in both linear and nonlinear systems for specific system parameters. We also derive the sufficient conditions for having CPA. We further show that, while CPA in a linear system is insensitive to the incident power level, in a nonlinear system CPA can be achieved only for discrete intensities with interesting hysteretic responses. Our unified formulation of CPA and waveguiding identifies them as opposite scattering phenomena. We further investigate light-induced CPA in on-resonant and off-resonant systems.

Investigation of linear and non-linear properties of oxide glass–metal nanoparticle composites by the strong-permittivity-fluctuation theory

The strong-permittivity-fluctuation theory (SPFT) is presented here for an isotropic, nonlinear composite medium under the long-wavelength approximation. The effective permittivity, effective susceptibility and figure of merit (FOM) of the homogenized composite medium are thereby estimated for the composition of the oxide glass and spherical metallic nanoparticles. The nonlinear properties SPFT is found to be insensitive to the choice of the correlation length between particles.

Instability of Solitary Waves in Nonlinear Composite Media

In this paper, we investigate a class of Hamiltonian systems arising in nonlinear composite media. By detailed analysis and computation we obtain a decaying estimates on the semigroup and prove the orbital instability of two families of explicit solitary wave solutions (slow family in anisotropic case and solitary waves in isotropic case), which theoretically verify the related guess and numerical results.

Stability of solitary waves in nonlinear composite media

The system of equations for planar waves in elastic composite media in the presence of anisotropy is considered. In anisotropic case two two-parametric families of solitary waves are found in an explicit form. In case of the absence of anisotropy these two families coalesce into the unique three parametric family. The solitary wave solutions are found to be orbitally stable in a certain range of their phase speeds (range of stability) both in an anisotropic as well as in an isotropic materials. It is also shown that the initial value problem for the governing equations is locally well posed which is needed to prove the stability result. The local well-posedness of the initial value problem along with stability of solitary waves implies global existence result provided the initial data lie in a neighbourhood of a stable solitary wave. This complements the previous results of blow-up for this type of equations.

Instability of solitary waves in non-linear composite media

A problem on the dynamic instability of soliton solutions (solitary waves) of Hamilton's equations, describing plane waves in non-linear elastic composite media with or without anisotropy, is considered. In the anisotropic case, there are two two-parameter families of solitary waves: fast and slow and, when there is no anisotropy, there is one three-parameter family. A classification of the instability of solitary waves of the fast family in the anisotropic case and of representatives of families of solitary waves, the velocities of which lie outside of the range of stability when there is anisotropy and when there is no anisotropy, is given on the basis of a numerical solution of a Cauchy problem for the model equations. In this paper, the fundamental equations describing plane waves in non-linear, anisotropic, elastic composites are derived, the Hamilton form of the basic equations is presented, the symmetries in the anisotropic and isotropic cases are considered, the conserved quantities and the soliton solutions, that is, the solitary waves are presented, the nature of the instability of representatives of all three families is investigated, brief formulation of the results is presented and problems of the instability of the fast family in the anisotropic case and of representatives of the families, the velocities of which lie outside of the range of stability in the presence and absence of anisotropy (explosive instability), are discussed.

Stability of solitons in nonlinear composite media

An analysis is made of the dynamic stability of soliton solutions of the Hamilton equations describing plane waves in nonlinear elastic composite media in the presence and absence of anisotropy. In the anisotropiccase two two-parameter soliton families, fast and slow, are obtained in analytic form; in the absence of anisotropy there is a single three-parameter soliton family. It is shown that solitons from the slow family in an anisotropic composite and solitons in an isotropic composite are dynamically stable if their velocities lie in a certain range known as the range of stability. The analysis of stability is based on the spectral properties of the “linearized Hamiltonian” ℋ. It is shown that the operator ℋ is positively semidefinite on some linear subspace of the main solution space from which stability follows. Problems of instability of the fast soliton family in the anisotropic case and representatives of soliton families whose velocities lie outside the range of stability in the presence and absence of anisotropy are discussed.

Electrostatic potential of strongly nonlinear composites: homotopy continuation approach

The homotopy continuation method is used to solve the electrostatic boundary-value problems of strongly nonlinear composite media, which obey a current-field relation of J = σE + χ|E|2E. With the mode expansion, the approximate analytical solutions of electric potential in host and inclusion regions are obtained by solving a set of nonlinear ordinary different equations, which are derived from the original equations with homotopy method. As an example in dimension two, we apply the method to deal with a nonlinear cylindrical inclusion embedded in a host. Comparing the approximate analytical solution of the potential obtained by homotopy method with that of numerical method, we can obverse that the homotopy method is valid for solving boundary-value problems of weakly and strongly nonlinear media.

Optical Bistability in Nonlinear Composite Media

The mean-field approximation method is proposed to investigate the intrinsic optical bistability in nonlinear composite media, which consists of nonlinear metallic granules embedded in nonlinear dielectric host. The effect of nonlinear susceptibility on the bistable behavior is analyzed. It is found that nonlinear metallic granules and nonlinear host medium have different effects and the nonlinearity of metallic granules is more effective in minimizing the threshould value of the bistable behavior. We also investigate the effect of the shape factor of metallic granules on the threshold value.

Optical Bistability in Nonlinear Composite Media

The mean-field approximation method is proposed to investigate the intrinsic optical bistability in nonlinear composite media, which consists of nonlinear metallic granules embedded in nonlinear dielectric host. The effect of nonlinear susceptibility on the bistable behavior is analyzed. It is found that nonlinear metallic granules and nonlinear host medium have different effects and the nonlinearity of metallic granules is more effective in minimizing the threshould value of the bistable behavior. We also investigate the effect of the shape factor of metallic granules on the threshold value.

Second and third harmonic generations in random composites of nonlinear dielectrics

We study the effective nonlinear susceptibility tensor d(−2ω; ω, ω) for second-harmonic generation and χ for third-harmonic generation in a nonlinear composite medium. Simple expressions for these susceptibilities in terms of the position-dependent nonlinear susceptibilities of the constituents and local field factors in a corresponding linear medium are used to evaluate the nonlinear response. These expressions are useful starting points to develop effective medium approximations.

Theory of third harmonic generation in random composites of nonlinear dielectrics

We consider the effective nonlinear susceptibility tensor χ for third harmonic generation (THG) in a nonlinear composite medium in which the components may have nonvanishing second- and third-order nonlinear susceptibilities. We derive an expression for this susceptibility in terms of the positional-dependent second- and third-order susceptibilities within the composite, as well as several factors which describe the local field effect in a corresponding linear medium. We consider both the THG due to the presence of THG susceptibility in the components, and the induced THG due to the presence of second-order nonlinear susceptibilities in the components. The resulting expression can be used to calculate both local field and percolation effects on χ in a wide range of geometries. The general expression reduces to a simple result in the dilute limit, which is similar to that previously derived. An effective medium approximation, which is applicable to the whole range of concentration, is proposed for both the effective second and third harmonic susceptibilities. Results obtained from the general expression and the effective medium approximation are found to be in good agreement with those obtained by numerical simulations for a model system of nonlinear composites consisting of a nonlinear metallic component and a linear insulating component.

Theory of second harmonic generation in composites of nonlinear dielectrics

We consider the effective nonlinear susceptibility tensor d(−2ω;ω,ω) for second harmonic generation in a nonlinear composite medium. We derive a simple expression for this susceptibility in terms of the position-dependent tensor d, and three factors that describe the local field enhancement in a corresponding linear medium. The resulting expression can be used to calculate the local-field enhancement of d in many geometries. In the dilute limit, the general expression reduces to a result previously derived.

Theory of optical bistability in a weakly nonlinear composite medium.

A variational approach is used to discuss bistable behavior in composite media where one component is a nonlinear dielectric while the other has a field independent complex dielectric constant with a negative real part. Under certain conditions, the physical parameters may be adjusted so that bistability appears even though the nonlinear behavior is everywhere weak, thus allowing it to be treated as a small perturbation to the leading linear behavior.

Effective-medium theory of a nonlinear composite medium using the T-matrix approach: Exact results for spherical grains.

Effective-medium theory of a nonlinear composite medium using the T-matrix approach: Exact results for spherical grains.

Light propagation in a two-component nonlinear composite medium

The propagation of intense light through a two-component nonlinear heterogeneous medium is considered by treating the medium as a composite medium. Introduction of dispersion and Kerr-type nonlinear terms leads to a nonlinear Schrödinger-type scattering equation. The effect of nonlinear scattering loss on soliton propagation is studied numerically. The propagation of two oppositely traveling waves is also discussed.

A variational approach to the overall sink strength of a nonlinear lossy composite medium

An extension of the Hashin-Shtrikman variational structure to nonlinear problems, initiated by J. R. Willis (J. appl. Mech. 50, 1202-1209 (1983)) and developed generally by D. R. S. Talbot & J. R. Willis (IMA J. appl. Math.35, 39-54 (1985)) is applied to the problem of homogenization of the semilinear steady-state diffusion equation ∇2c- (∂W/∂c) (c, x) +K(x)= 0, where the functionWis convex incbut varies randomly with positionx. A strict definition for an ‘overall’ functionŴwhich defines the homogenized medium is given and its properties are discussed. Bounds forŴare then developed from variational principles. Classical energy principles yield bounds analogous to the Voigt and Reuss bounds of elasticity theory while the new ‘Hashin-Shtrikman’ structure yields tighter bounds, which are sensitive to the two-point statistics of the medium. Explicit results are presented for a particular two-phase com­posite medium for which one phase is linear (so thatWis quadratic) whereas the second has a quadratic nonlinearity (so thatWis cubic).