We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.

We study numerically the localization properties of eigenstates in a onedimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual localization anomalies where a weaker localization is observed, the localization of the eigenstates near the band center is strongly enhanced in the present non-Hermitian model. This phenomenon is associated with the occurrence of a large number of strongly-localized states with pure imaginary energy eigenvalues.

When surface plasmons are excited at a metal-dielectric interface, the electromagnetic field takes a very large value near the interface. If the dielectric is a nonlinear Kerr medium, then the effect of nonlinearity can be greatly amplified due to the field enhancement. In this paper, we calculate the lateral shift of p wave beams incident on metal-dielectric multilayer systems in the Otto configuration in a numerically exact manner, using the invariant imbedding method of wave propagation in nonlinear stratified media. In the linear case, we find that the lateral shift becomes very large at the incident angles where the surface plasmons are excited. As the nonlinearity is turned on, the value of the lateral shift changes rapidly. We find that even a small change of the intensity of the incident wave can cause a huge change of the lateral shift. We propose that this phenomenon can be applied to designing precise optical switches operating at small powers.

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