Surface optical waves at the boundary with a nonlinear Kerr medium

A rigorous solution consistent with a plane wave approximation is given to the boundary problem for Maxwell’s equations for surface optical waves at the boundary with a nonlinear Kerr medium. Exact formulas for the flux intensity (J ₀) and energy density (W ₀) of these waves are derived depending on the parameters of the adjacent media and the propagation constant (ξ). It is shown that these variables as functions of ξ have minima. Thus, J ₀ and W ₀ increase sharply as the propagation constant deviates from the minimum value ξ_min. Their values are greater, the larger the difference between the dielectric constants of the linear and nonlinear media is. An expression for the propagation velocity of a nonlinear surface wave is also obtained.     

Surface waves at the boundary of a chiral medium

The exact analytical solution of the dispersion relation for the propagation constant of the surface waves existing at the plane interface between chiral and magnetodielectric media is given and studied. An enhancement of the chirality effect due to matching of the permittivities of the media is noted.     

Energy exchange between parametric modes in a nonlinear optical medium

The behaviour of a nonlinear atom-field model for parametric oscillation is analysed. Constants of motion are found from which energy relations are obtained. Numerical results concerning the evolution of photon numbers and the atomic inversion stemming from given atom-field initial states are presented.     

Photon reflection at the boundary of an inverted medium

The index change near a quantum transition is shown to cause significant feedback into a gain medium. Criteria are given for the onset of self-lasing in an extended material. The distortion of a reflected pulse is also considered.     

On the nonlinear dynamics of a saline boundary layer formed by throughflow near the surface of a porous medium

We consider gravitational instability of saline boundary layers, observed at the subsurface of salt lakes. This boundary layer is the result of the convective transport induced by the evaporation at the horizontal surface of a confined porous medium. When this upward transport is balanced by salt dispersion, a steady state boundary layer is formed. However, this boundary layer can be unstable when perturbed. This results in complex groundwater motion and density fields. The aim of this paper is to investigate the existence of finite amplitude solutions describing these resulting patterns (both the number of solutions and their structure), their stability, and their dependency on the system Rayleigh and Péclet numbers. For this purpose we construct a low-dimensional dynamical system (a reduced model) by projecting the nonlinear model equations onto a relatively small set of eigenfunctions of the problem linearized at criticality. The Galerkin projection approach is complicated by the fact that the problem under consideration is non-self-adjoint due to the existing evaporation. This implies that the eigenfunctions do not form an orthogonal set and therefore the adjoint eigenfunctions are used for the projection. The reduced model is constructed in such a way that it is capable of providing solutions in the strongly nonlinear regime as well. Convergence of these solutions towards the fully nonlinear model results is shown by means of direct numerical simulations. Further, the reduced model seems to partly capture the complex nonlinear behavior as seen in Hele-Shaw experiments by Wooding et al. [R.A. Wooding, S.W. Tyler, I. White, P.A. Anderson, Convection in groundwater below an evaporating salt lake: 2. evolution of fingers or plumes, Water Resour. Res. 33 (6) (1997) 1219-1228]. The physical transition mechanism that explains the occurrence of some observed bifurcation types is presented as well.     

Basic properties of nonlinear surface charge waves at a plasma boundary

The nonlinear properties of surface charges are here analyzed under ideal conditions. We thus deduce a new single equation from the wellknown equations which govern the cold electron plasma motion. Simple formulas that describe the propagation of surface charge perturbations along the plasma boundary are also found.     

Corrections to the classical continuity boundary conditions at the interface of a composite medium

Using the multiple-scales homogenization method, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the interface between two media, one of which is free-space and the other a certain type of composite material. The parameters in these new boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the composite. We show that the effective tangential E and H fields are not continuous across the interface except in the limit when the lattice constant (the spacing between the scatterers—atoms, molecules or inclusions in the case of a composite material) of the composite medium is very small compared to a wavelength. We derive first-order corrections to the classical continuity conditions. For naturally occurring materials whose lattice constants are on an atomic scale, these effects are shown to be negligible for waves at optical frequencies or lower. However, once the lattice constant becomes a significant fraction of a wavelength (which is the case for many artificial dielectrics and metamaterials), the corrections can be important. In previous work we have alluded to the fact that such a GSTC is needed to correctly account for the surface effects when extracting the effective material properties of a metamaterial. The results of this current paper justify the assumptions made in that previous work. In general, these GSTCs will result in corrections to the classical Fresnel reflection and transmission coefficients (which are themselves merely zeroth-order approximations to the actual reflection and transmission coefficients), and in a separate publication we will use these GSTCs to address this issue.     

Reflection of quadratic solitons at the boundary of nonlinear media

We report experimental evidence of soliton reflection at the boundary of quadratic nonlinear media. The evolution of beams incident upon the interface of periodically poled LiNbO3 and uniform LiNbO3 is considered; in the whole device the linear refractive index is homogeneous. Linear beam transmission and soliton reflection at the nonlinear phase-mismatched boundary were observed. Numerical simulations that correspond to the experiments are also presented.     

Soliton emission at a phase-mismatch boundary in a quadratic nonlinear film waveguide

We report the experimental demonstration of spatial nonlinear beam displacement caused by an interface between periodically modulated and uniform quadratic nonlinearity. We observe intensity- and phase-mismatch-dependent spatial beam displacement at 1548 nm in lithium niobate waveguides. The device has the potential to provide a soliton-emission-based, ultrafast all-optical switch.     

Optical surface <Emphasis Type="Italic">TM</Emphasis>-waves at the boundary of a nonlinear Kerr-type medium

Solutions for a nonlinear system of Maxwell’s equations and for a corresponding boundary problem describing the propagation of a surface TM-wave (p-polarization) along an interface with an optically nonlinear Kerr-type medium are presented. An analytical expression for the intensity of an integrated flux J₀ carried by such a wave along the interface between two media has been derived as a function of both the wave propagation constant ξ and the optical characteristics of the adjacent media. It is shown that flux intensities corresponding to the same values of the propagation constant ξ are much smaller for p-polarization than for s-polarization.