Search

We analyse the electric field transverse distributions in light beams with a tripled frequency and with a frequency of 2ω1– ω2, which arise in the bulk of an isotropic cubic-nonlinear medium upon the propagation of nonuniformly polarised beams of fundamental radiation with a multimode transverse structure described by a superposition of Laguerre – Gaussian modes. A relation is found between the total topological indices of the circular polarisation singularity points in the transverse sections of the generated signal beams and the corresponding total indices in the beams of fundamental radiation.

A theoretical investigation is reported of the influence of the finite spatial size of a pump wave on second-harmonic generation by surface reflection of a two-dimensional Gaussian beam (treated as an example) incident on the surface of a nonabsorbing isotropic gyrotropic medium. Formulas are obtained for expressing the field of the reflected second-harmonic wave in terms of parameters representing the geometry of the problem and in terms of the components of the material tensors which describe the quadratic optical response of the surface and the spatial dispersion of the nonlinearity of the medium. It is shown that in this case the doubled-frequency signal can be represented by a superposition of a two-dimensional Gaussian beam and a non-Gaussian component. This component appears most clearly for normal incidence of the pump wave when second-harmonic generation is altogether impossible in the plane-wave approximation. The inhomogeneity of the surface region and the spatial dispersion of the optical response of the medium are taken into account by adopting modified boundary conditions for an electromagnetic field. These conditions include the surface density of the bound-charge current.

AbstractA sharp drop in saturation magnetization is known to occur within a narrow range of the Fe-Pt alloy composition of nearly 25 at.% Pt. So far the nature of this phenomenon has not been entirely clarified. Fe3Pt alloy different thermal treatment was studied by X-ray diffraction and Mossbauer spectroscopy at room temperature. Owing to different thermal treatments of the alloy having initially a bcc structure, its fcc modification is obtained either in an ordered or disordered state. It is shown that the disordered fcc structure could be in two spin (ferromagnetic and paramagnetic) states whereas the ordered structure has only a ferromagnetic state. The availability of the paramagnetic state in the disordered structure suggests an explanation of the above phenomenon.

A theoretical investigation is made of second- harmonic generation in the interior of an isotropic and gyrotropic medium on a fourth-order optical nonlinearity. It is shown that a correct description of this experimentally detected effect requires taking into account the spatially finite nature of the fundamental-frequency wave, giving rise to a small longitudinal (directed along the beam axis) component of the electric field. Quadrature formulas are derived for the transverse distribution of the second harmonic field and for the total power of the harmonic. A detailed study is made of the special cases of tight focusing of the pump (fundamental-frequency) wave at the centre of a long medium and of exact phase matching. In these cases the quadrature expressions can be reduced to an analytic form. A study is reported of the characteristic features of the transverse profile of the second-harmonic intensity and of the dependence of the harmonic power on the state of polarisation of the pump wave.

We have analysed expressions for the spin part of the density vector of the angular momentum (moment of momentum) of elliptically polarised cnoidal waves and breathers propagating in an isotropic gyrotropic medium with second order frequency dispersion and spatial cubic nonlinearity dispersion. We have found that, due to nonlinear gyration, the density of the angular momentum depends on time and propagation coordinates.

Using the example of the interaction of two cnoidal waves with essentially different periods, we compare the results of the application of the adiabatic approximation and its simplified version in the process of solving a nonintegrable system of nonlinear Schrödinger equations. The time boundary of the region of applicability of the simplified adiabatic-approximation version is estimated.

We analyse the evolution of the spectra of an approximate solution of the adiabatic interaction problem of two waves with orthogonal circular polarisations in an isotropic gyrotropic nonlinear medium with the second-order group velocity dispersion. It is shown that a gradual ‘chaotisation’ of the approximate solution for the amplitude of a rapidly changing wave is associated with its non-equidistant frequency spectrum.

Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportional to two different elliptic Jacobi functions with the same periods.

The adiabatic approximation is used to obtain an analytical solution to a nonintegrable problem of propagation of a plane elliptically polarised light wave with zero mean amplitudes of orthogonal circularly polarised field components through an isotropic gyrotropic medium with local and nonlocal components of Kerr nonlinearity and second-order group velocity dispersion. We describe the aperiodic evolution of bound (attributable to the medium nonlinearity) paired states, which are responsible for the propagation of two orthogonal polarisation components – cnoidal waves with significantly different periods.

Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and ‘chaotic’ change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed.

We have analysed self-similar solutions to the propagation problem of a slit beam with a plane wavefront in a linear medium and in a photorefractive crystal with diffusion nonlinearity. It is shown that in the latter case, despite the presence of the nonlinear term in the wave equation, the linear superposition principle holds true for the solutions of this class due to saturation. At the same time, the mirror symmetry violation of the wave equation for the transverse coordinate in the nonlinear case and the requirement to the spatial localisation modify one of the localised partial solutions (Airy beam) to the corresponding linear problem and prohibit the existence of other solutions of this class.