Andrei V. Lavrinenko

Dielectric multilayer waveguides for TE and TM mode matching

We analyse theoretically for the first time to our knowledge the perfect phase matching of guided TE and TM modes with a multilayer waveguide composed of linear isotropic dielectric materials. Alongside strict investigation into dispersion relations for multilayer systems, we give an explicit qualitative explanation for the phenomenon of mode matching on the basis of the standard one-dimensional homogenization technique, and discuss the minimum number of layers and the refractive index profile for the proposed device scheme. Direct applications of the scheme include polarization-insensitive, intermodal dispersion-free planar propagation, efficient fibre-to-planar waveguide coupling and, potentially, mode filtering. As a self-sufficient result, we present compact analytical expressions for the mode dispersion in a finite, N-period, three-layer dielectric superlattice.

Analytical derivation of spectral scalability in self-similar multilayer structures

Optical spectra for fractal multilayer structures have been shown to possess scalability. The scaling relations, as well as analytical derivation of scalability on the basis of the structures geometrical self-similarity, have been established.

Polarization spectroscopy with arbitrary polarized noncollinear pumping

We present a theoretical analysis of a noncollinear polarization-spectroscopy (PS) scheme, taking into account the polarization incoherence of an arbitrarily polarized pump beam. It is based on a light-induced anisotropy (LIA) tensor formalism. Our most important results are analytical expressions for the LIA tensor, which permit classification of the nonlinear medium with LIA in terms of the polarization properties. An expression is derived for the dependence of the PS-signal intensity on the beam-crossing angle, and the usefulness of that expression for spectroscopic purposes is demonstrated.

Scaling properties of multilayer fractal structures

Multilayer fractal structures, being a subclass of nonperiodic yet deterministic media are studied in relation to the problem of classical wave propagation. A general case of fractal multilayers is considered. Numerical calculations reveal that the geometry and optical spectra of such structures are directly connected. Namely, it has been found that structures and spectra exhibit exactly the same scaling relations, which are easily derived from the parameters used in the stack construction procedure. Sharp resonant transmission peaks are found to split when the number of generation of the fractal structure increases, and the number of components in such split multiplets is again directly linked to the stack geometrical features. Treating a multilayer structure as a complex coupled-cavity system yields straightforward physical explanations of the properties found. Likeness of fractal properties to occur in the spectra of fractal multilayers is discussed.

Theory of optically heterodyned polarization (vectorial) interferometry on the basis of Fedorov's covariant approach

We present consistent theoretical studies of optically heterodyned polarization interferometry (OHPI) with noncollinear arbitrary polarized interacting beams in the framework of the cubic nonlinear optical susceptiblity formalism. Our theoretical treatment is based on the covariant tensorial approach introduced by F I Fedorov. We were able to derive the analytical expressions for the detected OHPI signal. Different methods for measuring the nonlinear susceptibility are also suggested.

Free-coordinate formalism for nonlinear photoanisotropy optics description and light propagation effects in periodic anisotropic structures

A theoretical study of two-wave polarization spectroscopy signal dependencies on crossing angle is presented. The quantitative expressions are obtained, which are in good agreement with the experimental data. The advantages of free-coordinate operator method are illustrated under treatment of band-gap formation in anisotropic stratified periodic structure problems. A method for radiation control based on pumping wave polarization tuning is proposed.

OPTICAL WAVES IN ONE-DIMENSIONAL FRACTAL INHOMOGENEOUS MEDIA

Fractal multilayer structures as a class of deterministic non-periodic discrete inhomogeneous media are investigated on the basis of classical wave propagation. This includes optical properties of dielectric layered media and quantum particle behaviour in a fractal stepwise potential. The primary focus of the present review is drawing a correlation between topological properties and eigenvalue spectra. Namely, it is shown both numerically and analytically that geometrical self-similarity of fractal structures directly results in spectral scalability. Some other spectral properties resulting from minor topological details of fractal multilayers (such as resonance peak splitting and spectral self-similarity) are considered.

Optical properties of fractal Cantor-like multilayer nanostructures

Optical properties of fractal Cantor-like multilayer nanostructures are investigated numerically and experimentally. Strong correlation between the stack geometry and the properties of optical transmission spectra is found, namely spectral scalability and sequential splitting. A good agreement is achieved between the experimentally measured and calculated spectra.

New peculiarities of spectroscopic measurements with noncollinear scheme and nonpolarized light

We present theoretical analysis of noncollinear two-wave spectroscopic schemes taking into account polarization incoherence of arbitrary polarized pumping. Our very general treatment is based on a coordinate-free method of wave operators. The analytical expressions for the signal dependencies on beam-crossing angle (noncollinearity angle) and polarization parameters have been obtained for the cases of saturation spectroscopy, nonlinear polarization spectroscopy and optically heterodyned polarization interferometry (OHPI). The comprehensive studies of the OHPI scheme with noncollinear partially polarized light are given. Three different methods of nonlinear susceptibility measurements are suggested.

Effective anisotropic plane-stratified polarizer and its optimization by the analysis of density of modes

For a bilayered, N-period, photonic band gap (PBG) structure produced of anisotropic and isotropic layers, we derive analytic expressions for the tensorial density of modes (DOM) and optical transmittance of the structure as a whole. The computations of the DOM-tensor for different physically realizable PBG structures prove the possibility of considerable enhancement of one normal electromagnetic mode and simultaneous depression of the other one. This effect, which is called polarization selection of modes in anisotropic one-dimensional PBG crystals, enables us to design an effective plane-stratified polarizer working in near-optical frequency range, totally reflecting one normal mode and transmitting the other.