Aleksey I. Bychenkov

Numerical modeling technique for waveguides: quality of the modified method of moments

Recently developed version of the modified generalized method of moments for misaligned astigmatic beams in nonlinear waveguides is compared with the direct numerical scheme making use of Gauss-Laguerre decomposition of the asymmetric beam profile. It is demonstrated that the approximation of the beam by a flexible generalized Gaussian function provides a correct description of the global beam behavior even for relatively strong nonlinearities.

Numerical modeling of light beam propagation in nonlinear waveguide media: effects of misalignment and inhomogeneous broadening

Using the modified generalized method of moments the equation of motion are derived for the parameters of a misaligned astigmatic Gaussian beam with torsion in an axially symmetric nonlinear medium. Nontrivial features of beam dynamics are revealed in a parabolic waveguide with Kerr nonlinearity. Peculiarities of near-resonance self- action of an axial beam depending upon the Lorentz-to- Doppler linewidth ratio are analyzed numerically.

Some new approaches to modeling wave packets of Rydberg states

We propose an approximate method for modeling the so-called Trojan wave packets of Rydberg states in a hydrogen-like atom subjected to a circularly polarized microwave field and a constant magnetic field. The method implies the reduction of the Schrodinger wave equation to a set of ordinary nonlinear differential equations for the parameters of the wave packet. Earlier we applied this method to solve the Schrodinger-like parabolic equation in nonlinear optics to describe misaligned beams in waveguide systems. The optimal values of the wave packet initial parameters are obtained. The numerical solution of the obtained differential equations show, that for these parameters the Trojan wave packet moves along a circle orbit.

Laser-induced and spontaneous formation of Saturnian hydrogen atoms in low-density plasma

Non-dispersing wave packet states of the electron in a hydrogen atom in constant magnetic and rotating electric fields are considered. These states, referred as the states of Satrurnian atom, may be presented as eigenstates of an effective Hamiltonian in the coordinate frame rotating with the electric field. We start from solving the eigenvalue problem in the plane zequals0 of the electron wave packet orbit. General approach valid for arbitrary z is formulated in terms of the solutions of a parametric eigenvalue problem. The results of 2D calculations are used to justify the rough approximation for the wave functions of the ground oscillatory and the continuum states. Using these functions the probabilities of induced and spontaneous transitions from the lower continuum state to the ground state of a Saturnian atom are roughly estimated in a very simple analytical way.

New approaches to modeling the dynamics of misaligned beams in nonlinear gradient waveguides

The propagation of a misaligned paraxial beam through a nonlinear waveguide medium can be presented as a nonlinear dynamical problem, where the longitudinal coordinate z plays the role of time, while the transverse pattern of the field is the dynamical system evolving with z. The reduction to a finite-dimensional system is possible within the framework of the approximate method using Gaussian probe functions whose parameters are determined by Galerkins criterion in the basis of a small number of flexible Gaussian modes. This method is referred as the modified generalized method of moments (MGMM). Using the MGMM we studied the dynamics of an off-axis initially Gaussian beam propagating through a Kerr nonlinear parabolic waveguide and revealed stationary, periodic and quasiperiodic regimes, as well as nontrivial phenomena, such as phase locking, cycle generation, etc. In particular, the behavior of the beam variables in the vicinity of the stationary states was analyzed. However, direct numerical modeling shows significant non-Gaussian distortions of the beam caused by Kerr nonlinearity, so MGMM is expected to describe correctly the dynamics of the beam moments rather than the field transverse pattern itself. To check this idea alternative approaches are desirable. The method proposed here involves the exact numerical calculation of nonlinear modes followed by the linear analysis of small nonstationary perturbations of these modes based on Bogoliubovs equations.

Modeling of off-axis Gaussian beams in elliptical waveguides: application to mode-locking devices

In contrast to the earlier papers devoted to misaligned beams in circular waveguide media, in the present paper we consider an elliptical gradient waveguide with parabolic transverse profile of linear refraction index and Kerr nonlinearity. In our analysis of the beam dynamics we focus our attention at the features promising for application in mode-locking devices.

Astigmatic twisted beams: reducing the peak intensity in high-power waveguides

We show that under the condition of local field limitation the total power transported through a waveguide can be substantially increased using twisted astigmatic generalized Gaussian beams. Numerical modeling of such beams in a parabolic waveguide with Kerr nonlinearity is carried out basing on the modified generalized moments method. The conditions are found that provide the optimal propagation regime in which the fixed-size beam spot rotates uniformly around the beam axis. It is shown that in this regime the peak intensity of the beam may be sufficiently lower than in stable axially-symmetric beams of the same total power.

Numerical scheme with external complex scaling for 2D Schroedinger equation in paraxial optics

We propose a stable numerical scheme for solving Schrodinger equations that arise in the scalar paraxial theory of optical waveguides as well as in the quantum mechanics of a particle in a potential field. The scheme makes use of a multi-coordinate version of the split-step approach combined with the complex scaling that assures the implementation of boundary conditions. Beam propagation in a Gaussian waveguide is considered to illustrate the ability of the scheme to account for both waveguide and radiation modes.

Reduced numerical models for misaligned beam propagation dynamics in nonlinear gradient waveguides

We briefly summarize our results based on the modified generalised moment method (MGMM) approach to misaligned beam dynamics in waveguides having parabolic profile of the linear refraction index and homogeneous Kerr nonlinearity. The limitations of the model are analysed. A more realistic model that allows direct application of MGMM and takes the leaky modes into account is proposed. Comparison with direct numerical solution of the paraxial wave equation in the symmetric case is carried out. General limitations of MGMM to transit phenomena that take place at the initial staged of propagation are discussed.

Long-trace behavior of a misaligned astigmatic twisted beam in a dissipative nonlinear waveguide

General properties of the dynamical model describing the propagation of a misaligned astigmatic twisted Gaussian beam in axially symmetric nonlinear waveguides are studied. Nontrivial dynamical regimes are revealed in different types of waveguide media including those with dissipation and possible applications are discussed.