Andrey I. Konukhov

Numerical studies of beam and pulse propagation in lasers and nonlinear media: Transverse pattern dynamics and nonparaxial effects☆

Abstract A review of recent work in numerical modelling of transverse pattern formation and dynamics in lasers and nonparaxial beam propagation is presented. The algorithms developed involve the field decomposition in terms of the Gaussian-Laguerre modes. Three models are discussed in detail. In the first one, the transverse pattern evolution of a short pulse in a ring unidirectional laser with a homogeneously broadened optically thin active medium is considered under the approximation of transversely synchronous pulse. The pulse-train envelope and transverse pattern dynamics are studied numerically using more than 200 empty cavity modes. In the second model the limitation of thin active medium is removed, and the propagation of self-acting beam through the active medium of arbitrary thickness is taken into account solving the conventional paraxial wave equation. Stationary regimes with deformed modes, quasi-periodic oscillations, and mode-locking regimes are observed. Phase singularities (optical vortices) in the transverse field pattern are demonstrated. In the third model, the Gauss-Laguerre decomposition is used to solve the Helmholtz equation describing wide-angle (nonparaxial) beam propagation in nonlinear media. The role of backward waves in wide-angle Kerr self-focusing is discussed.

Pulse-train dynamics simulation in Kerr-lens mode-locked solid state laser using a full spatiotemporal numerical model

A full spatio-temporal model of the Kerr-lens mode-locking laser is first presented. Nonlinear dynamics of the Z-cavity Ti:Sph laser with Kerr-lens mode locking is numerically investigated.

Transverse pattern dynamics in a short-pulse mode-locked solid-state laser

Abstract The transverse pattern evolution of pulse in a ring unidirectional laser with a homogeneously broadened active medium is considered under the approximation of transverse synchronous pulse. The pulse-train envelope and transverse-pattern dynamics are investigated numerically using field decomposition including more than 200 empty-cavity modes.

Polarization transverse pattern dynamics in lasers with anisotropic cavities

Polarization transverse pattern dynamics in lasers with an image-rotating cavity is studied taking the Zeeman sublevel structure of the lasing transition into account. For a class-A laser with an arbitrary transverse mode number, the field dynamics and the regimes of oscillations have been investigated numerically.

Dynamics of polarization transverse patterns in lasers

Short review of the papers on transverse and polarization transverse pattern dynamics in lasers is presented. The theoretical and numerical models are discussed including cavities with image rotation and allowing for the Zeeman sublevels structure of the lasing transition. The results of numerical modelling of the field dynamics, oscillation regimes, and effect of the spontaneous emission on the pattern resulted are presented and discussed for the class A lasers with the polarization isotropic cavity and unlimited transverse mode number.

Kinetics of defects and phase curves in transverse pattern of lasers

Different behaviors of isophase curves presenting zero values of the real and imaginary parts of the transverse varying scalar electric field of a laser are presented. We illustrate how phase singularities (isophase crossings) might evolve by variation of the amplitudes of superposed Laguerre-Gaussian cavity modes. These show the formation of closed loops and kinks. Numerical simulations of the transverse pattern dynamics give similar forms of phase singularity motion and evolution.

Generation of THz radiation based on Raman effect in photonic crystal fiber

We propose a method of generation terahertz radiation based on difference frequency mixing of colliding femtosecond pulses in the wavelength range 1550 nm. Obtaining a defined frequency difference is due to stimulated Raman soliton generation via splitting of multisoliton replica pulses in a photonic-crystal fiber. Pulse train is generated by a single laser. The results of numerical simulation of such process, based on the solution of the modified nonlinear Schrödinger equation, which includes the impact of higher-order dispersion, the optical Kerr effect and Raman amplification are presented. One of the easiest ways to generate pulses with a frequency difference is to use the fibers with variable dispersion.

Spatio-temporal carrier dynamics of a dualwavelength vertical external cavity surface-emitting laser

The mathematical model of a dual-wavelength emission from a vertical external cavity surface-emitting laser taking into account the transverse distribution both of optical fields and pump carrier flux density is built. Spatio-temporal dynamics of charge carriers and photons is analyzed. It is shown that the most pronounced optical hole-burning can be observed near the optical axis of the laser.

Femtosecond soliton supercontinuum generation in anisotropic microstructure fibre

The polarization anisotropy of microstructure fibre may be introduced especially to provide more possibilities to control the supercontinuum production. Thus polarization degree of freedom should be incorporated to the numerical model. In this paper we analyze numerically the supercontinuum generation in the microstructure fibres with periodically modulated holes ellipticity. Femtosecond pulse propagation in single mode microstructure fibre was described by NSE-type equation, including Raman delayed response. Propagation constant of fundamental mode was calculated by a full vector numerical model based on the plane-wave method. The holes ellipticity was assumed to be periodically modulated along the fibre with the period near 10 mm. The results are the next: ellipticity (no modulation) leads to spectrum splitting which decrease when ellipticity goes to 1. The splitting is about 15 THz for ellipticity 0.5. The pulses in both polarizations were split into solitonic part (un-shifted) and two delayed Raman solitons (also un-shifted). For larger ellipticity the solitonic and Raman soliton pulses acquire temporal shift up to 7000 fs. Modulation of the ellipticity leads to spectral broadening and disappearing of the spectral gaps between spectrum of solitonic part and dispersion wave. Controlling the fibre anisotropy allows to generate the pulses with different polarization having control temporal and spectral shift.

Generation of two colliding pulses with tunable THz-range frequency difference in high-nonlinear photonic crystal fiber

Two-wavelength light sources are of interest for THz-range oscillators based on difference frequency generation [1–5], and also for the oscillators, based on the optical rectification [6]. Easy way to produce pulses with frequency difference is the use of dispersion oscillating fiber [7]. We discuss the possibility to use a highly nonlinear photonic crystal fiber for generation the overlapping pulse pairs with the difference of carrier frequencies in THz range from femtosecond pulses train from only one laser. First, each pulse from the laser should be duplicated using beamsplitter. Then the pulses should be launched sequently into photonic crystal fiber. The pulse frequency is to be in anomalous dispersion regions, and pulses are to be high-order solitons. Due to Raman effect these solitons split to fundamental soliton with red shift and other smaller pulses with nonshifted frequency. Due to group velocity dispersion (GVD) the Raman-shifted pulse propagate slower depending on pulse parameters. Thus there exist some definite length in the fiber where Raman-shifted pulse collides with unshifted pulse. This distance and the value of the shift can be controlled by pulse parameters and depend on the fiber parameters. The results of numerical modeling of the nonlinear propagation of multi-soliton pairs of pulses in photonic crystal fiber are presented below.