Nonlinear Dynamics and Optics

Based on an improved cavitation model for the electron dynamics, an exact analysis is presented of the generation of axial magnetic fields in the relativistic self-focusing channels produced by circularly polarized light in plasmas. Two kinds of waveguiding structures are considered: single-channel waveguides and plasma filaments surrounded by a light field. It is found that due to large electron density gradients in the cavitation plasma, magnetic fields of megagauss values with opposite directions separated by a neutral sheet, where the magnetic field passes through zero, can be produced.

An analysis is made of the phenomenon of self-induced erosion and spectral breaking of ionizing high-power microwave pulses propagating in a gas. The analysis describes in an analytically explicit and physically clear way the consistent interaction between the microwave pulse and the self-induced breakdown plasma. In particular, it clarifies, both qualitatively and quantitatively, the mechanisms behind the pulse erosion and the spectral breaking phenomenon, i.e. the splitting of the pulse spectrum into a redshifted and a blueshifted peak as observed in numerical simulation results as well as in experiments.

Two scenarios for the penetration of relativistically intense laser radiation into an overdense plasma, accessible by self-induced transparency, are presented. For supercritical densities less than 1.5 times the critical one, penetration of laser energy occurs by soliton-like structures moving into the plasma. At higher background densities laser light penetrates over a finite length only, that increases with the incident intensity. In this regime plasma-field structures represent alternating electron layers separated by about half a wavelength by depleted regions.

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.

An exact analytical investigation of the stationary solutions describing the interaction between high-intensity laser radiation and an overdense plasma is presented. Both the relativistic and striction nonlinearities are taken into account, and their joint action gives rise to a solitary solution. This solution clearly shows that there exists an inherent limit of the induced transparency on the density of the overdense plasma in order to obtain a stationary physical solution. Furthermore, it is found that the striction nonlinearity tends to create a strong peaking of the plasma electron density, which suppresses the laser penetration and significantly enhances the threshold intensity for induced transparency.

The theory of strong frequency upconversion of the powerful ionizing electromagnetic radiation in gases is presented based on the modified nonlinear geometrical optics approximation. The permanent spectrum upshift versus propagation path, exceeding considerably the initial frequency, is demonstrated without strong wave dissipation for the cases of impact and field-induced ionization in the high-intensity field range. Reflectionless propagation into the supercritical plasma and broad-band tuning of the laser radiation are emphasized as highly promising physical applications of the phenomenon described

The properties of microwave-induced breakdown of
air in narrow metallic slots are investigated, both theoretically and
experimentally, with emphasis on factors important for protection
against transmission of incident high-power microwave radiation.
The key factors investigated are breakdown power threshold,
breakdown time, peak-leakage power, and total transmitted
energy, as functions of incident pulse shape and power density.
The theoretical investigation includes estimates of the electric
field intensification in narrow slots and basic breakdown plasma
modeling. New results important for application to the high-power
microwave field, such as the influence of pulse shape on breakdown
time and peak-leakage power, are presented. The experimental
investigation comprises a set of slot breakdown experiments at
atmospheric pressure, which are analyzed to extract key parameters,
such as transmission cross section, breakdown time, peak
leakage power, and transmitted energy. The experimental data
is compared and shown to be in good agreement with results
obtained in the theoretical investigation.

The structure and stability of the ionization front, which occurs as a high intensity electron beam propagates through an insulator, are considered. It is found that, due to the electric field ionization, the velocity of the front, V_f , has a nonmonotonic dependence on the beam density, n_b , and in some particular beam density range V f increases with increasing n_b . Two instabilities of the ionization front associated with the electric field ionization process of the insulator are found: a long wavelength (few micron) and relatively slow (10^13 s^-1) corrugation instability and a short wavelength (submicron) and relatively fast (few.10^13 s^-1) electric field ionization instability.

A novel explanation of the relativistic self-induced transparency effect during superintense laser interaction with an overdense plasma is proposed. It was studied analytically and verified with direct modeling by particle-in-cell simulations. Based on this treatment, a method of ultrashort high-energy electron bunch generation with durations on a femtosecond time scale is also proposed and studied via numerical simulation.

A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play.
An exact analysis of a circularly polarized laser interacting with plasmas is presented. We define fundamental notions, such as nonlinear dielectric permittivity, ponderomotive and dissipative forces acting in a plasma. Plasma-field structures arising during the ultra-relativisitc interactions are also calculated. Based on these solutions, we show that about 50% of laser energy can be converted into gamma-rays in the optimal conditions of laser-foil interaction.

xact soliton solutions containing only a few cycles are found within the framework of a nonlinear full wave equation in a Kerr medium. It is proven numerically that they are stable and play a fundamental role in the pulse propagation dynamics. These wave solitons cover the range from the fundamental Schrödinger solitons, which occur for long pulses involving many field oscillations, to extremely short pulses, which contain only one optical period.

A basic set of equations describing the interaction of a Bose-Einstein condensate (BEC) with a laser field is derived based on a semiclassical model and applied to the problem of mutual guiding of laser and BEC atomic beams. Within this framework we have studied stationary spatially localized solutions of the nonlinear system which describe possible laser and BEC atomic beam guiding and have shown their stability as well. It is also
shown that a self-guiding effect can be realized through both single- and multiple-scaled structures of a BEC atomic and a laser beam.

We have studied the details of the formation of mutually guided and localized structures of co-propagating coherent electromagnetic radiation and a Bose-Einstein condensate (BEC). In the limit of zero temperature and large detuning, we have used a semiclassical model based on Maxwell equations coupled to the Schrodinger equation which includes the back action of the atoms on the radiation. Following numerically the two systems, we have found that a variety of effects can be displayed depending on the initial conditions: The formation of
single-hump mutually guided structures of atoms and radiation seems to be only one of the possible outcomes of the interaction. Other effects we have observed via numerical simulations are, for instance, the creation of atom-laser solitarylike structures which are then symmetrically ejected from the initial central peak or similar symmetrical structures trapped in a bound state and thus oscillating about the central point in a way somehow reminiscent of purely nonlinear optics effect.

We present a class of few-cycle elliptically polarized solitary waves in an isotropic Kerr medium. It is proved numerically that they are stable and can be easily excited during pulse propagation. We also propose a method of producing multisolitons with different polarization states and study their binary collisions. It is shown that collisional properties strongly depend on their relative polarization rotation.