Daniela A. Georgieva

Energy transfer between two filaments and degenerate four-photon parametric processes

Recently, energy exchange between two filaments crossing at small angle and with power slightly above the critical for self-focusing Pcr was experimentally demonstrated. In this paper we present a model describing the process of this transfer through degenerate four-photon parametric mixing. Our model confirms the experimental results that the direction of energy exchange depends on the relative transverse velocity (incident angle), laser intensity and initial distance between the pulses (relative initial phase). We also investigate the interaction between two collinear filaments in order to explain the filament number reduction for powers close to Pcr in multi-filamental propagation.

Electromagnetic shock wave in nonlinear vacuum: exact solution.

An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.Contemporary hight-power laser facilities can generate optical pulses with intensities of order 10 W/cm. At the same time the critical power for observation selfaction effects due to virtual electron-positron pairs is of order [1–3] Pcr = λ 2/8n0n2 = 2.5 − 4.4 × 10 24 W, at a wavelength 1 μm. Thus, for a laser pulse with waist r⊥ = 1 mm the corresponding intensity becomes I cr = Pcr/r 2 ⊥ = 2.5− 4.4× 10 W/cm, which is above the range of the new high-power lasers. The nonlinear addition to the refractive index in vacuum depends also on the magnetic field. That is why new different nonlinear effects can be expected. There are not only self-action effects, but also vacuum birefringence [4,6], different kinds of four wave interaction [5, 7, 8] and higher order harmonic generation [9]. In this paper we shall investigate the self-action effect only for intensities of order I cr . Euler, Heisenberg and Kockel [10, 11] predict one intrinsic nonlinearity of the electromagnetic vacuum due to the electron-positron nonlinear polarization. The classical field-dependent nonlinear vacuum dielectric tensor can be written in the form

Avalanche parametric conversion in the initial moment of filamentation

We present experimental and theoretical investigation of the first picoseconds of formation of white continuum from 100 fs laser pulse in 0.5 cm BK7 glass. The theory gives an answer to the question of the physical mechanism of asymmetrical ultra-broadening of the pulses in the initial moment of filamentation. The spectra obtained from the experiment are compared with the spectrum profiles of the physical model and are in very good coincidence.

Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments

We investigate two types of nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing . In the first case we study energy exchange between filaments. The model describes this process through a degenerate four-photon parametric mixing (FPPM) scheme and requests initial phase difference between the waves. When there is no initial phase difference between the pulses, the FPPM process does not work. In this case the second type of interaction is obtained as merging between two, three or four filaments in a single filament with higher power. It is found that in the second case the interflow between the filaments has the potential for interaction due to cross-phase modulation (CPM).

The long range filament stability: balance between non-paraxial diffraction and third-order nonlinearity

We investigate the propagation in air of laser pulses in linear and nonlinear regime. The mathematical model presented in the paper describes the propagation of pulses with narrow-band spectrum, as well as the evolution of broad-band ones. It is shown that the diffraction of pulses with super-broad spectrum or pulses with a few cycles under the envelope is closer to wave type. For such pulses, a new physical mechanism of balance between non-paraxial diffraction and third order nonlinearity appears. We investigate in more detail the nonlinear third order polarization, taking into account the carrier to envelope phase. This additional phase transforms the third harmonic term to GHz terms, which start to generate radiation when the pulse duration reaches the femtosecond range.

Phases of Soliton‐like Solutions in the Scalar‐tensor Theories of Gravity

The aim of the present work is to investigate numerically phases of soliton‐like solutions coupled to non‐linear electrodynamics in the scalar‐tensor theories of gravity. As a result of the numerical experiments new non‐unique solutions of the corresponding boundary value problem and their general properties were found.

Mathematical Modeling of Soliton‐like Solutions in the Scalar‐tensor Theories of Gravity

In the present, work we find new numerical solutions describing soliton‐like objects coupled to non‐linear electrodynamics in the scalar‐tensor theories of gravity. Approximate solutions have been also obtained and a comparison to the numerical results has been made. The non‐existence of black holes for the specific choice of lagrangian of the nonlinear electrodynamics has been also proved.

Charged Black Holes with Massive Scalar Field

In the present work static and spherically symmetric magnetically charged black holes coupled to Euler‐Heisenberg type non‐linear electrodynamics in the scalar‐tensor theories of gravity with massive scalar field are investigated numerically. For the numerical solving of the corresponding boundary‐value problem with free boundary the Continuous Analogue of Newton Method is used. As a result of the numerical experiments some general properties of the solutions were found.