Self-focusing Regime Research Articles

Characteristics of filaments during high-power femtosecond laser radiation propagation in air and water: I. Qualitative analysis

The problem of propagation of high-power femtosecond laser pulses in a self-focusing regime and formation of filaments is considered. Comparative analysis of key parameters of the filaments formed in a laser beam in two physically distinct media (atmospheric air and water) is carried out. It is established that the cardinal distinctions in optical parameters of water and air, and, first of all, in values of the Kerr coefficient, chromatic dispersion, and photoionization probability of molecules lead to changes in key characteristics of light and plasma filaments generated in the channel.

Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium

Propagation of an asymmetric Gaussian beam in a cubic-quintic absorbing medium is analyzed and compared with that of a symmetric beam in both lossless and lossy media. A ``collective variable approach'' technique, based on trial functions, is used for solution of the general nonlinear Schr\odinger equation. Using this variational approach, we investigate the self-focusing and breathing of an intense asymmetric Gaussian beam, taking into account both linear and nonlinear absorption. For a lossless medium, we define regions of oscillatory and diffractive beam propagation, for both symmetric and asymmetric beams. In particular, for an asymmetric beam, we find that there is no sharp boundary between the oscillatory self-focusing and oscillatory diffractive regimes of propagation. In the oscillatory region, we detect an interesting phenomenon---``beats'' of the amplitude and perpendicular widths of the beam. For a lossy medium, significant differences between the amplitudes, widths, and phases of the symmetric and asymmetric beams have been predicted.

Filamentation of high-power laser radiation in air and water: Comparative analysis

The propagation of high-power femtosecond laser pulses is considered in the self-focusing and filamentation formation regime. Similarities and differences in the character of the laser beam filamentation are analysed qualitatively and quantitatively in the atmospheric air and water. Based on the numerical results, the most important parameters (radius, intensity, free electron density) in light and plasma filaments produced by ultrashort laser pulses are shown to depend strongly on the optical parameters of the propagation medium, and, first of all, on the Kerr nonlinearity coefficients and the photoionisation rate of the medium molecules.

Nonlinear surface waves in one-dimensional photonic crystals containing left-handed metamaterials

The nonlinear TE-polarized surface waves localized at the interface between a nonlinear uniform material and a semi-infinite one-dimensional photonic crystal are investigated. We assume that the nonlinear material is right handed and the photonic crystal is made of alternate left-handed metamaterial and right-handed material. We study the intensity-dependent properties of the nonlinear surface waves for both self-focusing and defocusing Kerr-like nonlinearity. Unlike the linear regime, it is shown that in the case of self-focusing nonlinearity the dispersion curve has two branches corresponding to two types of surface mode structures (one structure with a hump at the interface and the other one with two humps). While, in the case of defocusing nonlinearity the dispersion curve has a single branch. We also show that the existence region of the surface waves is intensity dependent (independent) in the case of self-focusing (defocusing) nonlinear regime and the presence of left-handed materials and nonlinear medium provides a possibility for forward or backward waves selection in the given structure by adjusting the intensity parameter at the interface.

Sub-critical regime of femtosecond inscription

We apply well known nonlinear diffraction theory governing focusing of a powerful light beam of arbitrary shape in medium with Kerr nonlinearity to the analysis of femtosecond (fs) laser processing of dielectric in sub-critical (input power less than the critical power of self-focusing) regime. Simple analytical expressions are derived for the input beam power and spatial focusing parameter (numerical aperture) that are required for achieving an inscription threshold. Application of non-Gaussian laser beams for better controlled fs inscription at higher powers is also discussed.

Self-focusing and defocusing of self-similar π pulses in an amplifying two-level medium

The effect of transverse perturbations on the propagation of electromagnetic π pulses in an amplifying two-level medium is studied. The cases of quasi-monochromatic and extremely short pulses are considered. The equations describing the behavior of the transverse size of the pulse during its propagation in the medium are derived. It is shown that, if the ratios of the diffraction length to the length of dispersion spreading are smaller than certain critical values, self-focusing regimes are realized for both types of pulses. Otherwise, at a finite distance, blowup of defocusing occurs, after which the amplified pulse propagates as if it is a one-dimensional pulse, with the velocity equal to the velocity of light in vacuum. Similarities and distinctions in the dynamics of propagation of extremely short and quasi-monochromatic pulses are indicated.

The Influence of Transverse Perturbations on the Propagation of Picosecond Acoustic Pulses in a Paramagnetic Crystal

The influence of transverse perturbations on the dynamics of a picosecond soliton-like acoustic pulse in a paramagnetic crystal in an external magnetic field is investigated. The nonlinear and dispersion effects are governed by the intrinsic properties of the crystal and the spin-phonon interaction. The effect of different nonlinear mechanisms and an external magnetic field on the stability against transverse perturbations is analyzed. It is shown that, in the absence of paramagnetic impurities, there can exist only a compression pulse that propagates in a defocusing regime. In the presence of paramagnetic ions in the crystal, there can arise rarefaction pulses that, under specific conditions, can propagate in self-focusing and self-channeling regimes.

Instability versus equilibrium propagation of a laser beam in plasma.

We obtain, for the first time, an analytic theory of the forward stimulated Brillouin scattering instability of a spatially and temporally incoherent laser beam that controls the transition between statistical equilibrium and nonequilibrium (unstable) self-focusing regimes of beam propagation. The stability boundary may be used as a comprehensive guide for inertial confinement fusion designs. Well into the stable regime, an analytic expression for the angular diffusion coefficient is obtained, which provides an essential correction to a geometric optic approximation for beam propagation.

Bunch self-focusing regime of laser wakefield acceleration with reduced emittance growth.

A new regime of laser wakefield acceleration of an injected electron bunch is described. In this regime, the bunch charge is so high that the bunch wakefields play an important role in the bunch dynamics. In particular, the transverse bunch wakefield induces a strong self-focusing that suppresses the transverse emittance growth arising from misalignment errors. The decelerating longitudinal bunch wakefield, however, is not so strong that it completely cancels the accelerating laser wakefield. In fact, the induced energy spread can be compensated by exploiting phase slippage effects. These features make the new regime interesting for high beam quality laser wakefield acceleration.

Propagation of partially coherent Gaussian Schell-model sources in nonlinear media

Propagation of mutual coherence functions of partially coherent Gaussian Schell-model beams in a medium with third-order nonlinearities is considered. It is shown that incoherence suppresses self-focusing. The spatial coherence of the axial part of the beam improves in the self-focusing regime, whereas the transverse correlation length of the beam decreases in the same region. At high powers, waveguide formation is also studied in media with saturating nonlinearity.

Two-dimensional nonlinear Schrödinger equations and their properties

This paper studies a general class of two-dimensional systems of the cubic nonlinear Schrödinger type (2DNLS), defined by i∂ t q + O 1 q = pq and O 2p = O 3 (q ∗q) , where each O n  D ( n) ij ∂ i ∂ j , n = 1,2,3, is a linear, second-order, operator with constant coefficients. This class generalizes the Djordjevic-Redekopp (DR) system, which has previously been encountered in the context of water waves. Integrability is characterized simply in terms of covariant conditions on the O n . We obtain all integrable cases, including the known cases Davey-Stewartson I, II and II′, as well as other known integrable cases. The 2DNLS is modulationally stable if D (1) D (2) D (3) > 0↭k , where D (n) = k ik jD (n) ij . All other regimes are modulationally unstable and have projections satisfying the ordinary (1D) NLS with soliton solutions, though in all known cases these 1D solitons are unstable with respect to transverse perturbations. The self-focusing regime is characterized by the eigenvalues of the D (n) ij : O 1 and O 2 must both be elliptic, and for that choice of variables for which D (1) ij and D (2) ij both have positive signature, D (3) ij must have at least one negative eigenvalue. The self-focusing regime is distinct from the modulationally stable regime and also from the integrable regime, while the integrable cases may be modulationally stable or unstable. There are no soliton solutions known in those integrable cases that are modulationally stable, whereas those integrable cases in which 2D solitons are known correspond to the modulational instability regime.

Nonlinear evolution of Langmuir and electromagnetic pulses in a warm, unmagnetized plasma: modulational instability, integrability and self-focusing in 2 + 1 dimensions

The nonlinear dynamics of wave envelopes modulated in 2 + 1 dimensions is considered for two systems in plasma physics: (i) Langmuir pulses and (ii) intense (but weakly relativistic) electromagnetic (EM) pulses. Using singular perturbation techniques applied to an envelope approximation, both problems are reduced to the two-dimensional nonlinear Schrödinger (2DNLS) system, which describes the dynamics of two coupled slowly varying potentials. The general 2DNLS system exhibits a rich variety of phenomena, including enhanced (compared with ‘longitudinal’ propagation) modulational stability and (1D) soliton formation; decay of 1D solitons over long time scales; self- focusing regimes (determined by a virial-type condition); as well as integrability and 2D solitons. Applying our recent results on the 2DNLS system, we determine which of these phenomena can actually occur here and compute the parameter regimes. (i) The 2DNLS system for the Zakharov equations is modulationally unstable for all parameter values. It also has an integrable sector and a self-focusing regime. (ii) The 2DNLS system describes coupled ‘longitudinal’ and ‘transverse’ modulations of linearly or circularly polarized EM pulses propagating through a warm unmagnetized two-component neutral plasma with arbitrary masses (i.e. electron—positron or electron—ion). The pulse can accelerate particles to weakly (but not fully) relativistic velocities; relativistic, ponderomotive and harmonic effects all contribute to the nonlinear terms. The resulting 2DNLS system does not admit a self-focusing regime. Parameter values leading to an integrable case (the so-called ‘Davey—Stewartson I’ equations, which admit 2D soliton solutions) are computed; however, the required values would not be attainable in a laboratory or astrophysical setting. None the less, the existence of new nonlinear modulational instabilities associated with the second spatial degree of freedom already represents an important potential limitation on any (1 + 1)-dimensional approach to nonlinear evolution and modulational instability of plasma EM waves.

Self-focusing of two orthogonally polarized light beams in a nonlinear medium

The propagation of two light beams with orthogonal polarization in a nonlinear medium is considered. It is shown that because of the interaction of the beams there are two different self-focusing regimes: monotonous and oscillatory. Analytical results are confirmed by computer simulation.

Solitary pulses in an amplified nonlinear dispersive medium

An analytical solution is obtained for solitary pulse propagation in an amplified nonlinear dispersive system. For a homogeneously broadened gain medium, this solitary pulse has a hyperbolic secant amplitude and a hyperbolic tangent instantaneous frequency variation. The pulse is a gain-guided pulse in either the positive or the negative dispersion regime as well as in the self-focusing or self-defocusing regime. A dark solitary pulse that has a hyperbolic tangent amplitude and a similar instantaneous frequency variation is also obtained.

Nonlinear propagation ofN intense waves: polarization states, refractive indices and self-focusing

This paper presents a theoretical study of the nonlinear propagation ofN polarized intense waves in a macroscopically isotropic medium. General formulae are obtained for the polarization states and the nonlinear dependence of the index of refraction. In the absence of self-focusing, it is shown thatN linearly or circularly polarized waves retain their initial state of polarization during propagation. Results have been tabulated for the refractive indices and the polarization states ofN waves according to their initial polarization states. In the self-focusing regime, only circularly polarized waves conserve their polarization. This paper presents a description of the phenomenon of cross-focusing: in a certain power range, a wave of higher power induces self-focusing of a wave of lower power, whereas in some other situation, a stronger wave self-defocuses in the presence of a weak wave. In one of the situations, the phenomenon of an oscillatory waveguide is also exhibited. The polarization states of two waves in the self-focusing range have also been discussed.

Adiabatic model of resonance two-photon self-focusing and defocusing of optical beams

A numerical and analytic investigation is made of the self-interaction of Gaussian beams under two-photon resonance conditions when the pulse duration is shorter than the relaxation times and the frequency detuning from resonance exceeds appreciably the spectral width of the radiation (adiabatic model). An analysis is made of defocusing (up-detuning) and self-focusing processes (down-detuning) in two-photon resonance. Three characteristic adiabatic self-focusing regimes are identified: a steady-state waveguide and weak and strong quasiwaveguide propagation. Expressions are derived for the critical powers and minimal self-focusing length.