Vitali E. Gruzdev

Laser-induced ionization of solids: back to Keldysh

The aim of our consideration is to clarify the influence of band structure of crystalline solids on ionization rate described in the framework of the Keldysh model. In this connection we compare the Keldysh formula with its analogs obtained for several models of band structure. We clearly demonstrate strong dependence of the ionization rate on band model especially in case of the transitional (from multiphoton to tunneling) and the tunneling regimes. An expression for the adiabatic parameter also depends on particular band model, and we present its new definition relating it to lattice constant, electric-field strength and laser frequency. We demonstrate possibility of a new regime of ionization referred to as collective ionization in which conditions for an effective jump of almost all valence electrons over the forbidden band within one period of field oscillations are provided. We present rigorous estimation of the threshold for that effect and show it to be close to 10 TW per square cm for most transparent materials. The influence of band model on multiphoton ionization rate depends on ratio of band gap to photon energy and is the weakest if the ration is slightly below an integer. In this connection we demonstrate that a proper choice of a band model can explain the well-known difference between calculated and measured values of ionization rate.

Computer simulation of light propagation through optical coatings with inhomogeneous microstructure

There are presented initial results of investigation of influence of local optical and thermal parameters of thin dielectric films and optical coatings with inhomogeneous micromorphology on light propagation. Linear and nonlinear light propagation accompanied by laser-induced heating have been considered. Modeling is used to investigate the process described by coupled nonlinear equations. Obtained results show critical role of nonlinear phenomena resulting in formation of local maxima of laser intensity inside the films which is followed by highly inhomogeneous local heating of the films.

Formation of shock electromagnetic waves during femtosecond pulse propagation in transparent solids

There is considered formation and propagation of shock electromagnetic waves (SEW) of visible spectral range as possible nonlinear optical phenomenon taking place at laser intensities characteristic of femtosecond laser interaction with transparent solids. Main regularities of SHEW formation are studied on the basis of 1D model of plane-wave propagation in isotropic dielectric with nonlinear optical response. Special attention is paid to influence of color dispersion and absorption on SEW formation and propagation. Necessary conditions for appearing of SHEW are obtained, in particular, threshold amplitude is estimated. There is presented a model for numerical simulation of SHEW formation and propagation influenced by dispersion of linear and nonlinear parts of refractive index. Using the simulation, we studied dynamics of SHEW formation on several first optical cycles of femtosecond laser pulse in transparent medium. Important observed features of SHEW of optical frequency are discussed. Obtained results are considered from the viewpoint of experiments on femtosecond laser interaction, in particular, laser-induced damage.

Resonance increase of high-power laser field with nodule defects in multilayer optical coatings: theory and simulation

There are presented results of computer modeling of laser- field evolution in nodular defects in multilayer optical coatings. It is investigated dynamics of laser-wave propagation through both linear and nonlinear nodules. Formation of field maxima is studied. There are presented theoretical estimates of field amplification for resonant case. The presented results are discussed from the viewpoint of laser-induced damage of optical coatings.

Nonthermal effects in femtosecond laser damage of transparent materials

There are considered non-thermal processes of femtosecond laser-induced damage of wide band-gap transparent materials. Dominating of thermal or non-thermal effects depends on radiation and material parameters among which pulse repetition rate, focal spot size and absorption play key role. Non-thermal mechanisms of damage and ablation can dominate at initiating stage and at low repetition rates. They are attributed to nonlinear electrodynamical processes such as higher harmonic generation of formation of shock electromagnetic waves. Considering interaction of shock electromagnetic wave with a particle in potential well, we derive expression for threshold of laser-induced ionization and delocalization. Thermal mechanisms can dominate at later stages of damage and ablation at repetition rates above 10 kHz. There are also discussed after-heating and non- equilibrium non-thermal processes taking place between initiating and thermal stages. There are considered several mechanisms of laser-induced ionization - multiphoton, tunneling, avalanche ionization, also ionization by higher harmonics and by shock-wave front. Estimations of ionization rates show that the latter two mechanisms can dominate at initiating stage of femtosecond damage and determine critically following ionization processes. Obtained results are compared with experimental data.

Laser-induced damage of transparent solids by femtosecond laser pulses

Our paper is devoted to theoretical analysis of mechanisms of laser-induced dmaage of transparent solids by femtosecond laser pulses in single-shot regime. The duration of the pulses is so small that the phonon sub-system practically does not take part in the processes occurring during the direct action of laser pulse. It means that the process of direct damage starts with a certain delay after the laser pulse. We have come to conclusion that it is reasonable to separate out three main stages of the process of macroscopic damage: 1) the direct laser-solid interaction during pulse action including mulitphoton absorption, excitation of the electron subsystem near the material surface and fast leaving of the irradiated area by electrons (e.g., through photoelectron emission); 2) fast after-action including breaking of electrical neutrality in thin near-surface layer and acceleration of ions; 3) slow or delayed after-action including moving of fast ions into bulk accompanied by heating up of the material through collisions resulting in macroscopic thermal damage. In this presentation we focus on the first two stages, i.e., excitation of the electron sub-system, electron emission and development of electrostatic instability often referred to as Coulomb explosion. Estimations performed on the basis of the Keldysh formula show possibility to reach extremely high density of electrons in conduction band (up to 50% of total number of valence electrons) at laser intensity slightly above 10 TW per sq. cm. The electrons can leave the irradiated area before the laser pulse ends. We utilize Keldysh formula to estimate the total number of electrons lost through emission and show the number to be high enough for significant breaking of electrical neutrality and fomration of relatively large positive charge localized in the irradiated area. Assuming the multiphoton ionization to give the dominant contribution to absorption, we estimate the total number of electrons lost through emission and show the number to be high enough for significant breaking of electrical neutrality and formation of relatively large positive charge localized in the irradiated area. Assuming the mulitphoton ionization to give the dominant contribution to absorption, we estimate the characteristic thickness of the ionized layer and show the positive charge to be localized in the layer which is approximately 1 micrometer thick. Then we estimate velocities and energies of ions accelerated by the laser-induced charge and show possibility of appearing ions with MeV energies. The penetration depth characteristic of those ions is an order of 10 micrometers what implies possibility of heating and thermal damage of the material with formation of deep craters.

Nonlinear self-depolarization effect of high-intensity tightly focused laser beams in transparent isotropic dielectric

There are presented results of theoretical investigation of nonlinear self-depolarization effect resulting in variation of space distribution of polarization-ellipse parameters of monochromatic high-intensity focused laser beam. Both qualitative consideration of symmetry properties and numerical calculations for Gaussian beams of low order (TE00, TE01, TE10 and TE11) show that linear and circular initial polarizations change and turn into elliptic polarization with inhomogeneous distribution of polarization-ellipse parameters in focal area. Bearing in mind obtained results, we discuss specific symmetry structure of self-depolarization effect allowing experimental checking of described phenomenon. There are analyzed and estimated other contributions to depolarization effect resulting from low-intensity diffraction. Obtained results are generalized for the case of laser pulses and other types of nonlinear optical response of isotropic dielectric.

Finite-difference time-domain modeling of laser beam propagation and scattering in dielectric materials

Modified finite-difference time-domain (FDTD) approach to numerical investigation of propagation of laser pulses and beams in transparent materials is presented. In contrary to traditional FDTD technique, it is based on description of wave propagation by wave equation. To take into account important material properties, presented approach can include integrating of a set of coupled nonlinear equations including equations describing dispersion of linear and nonlinear parts of refractive index, linear and two-photon absorption. Developed technique is illustrated with several examples including scattering of laser radiation by diffraction grating (sine relief) and focusing by a dielectric cylinder. There are discussed problems of calculation stability, control of errors, decreasing of required computation time and memory. Application of developed approach to modeling of micro-optical elements for modern areas of optoelectronics is considered.

Interaction of shock electromagnetic waves with transparent materials: classical approach

There is discussed a theoretical model of initiating of laser-induced damage and ablation of transparent materials by femtosecond pluses based on properties of shock electromagnetic wave (SHEW). Advantages of this model are increased efficiency of SHEW-induced ionization and possibility of effective straight action of SHEW front on ions at crystal-lattice points. It is presented simplified description of SHEW-induced processes within approach of classical mechanics and electrodynamics: atoms are described as dipoles with certain ionization energy interacting with SHEW in potential well formed by crystal lattice. There are considered possibilities of laser-induced ionization by higher harmonics appearing during SHEW formation and point- defect formation and delocalization of ions at crystal points by SHEW. Obtained results and predictions are compared with experimental data and shown to be capable of explaining many observed regulations of femtosecond laser interactions with transparent media.

Light scattering by rough dielectric surface

Numerical modelling is applied to investigation of scattering of plane linearly polarized monochromatic wave by sine variations of dielectric surface relief. The modelling is based on finite-difference time-domain technique. Results of modelling include 1) space distribution of scattered light, 2) dependence of field amplification on ratio of roughness amplitude to laser wavelength, and 3) dependence of field amplification on ratio of roughness period to laser wavelength. Obtained results show that for TE polarization a) transmitted signal is more sensitive to roughness parameters than reflected one, b) there is narrow resonance in dependence of amplitude of scattered field on laser wavelength and roughness period, c) dependence of amplitude of scattered field on roughness amplitude is described by parabolic function for small values of relief amplitude. Depending on relief amplitude and period, scattering by sine roughness can result in formation of inhomogeneous space field distribution consisting of periodic field maxima inside dielectric or formation of homogeneous distribution such that both transmitted and reflected signals are close to plane wave. We consider the following applications of obtained results: 1) possibility to develop a new technique for in-situ surface roughness charactensation, 2) possible mechanisms of feedbacks during laser-induced formation of surface ripples, and 3) anti-reflection effect.