Modeling the propagation of a high-average-power train of ultrashort laser pulses.

We investigate the interpulse thermal interaction of a train of ultrashort laser pulses and develop a model to describe the isobaric heating of air by a train of pulses undergoing filamentation. We calculate the heating of air from a single laser pulse and the resulting refractive index perturbation encountered by subsequent pulses, and use this to simulate the propagation of a high-power pulse train. The simulations show deflection of laser filaments by the thermal refractive index consistent with previous experimental measurements.

Modeling of short-pulse laser-metal interactions in the warm dense matter regime using the two-temperature model.

A numerical model for laser-matter interactions in the warm dense matter regime is presented with broad applications, e.g., ablation, thermionic emission, and radiation. A unique approach is adopted, in which a complete set of collisional and transport data is calculated using a quantum model and incorporated into the classical two-temperature model for the electron and lattice-ion temperatures. The data set was produced by the average atom model that combines speed, conceptual simplicity, and straightforward numerical development. Such data are suitable for use in the warm dense matter regime, where most of the laser-matter interactions at moderate intensities occur, thus eliminating deficiencies of previous models, e.g., interpolation between solid and ideal plasma regimes. In contrast to other works, we use a more rigorous definition of solid and plasma states of the metal, based on the physical condition of the lattice, crystalline (ordered) versus melted (disordered), rather than a definition based on electron temperature. The synergy between the two-temperature and average atom models has been demonstrated on a problem involving heating and melting of the interior of Al by a short-pulse laser with duration 0.1-1 ps and laser fluences 1×10^{3}-3×10^{4}J/m^{2}(0.1-3J/cm^{2}). The melting line, which separates the solid and plasma regimes, has been tracked in time and space. The maximum melting depth has been determined as a function of laser fluence: l_{melt}(µm)≅4×10^{3}F(J/m^{2}).

Bremsstrahlung from the interaction of short laser pulses with dielectrics.

An intense, short laser pulse incident on a transparent dielectric can excite electrons from the valence to the conduction band. As these electrons undergo scattering, both from phonons and ions, they emit bremsstrahlung. Here we present a theory of bremsstrahlung emission appropriate for the interaction of laser pulses with dielectrics. Simulations of the interaction, incorporating this theory, illustrate characteristics of the radiation (power, energy, and spectra) for arbitrary ratios of electron collision frequency to radiation frequency. The conversion efficiency of laser pulse energy into bremsstrahlung depends strongly on both the intensity and duration of the pulse, saturating at values of about 10^{-5}. Depending on whether the intensity is above or below the damage threshold of the material, the emission can originate either from the surface or the bulk of the dielectric, respectively. The bremsstrahlung emission may provide a broadband light source for diagnostics.

Laser beam self-focusing in turbulent dissipative media.

A high-power laser beam propagating through a dielectric in the presence of fluctuations is subject to diffraction, dissipation, and optical Kerr nonlinearity. A method of moments was applied to a stochastic, nonlinear enveloped wave equation to analyze the evolution of the long-term spot radius. For propagation in atmospheric turbulence described by a Kolmogorov-von Kármán spectral density, the analysis was benchmarked against field experiments in the low-power limit and compared with simulation results in the high-power regime. Dissipation reduced the effect of self-focusing and led to chromatic aberration.

Reciprocity breaking during nonlinear propagation of adapted beams through random media.

Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.

Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.

The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering.

Determination of absorption coefficient based on laser beam thermal blooming in gas-filled tube.

Thermal blooming of a laser beam propagating in a gas-filled tube is investigated both analytically and experimentally. A self-consistent formulation taking into account heating of the gas and the resultant laser beam spreading (including diffraction) is presented. The heat equation is used to determine the temperature variation while the paraxial wave equation is solved in the eikonal approximation to determine the temporal and spatial variation of the Gaussian laser spot radius, Gouy phase (longitudinal phase delay), and wavefront curvature. The analysis is benchmarked against a thermal blooming experiment in the literature using a CO2 laser beam propagating in a tube filled with air and propane. New experimental results are presented in which a CW fiber laser (1 µm) propagates in a tube filled with nitrogen and water vapor. By matching laboratory and theoretical results, the absorption coefficient of water vapor is found to agree with calculations using MODTRAN (the MODerate-resolution atmospheric TRANsmission molecular absorption database) and HITRAN (the HIgh-resolution atmospheric TRANsmission molecular absorption database).

Origin and control of the subpicosecond pedestal in femtosecond laser systems.

The picosecond time scale pedestal of a multiterawatt femtosecond laser pulse is investigated experimentally and analytically. The origin of the pedestal is related to the finite bandwidth of the laser system. By deliberately introducing a modulated spectrum with minima that match this limited bandwidth, the pedestal can be reduced, with no deleterious effect on the main pulse. Using this technique, we experimentally demonstrate a subpicosecond scale order of magnitude enhancement of contrast ratio while preserving the energy in the main pulse.

Boron nitride plasma micro lens for high intensity laser pre-pulse suppression.

We demonstrate that amplified spontaneous emission (ASE) and pre-pulses for high power lasers can be suppressed by propagating the pulse through a boron nitride plasma microlens. The microlens is created by ablating a boron-nitride (BN) disk with a central hole using an Nd:YAG laser . The plasma lens produced in the ablation process exhibits different focal lengths for the high intensity main pulse and low intensity pre-pulse that increases the main pulse/pre-pulse contrast ratio by one order of magnitude while maintaining high transmittance of the pulse energy.

Laser heating of uncoated optics in a convective medium.

Powerful, long-pulse lasers have a variety of applications. In many applications, optical elements are employed to direct, focus, or collimate the beam. Typically the optic is suspended in a gaseous environment (e.g., air) and can cool by convection. The variation of the optic temperature with time is obtained by combining the effects of laser heating, thermal conduction, and convective loss. Characteristics of the solutions in terms of the properties of the optic material, laser beam parameters, and the environment are discussed and compared with measurements at the Naval Research Laboratory, employing kW-class, 1 µm wavelength, continuous wave lasers and optical elements made of fused silica or BK7 glass. The calculated results are in good agreement with the measurements, given the approximations in the analysis and the expected variation in the absorption coefficients of the glasses used in the experiments.

(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: toward a quantitative agreement with experiments.

Three-dimensional numerical simulations and direct experimental measurements of the multifilamentation of femtosecond laser pulses propagating in air are quantitatively compared. Agreement is obtained in terms of the evolution of the filamentation pattern and in terms of the size and energy of the individual filaments through 12 m of propagation. These results are made possible by the combination of a massively parallel propagation code along with a nondestructive experimental diagnostic technique. Influence of the pulse duration is moreover addressed. The numerical calculations also show that single and multiple filaments exhibit almost identical spectral signature.

Transmission of intense femtosecond laser pulses into dielectrics.

The interaction of intense, femtosecond laser pulses with a dielectric medium is examined using a numerical simulation. The simulation uses the one-dimensional electromagnetic wave equation to model laser pulse propagation. In addition, it includes multiphoton ionization, electron attachment, Ohmic heating of free electrons, and temperature-dependent collisional ionization. Laser pulses considered in this study are characterized by peak intensities approximately 10(12) -10(14) W/cm(2) and pulse durations approximately 10-100 fsec . These laser pulses interacting with fused silica are shown to produce above-critical plasma densities and electron energy densities sufficient to attain experimentally measured damage thresholds. Significant transmission of laser energy is observed even in cases where the peak plasma density is above the critical density for reflection. A damage fluence based on absorbed laser energy is calculated for various pulse durations. The calculated damage fluence threshold is found to be consistent with recent experimental results.

Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces.

Intense, ultrashort laser pulses propagating in the atmosphere have been observed to emit sub-THz electromagnetic pulses (EMPS). The purpose of this paper is to analyze EMP generation from the interaction of ultrashort laser pulses with air and with dielectric surfaces and to determine the efficiency of conversion of laser energy to EMP energy. In our self-consistent model the laser pulse partially ionizes the medium, forms a plasma filament, and through the ponderomotive forces associated with the laser pulse, drives plasma currents which are the source of the EMP. The propagating laser pulse evolves under the influence of diffraction, Kerr focusing, plasma defocusing, and energy depletion due to electron collisions and ionization. Collective effects and recombination processes are also included in the model. The duration of the EMP in air, at a fixed point, is found to be a few hundred femtoseconds, i.e., on the order of the laser pulse duration plus the electron collision time. For steady state laser pulse propagation the flux of EMP energy is nonradiative and axially directed. Radiative EMP energy is present only for nonsteady state or transient laser pulse propagation. The analysis also considers the generation of EMP on the surface of a dielectric on which an ultrashort laser pulse is incident. For typical laser parameters, the power and energy conversion efficiency from laser radiation to EMP radiation in both air and from dielectric surfaces is found to be extremely small, < 10(-8). Results of full-scale, self-consistent, numerical simulations of atmospheric and dielectric surface EMP generation are presented. A recent experiment on atmospheric EMP generation is also simulated.

Stimulated Raman scattering of intense laser pulses in air.

Stimulated rotational Raman scattering (SRRS) is known to be one of the processes limiting the propagation of high-power laser beams in the atmosphere. In this paper, SRRS, Kerr nonlinearity effects, and group velocity dispersion of short laser pulses and pulse trains are analyzed and simulated. Fully time-dependent, three-dimensional, nonlinear propagation equations describing the Raman interaction, optical Kerr nonlinearity due to bound electrons, and group velocity dispersion are presented and discussed. The effective time-dependent nonlinear refractive index containing both Kerr and Raman processes is derived. Linear stability analysis is used to obtain growth rates and phase matching conditions for the SRRS, modulational, and filamentation instabilities. Numerical solutions of the propagation equations in three dimensions show the detailed evolution of the Raman scattering instability for various pulse formats. The dependence of the growth rate of SRRS on pulse duration is examined and under certain conditions it is shown that short (approximately psec) laser pulses are stable to the SRRS instability. The interaction of pulses in a train through the Raman polarization field is also illustrated.

Electron distribution function in short-pulse photoionization.

Two well-known limiting regimes of photoionization, when a laser beam interacts with a gas, correspond to the tunneling and the multiphoton processes. The latter dominates in the low-intensity regime, while the former is appropriate at higher intensities. Electrons are born with negligible velocity in tunneling ionization, while in l-photon ionization they are born with a fixed energy determined by l, the photon energy and the ionization potential of the molecule. The transport equation for the distribution function of electrons can be integrated along the characteristics defined by the classical equations of motion in the laser field. Expressions for the distribution function have been obtained in the two regimes using the appropriate analytical form for the ionization rate. Results from two-dimensional particle-in-cell simulations and illustrative plots of the distribution function are presented and discussed.

Asymmetric self-phase modulation and compression of short laser pulses in plasma channels.

A relativistically intense femtosecond laser pulse propagating in a plasma channel undergoes dramatic photon deceleration while propagating a distance on the order of a dephasing length. The deceleration of photons is localized to the back of the pulse and is accompanied by compression and explosive growth of the ponderomotive potential. Fully explicit particle-in-cell simulations are applied to the problem and are compared with ponderomotive guiding center simulations. A numerical Wigner transform is used to examine local frequency shifts within the pulse and to suggest an experimental diagnostic of plasma waves inside a capillary.

Propagation of intense short laser pulses in the atmosphere.

The propagation of short, intense laser pulses in the atmosphere is investigated theoretically and numerically. A set of three-dimensional (3D), nonlinear propagation equations is derived, which includes the effects of dispersion, nonlinear self-focusing, stimulated molecular Raman scattering, multiphoton and tunneling ionization, energy depletion due to ionization, relativistic focusing, and ponderomotively excited plasma wakefields. The instantaneous frequency spread along a laser pulse in air, which develops due to various nonlinear effects, is analyzed and discussed. Coupled equations for the power, spot size, and electron density are derived for an intense ionizing laser pulse. From these equations we obtain an equilibrium for a single optical-plasma filament, which involves a balancing between diffraction, nonlinear self-focusing, and plasma defocusing. The equilibrium is shown to require a specific distribution of power along the filament. It is found that in the presence of ionization a self-guided optical filament is not realizable. A method for generating a remote spark in the atmosphere is proposed, which utilizes the dispersive and nonlinear properties of air to cause a low-intensity chirped laser pulse to compress both longitudinally and transversely. For optimally chosen parameters, we find that the transverse and longitudinal focal lengths can be made to coincide, resulting in rapid intensity increase, ionization, and white light generation in a localized region far from the source. Coupled equations for the laser spot size and pulse duration are derived, which can describe the focusing and compression process in the low-intensity regime. More general examples involving beam focusing, compression, ionization, and white light generation near the focal region are studied by numerically solving the full set of 3D, nonlinear propagation equations.

Raman forward scattering and self-modulation of laser pulses in tapered plasma channels.

The propagation of intense laser pulses with durations longer than the plasma period through tapered plasma channels is investigated theoretically and numerically. General propagation equations are presented and reduced partial differential equations that separately describe the forward Raman (FR) and self-modulation (SM) instabilities in a nonuniform plasma are derived. Local dispersion relations for FR and SM instabilities are used to analyze the detuning process arising from a longitudinal density gradient. Full-scale numerical fluid simulations indicate parameters that favorably excite either the FR or SM instability. The suppression of the FR instability and the enhancement of the SM instability in a tapered channel in which the density increases longitudinally is demonstrated. For a pulse undergoing a self-modulation instability, calculations show that the phase velocity of the wakefield in an untapered channel can be significantly slower than the pulse group velocity. Simulations indicate that this wake slippage can be forestalled through the use of a tapered channel.

Seeding of the forward Raman instability by ionization fronts and Raman backscatter.

The self-modulated laser wakefield accelerator utilizes the forward Raman instability to drive a large-amplitude plasma wave. The effectiveness of this process could depend on how it competes with other processes such as self-focusing and cavitation, or other instabilities such as filamentation and hosing. The relative timing between the various processes is dependent on the nature of the seed for each instability. Both ionization fronts and Raman backscatter are capable of seeding the forward Raman instability. This causes the forward Raman instability to emerge much earlier than would otherwise be expected.

Apparent superluminal propagation of a laser pulse in a dispersive medium.

The distortion of a laser pulse propagating in a dispersive gain/absorptive medium is analyzed. The relationship between the distortion of the pulse and superluminal propagation is discussed. We present an analytical approach based on the laser envelope equation that is readily applicable to arbitrary input pulse shapes. This analysis is used to interpret recent experiments that claim to have observed distortionless superluminal laser pulse propagation.