High-power lasers for directed-energy applications: reply.

The comment by Vorontsov and Weyrauch [Appl. Opt.55, 9950 (2016)APOPAI0003-693510.1364/AO.55.009950] is aimed at rebutting the critiques in Sprangle et al. [Appl. Opt.54, F201 (2015)APOPAI0003-693510.1364/AO.54.00F201] and Nelson et al. [Appl. Opt.55, 1757 (2016)APOPAI0003-693510.1364/AO.55.001757]. In the comment, Vorontsov and colleagues describe their experiments aimed at demonstrating the feasibility of coherent combining of lasers on a distant target, using relatively low-power lasers and a cooperative retro-reflective target. The Naval Research Laboratory has demonstrated the capability to project high power on a distant target by making use of an incoherent combining architecture. The proof-of-concept experiments were performed in a realistic environment without employing cooperative targets and without sophisticated adaptive optics instrumentation.

Atmospheric propagation and combining of high-power lasers.

In this paper, we analyze beam combining and atmospheric propagation of high-power lasers for directed-energy (DE) applications. The large linewidths inherent in high-power fiber and slab lasers cause random phase and intensity fluctuations that occur on subnanosecond time scales. Coherently combining these high-power lasers would involve instruments capable of precise phase control and operation at rates greater than ∼10 GHz. To the best of our knowledge, this technology does not currently exist. This presents a challenging problem when attempting to phase lock high-power lasers that is not encountered when phase locking low-power lasers, for example, at milliwatt power levels. Regardless, we demonstrate that even if instruments are developed that can precisely control the phase of high-power lasers, coherent combining is problematic for DE applications. The dephasing effects of atmospheric turbulence typically encountered in DE applications will degrade the coherent properties of the beam before it reaches the target. Through simulations, we find that coherent beam combining in moderate turbulence and over multikilometer propagation distances has little advantage over incoherent combining. Additionally, in cases of strong turbulence and multikilometer propagation ranges, we find nearly indistinguishable intensity profiles and virtually no difference in the energy on the target between coherently and incoherently combined laser beams. Consequently, we find that coherent beam combining at the transmitter plane is ineffective under typical atmospheric conditions.

Atmospheric propagation and combining of high-power lasers: reply.

We do not believe that there is any inconsistency between the findings of our paper [Appl. Opt.55, 1757 (2016)APOPAI0003-693510.1364/AO.55.001757] and the observations of Goodno and Rothenberg [Appl. Opt.55, 8335 (2016)]. APOPAI0003-69351559-128X/16/298335-03.

Propagation of Bessel and Airy beams through atmospheric turbulence.

We investigate, through simulation, the modifications to Bessel and Airy beams during propagation through atmospheric turbulence. We find that atmospheric turbulence disrupts the quasi-non-diffracting nature of Bessel and Airy beams when the transverse coherence length (Fried parameter) nears the initial aperture diameter or diagonal, respectively. The turbulence-induced transverse phase distortion limits the effectiveness of Bessel and Airy beams for applications requiring propagation over long distances in the turbulent atmosphere.

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.

Enhanced proton acceleration by an ultrashort laser interaction with structured dynamic plasma targets.

We experimentally demonstrate a notably enhanced acceleration of protons to high energy by relatively modest ultrashort laser pulses and structured dynamical plasma targets. Realized by special deposition of snow targets on sapphire substrates and using carefully planned prepulses, high proton yields emitted in a narrow solid angle with energy above 21 MeV were detected from a 5 TW laser. Our simulations predict that using the proposed scheme protons can be accelerated to energies above 150 MeV by 100 TW laser systems.

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.

5.5-7.5 MeV proton generation by a moderate-intensity ultrashort-pulse laser interaction with H2O nanowire targets.

We report on the first generation of 5.5-7.5 MeV protons by a moderate-intensity short-pulse laser (∼5×10(17) W/cm(2), 40 fsec) interacting with frozen H(2)O nanometer-size structure droplets (snow nanowires) deposited on a sapphire substrate. In this setup, the laser intensity is locally enhanced by the snow nanowire, leading to high spatial gradients. Accordingly, the nanoplasma is subject to enhanced ponderomotive potential, and confined charge separation is obtained. Electrostatic fields of extremely high intensities are produced over the short scale length, and protons are accelerated to MeV-level energies.

(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.

Quasimonoenergetic electrons from unphased injection into channel guided laser wakefield accelerators.

A high-quality electron beam can be extracted from a channel guided laser wakefield accelerator without confining the injected particles to a small region of phase. By careful choice of the injection energy, a regime can be found where uniformly phased particles are quickly bunched by the accelerator itself and subsequently accelerated to high energy. The process is particularly effective in a plasma channel because of a favorable phase shift that occurs in the focusing fields. Furthermore, particle-in-cell simulations show that the self-fields of the injected bunches actually tend to reduce the energy spread on the final beam. The final beam characteristics can be calculated using a computationally inexpensive Hamiltonian formulation when beam-loading effects are minimal.

Stable laser-pulse propagation in plasma channels for GeV electron acceleration

To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA) it is necessary to propagate an intense laser pulse long distances in plasma without disruption. A 3D envelope equation for a laser pulse in a tapered plasma channel is derived, which includes wakefields and relativistic and nonparaxial effects, such as finite pulse length and group velocity dispersion. It is shown that electron energies of approximately GeV in a plasma-channel LWFA can be achieved by using short pulses where the forward Raman and modulation nonlinearities tend to cancel. Further energy gain can be achieved by tapering the plasma density to reduce electron dephasing.

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.

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.

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.

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.

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.

Simulation and design of stable channel-guided laser wakefield accelerators.

Most laser wakefield accelerator (LWFA) experiments to date have operated in the self-modulated (SM) regime and have been self-guided. A channel-guided LWFA operating in the standard or resonant regime is expected to offer the possibility of high electron energy gain and high accelerating gradients without the instabilities and poor electron beam quality associated with the SM regime. Plasma channels such as those produced by a capillary discharge have demonstrated guiding of intense laser pulses over distances of several centimeters. Optimizing the performance in a resonant LWFA constrains the on-axis plasma density in the channel to a relatively narrow range. A scaling model is presented that quantifies resonant LFWA performance in terms of the maximum accelerating gradient, dephasing length, and dephasing-limited energy gain. These performance quantities are expressed in terms of laser and channel experimental parameters, clearly illustrating some of the tradeoffs in the choice of parameters. The predicted energy gain in this model is generally lower than that indicated by simpler scaling models. Simulations agree well with the scaling model in both low and high plasma density regimes. Simulations of a channel-guided, self-modulated LWFA are also presented. Compared with the resonant LWFA regime, the requirements on laser and channel parameters in the SM regime are easier to achieve, and a channel-guided SM-LWFA is likely to be less unstable than a self-guided SM-LWFA.