There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Femtosecond filamentation in transparent media

Particle accelerators are used in a wide variety of fields, ranging from medicine and biology to high-energy physics. The accelerating fields in conventional accelerators are limited to a few tens of MeV m(-1), owing to material breakdown at the walls of the structure. Thus, the production of energetic particle beams currently requires large-scale accelerators and expensive infrastructures. Laser-plasma accelerators have been proposed as a next generation of compact accelerators because of the huge electric fields they can sustain (>100 GeV m(-1)). However, it has been difficult to use them efficiently for applications because they have produced poor-quality particle beams with large energy spreads, owing to a randomization of electrons in phase space. Here we demonstrate that this randomization can be suppressed and that the quality of the electron beams can be dramatically enhanced. Within a length of 3 mm, the laser drives a plasma bubble that traps and accelerates plasma electrons. The resulting electron beam is extremely collimated and quasi-monoenergetic, with a high charge of 0.5 nC at 170 MeV.

A laser-plasma accelerator producing monoenergetic electron beams

The rise in output power from rare-earth-doped fiber sources over the past decade, via the use of cladding-pumped fiber architectures, has been dramatic, leading to a range of fiber-based devices with outstanding performance in terms of output power, beam quality, overall efficiency, and flexibility with regard to operating wavelength and radiation format. This success in the high-power arena is largely due to the fiber’s geometry, which provides considerable resilience to the effects of heat generation in the core, and facilitates efficient conversion from relatively low-brightness diode pump radiation to high-brightness laser output. In this paper we review the current state of the art in terms of continuous-wave and pulsed performance of ytterbium-doped fiber lasers, the current fiber gain medium of choice, and by far the most developed in terms of high-power performance. We then review the current status and challenges of extending the technology to other rare-earth dopants and associated wavelengths of operation. Throughout we identify the key factors currently limiting fiber laser performance in different operating regimes—in particular thermal management, optical nonlinearity, and damage. Finally, we speculate as to the likely developments in pump laser technology, fiber design and fabrication, architectural approaches, and functionality that lie ahead in the coming decade and the implications they have on fiber laser performance and industrial/scientific adoption.

High power fiber lasers: current status and future perspectives [Invited]

The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of ${10}^{18}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of ${10}^{20}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

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Optics in the relativistic regime

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.

Propagation of intense short laser pulses in the atmosphere

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, $l{10}^{\ensuremath{-}8}$. 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.

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

High-power fiber lasers can be incoherently combined to form the basis of a directed high-energy laser system which is highly efficient, compact, robust, low-maintenance and has a long operating lifetime. This approach has a number of advantages over other beam combining methods. We present results of the first field demonstration of incoherent beam combining using kilowatt-class, single-mode fiber lasers. The experiment combined four fiber lasers using a beam director consisting of individually controlled steering mirrors. Propagation efficiencies of ~90%, at a range of 1.2 km, with transmitted continious-wave power levels of 3 kW were demonstrated in moderate atmospheric turbulence. We analyze the propagation of combined single-mode and multimode beams in atmospheric turbulence and find good agreement between theory, simulations and experiments.

Incoherent Combining and Atmospheric Propagation of High-Power Fiber Lasers for Directed-Energy Applications

The ponderomotive force associated with an intense laser beam expels electrons radially and can lead to cavitation in plasma. Relativistic effects as well as ponderomotive expulsion of electrons modify the refractive index. An envelope equation for the laser spot size is derived, using the source-dependent expansion method with Laguerre-Gaussian eigenfunctions, and reduced to quadrature. The envelope equation is valid for arbitrary laser intensity within the long pulse, quasistatic approximation and neglects instabilities. Solutions of the envelope equation are discussed in terms of an effective potential for the laser spot size. An analytical expression for the effective potential is given. For laser powers exceeding the critical power for relativistic self-focusing the analysis indicates that a significant contraction of the spot size and a corresponding increase in intensity is possible.

Relativistic focusing and ponderomotive channeling of intense laser beams

In this article, we review and discuss the research programs at the Naval Research Laboratory (NRL) on high-power lasers for directed-energy (DE) applications in the atmosphere. Physical processes affecting propagation include absorption/scattering, turbulence, and thermal blooming. The power levels needed for DE applications require combining a number of lasers. In atmospheric turbulence, there is a maximum intensity that can be placed on a target that is independent of the initial beam spot size and laser beam quality. By combining a number of kW-class fiber lasers, scientists at the NRL have successfully demonstrated high-power laser propagation in a turbulent atmosphere and wireless recharging. In the NRL experiments, four incoherently combined fiber lasers having a total power of 5 kW were propagated to a target 3.2 km away. These successful high-power experiments in a realistic atmosphere formed the basis of the Navy's Laser Weapon System. We compare the propagation characteristics of coherently and incoherently combined beams without adaptive optics. There is little difference in the energy on target between coherently and incoherently combined laser beams for multi-km propagation ranges and moderate to high levels of turbulence. Unlike incoherent combining, coherent combining places severe constraints on the individual lasers. These include the requirement of narrow power spectral linewidths in order to have long coherence times as well as polarization alignment of all the lasers. These requirements are extremely difficult for high-power lasers.

Bahman Hafizi

Papers

Propagation of intense short laser pulses in the atmosphere

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

Incoherent Combining and Atmospheric Propagation of High-Power Fiber Lasers for Directed-Energy Applications

Relativistic focusing and ponderomotive channeling of intense laser beams

High-power lasers for directed-energy applications.