Self-channeling of a multi-Joule 10†µm picosecond pulse train through long distances in air.

In the long-wave infrared (LWIR) range, where, due to wavelength scaling, the critical power of Kerr self-focusing Pcr in air increases to 300-400 GW, we demonstrate that without external focusing a train of picosecond CO2 laser pulses can propagate in the form of a single several-centimeter diameter channel over hundreds of meters. The train of 10 µm pulses, for which the total energy ≥20 J is distributed over several near-terawatt picosecond pulses with a maximum power ≤2Pcr, is generated naturally during short pulse amplification in a CO2 laser. It is observed that the high-power 10 µm beam forms a large diameter "hot gas" channel in the ambient air with a ≥ 50 ms lifetime. Simulations of the experiment show that such filamentation-free self-channeling regime has low propagation losses and can deliver multi-Joule/TW-power LWIR pulses over km-scale distances.

Gauge Invariant Formulation of the Semiconductor Bloch Equations.

We derive gauge invariant semiconductor Bloch equations (GI-SBEs) that contain only gauge invariant band structure; shift vectors, and triple phase products. The validity and utility of the GI-SBEs is demonstrated in intense laser driven solids with broken inversion symmetry and nontrivial topology. The GI-SBEs present a useful platform for modeling and interpreting light-matter interactions in solids, in which the gauge freedom of the Bloch basis functions obscures physics and creates numerical obstacles.

Subcycle spatiotemporal compression of infrared pulses in χ(2) semiconductors.

Using a full-field propagator model, we report on the emergence of highly localized, subcycle solitonic structures for few-cycle long-wave-infrared (LWIR) pulses propagating through optical semiconductor materials with efficient quadratic nonlinearities and broad anomalous transmission windows. We briefly discuss the theoretical basis for the observed spatiotemporal carrier-wave dynamics and compare it to simulations of a weakly perturbed pulse's propagation through two currently grown, low-loss IR semiconductor crystals.

Optical Carrier-Wave Subcycle Structures Associated with Supercritical Collapse of Long-Wavelength Intense Pulses Propagating in Weakly Anomalously Dispersive Media.

We predict the emergence of attosecond-duration structures on an optical carrier wave when intense, long-wavelength pulses propagate through bulk media with weak anomalous dispersion. Under certain conditions, these structures can undergo a new type of carrier-resolved supercritical collapse, forming infinite spatiotemporal gradients in the field. The mathematical conditions for the onset of this singularity are briefly overviewed, and we demonstrate with a full 3D+time (3+1) simulation that such structures persist under realistic conditions for a 10 micron laser pulse propagating in air.

Memory effects in the long-wave infrared avalanche ionization of gases: a review of recent progress.

There are currently intense efforts being directed towards extending the range and energy of long distance nonlinear pulse propagation in the atmosphere by moving to longer infrared wavelengths, with the purpose of mitigating the effects of turbulence. In addition, picosecond and longer pulse durations are being used to increase the pulse energy. While both of these tacks promise improvements in applications, such as remote sensing and directed energy, they open up fundamental issues regarding the standard model used to calculate the nonlinear optical properties of dilute gases. Amongst these issues is that for longer wavelengths and longer pulse durations, exponential growth of the laser-generated electron density, the so-called avalanche ionization, can limit the propagation range via nonlinear absorption and plasma defocusing. It is therefore important for the continued development of the field to assess the theory and role of avalanche ionization in gases for longer wavelengths. Here, after an overview of the standard model, we present a microscopically motivated approach for the analysis of avalanche ionization in gases that extends beyond the standard model and we contend is key for deepening our understanding of long distance propagation at long infrared wavelengths. Our new approach involves the mean electron kinetic energy, the plasma temperature, and the free electron density as dynamic variables. The rate of avalanche ionization is shown to depend on the full time history of the pulsed excitation, as opposed to the standard model in which the rate is proportional to the instantaneous intensity. Furthermore, the new approach has the added benefit that it is no more computationally intensive than the standard one. The resulting memory effects and some of their measurable physical consequences are demonstrated for the example of long-wavelength infrared avalanche ionization and long distance high-intensity pulse propagation in air. Our hope is that this report in progress will stimulate further discussion that will elucidate the physics and simulation of avalanche ionization at long infrared wavelengths and advance the field.

Non-equilibrium dynamics in the dual-wavelength operation of vertical external-cavity surface-emitting lasers.

Microscopic many-body theory coupled with Maxwell's equation is used to study dual-wavelength operation in vertical external-cavity surface-emitting lasers. The intrinsically dynamic nature of coexisting emission wavelengths in semiconductor lasers is associated with characteristic non-equilibrium carrier dynamics, which causes significant deformations of the quasi-equilibrium gain and carrier inversion. Extended numerical simulations are employed to efficiently investigate the parameter space to identify the regime for dual-wavelength operation. Using a frequency selective intracavity etalon, two families of modes are stabilized with dynamical interchange of the strongest emission peaks. For this operation mode, anti-correlated intensity noise is observed in agreement with the experiment. A method using effective frequency selective filtering is suggested for stabilization of genuine dual-wavelength output.

Control of the nonlinear response of bulk GaAs induced by long-wavelength infrared pulses.

The nonlinear optical response of GaAs is studied using extremely nonresonant 10 µm laser pulses with peak intensities greater than 2 GW/cm 2. We observe over an order of magnitude enhancement in the four-wave mixing efficiency by decreasing the CO 2 laser beat-wave frequency. This enhancement is attributed to currents of photoexcited unbound carriers modulated at the beat frequency, confirmed by measurements of nonlinear absorption at this long wavelength as well as a fully microscopic analysis of the excitation dynamics. Modeling of such nonperturbative semiconductor-laser interactions predicts that further decreasing the beat frequency can increase the nonlinear response and allow for its control over two orders of magnitude.

Self-Channeling of High-Power Long-Wave Infrared Pulses in Atomic Gases.

We simulate and elucidate the self-channeling of high-power 10 µm infrared pulses in atomic gases. The major new result is that the peak intensity can remain remarkably stable over many Rayleigh ranges. This arises from the balance between the self-focusing, diffraction, and defocusing caused by the excitation induced dephasing due to many-body Coulomb effects that enhance the low-intensity plasma densities. This new paradigm removes the Rayleigh range limit for sources in the 8-12 µm atmospheric transmission window and enables transport of individual multi-TW pulses over multiple kilometer ranges.

Modeling and simulation techniques in extreme nonlinear optics of gaseous and condensed media.

Computer simulation techniques for extreme nonlinear optics are reviewed with emphasis on the high light-intensity regimes in which both bound and freed electronic states contribute to the medium response and thus affect the optical pulse dynamics. The first part concentrates on the optical pulse propagation modeling, and provides a classification of various approaches to optical-field evolution equations. Light-matter interaction models are reviewed in the second part, which concentrates on methods that can be integrated with time- and space-resolved simulations encompassing realistic experimental scenarios.

Nonequilibrium and thermal effects in mode-locked VECSELs.

Ultrafast femtosecond timescale dynamics in Vertical External Cavity Surface Emitting Lasers (VECSELs) have recently been employed to achieve record average power and duration mode-locked pulses by employing different types of saturable absorbers and Kerr Lens elements. Microscopic many-body dynamics are expected to dominate when attempting to push pulse durations below 100 fs. We present a preliminary microscopic simulation of ultrafast mode-locking in order to expose the role of hot carrier distributions in establishing ultrafast mode-locking.

Simple model for the nonlinear optical response of gases in the transparency region.

We present a simple model for the nonlinear optical response of atomic gases for pulses with center wavelengths in the transparency region and peak fields for which ionization is not prevalent. By comparing with simulations based on the Schrödinger equation for a hydrogen atom we demonstrate that the model accurately captures the dispersion of the nonlinear polarization as well as noninstantaneous effects for a variety of photon energies and also a two-color pulse. Our approach should be of utility in simulating near- and mid-infrared pulse propagation in dielectric media for which extreme nonlinear effects can arise.

Self-focusing of ultraintense femtosecond optical vortices in air.

Our experiments show that the critical power for self-focusing collapse of femtosecond vortex beams in air is significantly higher than that of a flattop beam and grows approximately linearly with the vortex order. With less than 10% of initial transverse intensity modulation of the beam profiles, the dominant mode of self-focusing collapse is the azimuthal breakup of the vortex rings into individual filaments, the number of which grows with the input beam power. The generated bottlelike distributions of plasma filaments rotate on propagation in the direction determined by the sense of vorticity.

Nonequilibrium evolution of strong-field anisotropic ionized electrons towards a delayed plasma-state.

Rigorous quantum calculations of the femtosecond ionization of hydrogen atoms in air lead to highly anisotropic electron and ion angular (momentum) distributions. A quantum Monte-Carlo analysis of the subsequent many-body dynamics reveals two distinct relaxation steps, first to a nearly isotropic hot nonequilibrium and then to a quasi-equilibrium configuration. The collective isotropic plasma state is reached on a picosecond timescale well after the ultrashort ionizing pulse has passed.

On the relative roles of higher-order nonlinearity and ionization in ultrafast light-matter interactions.

Far off-resonant ultrafast and nonlinear light-matter interactions are studied using a one-dimensional atomic model. Results from a pump-probe diagnostic reveal that any higher-order nonlinear refraction is masked by ionization-induced defocusing before it becomes significant. On the other hand, we show that signatures of a higher-order nonlinearity may still be manifest via low-order harmonics of the pump center frequency. Implications for filamentation of femtosecond pulses are pointed out.

Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices.

We investigate the linear propagation of Gaussian-apodized solutions to the paraxial wave equation in free-space and first-order optical systems. In particular, we present complex coordinate transformations that yield a very general and efficient method to apply a Gaussian apodization (possibly with initial phase curvature) to a solution of the paraxial wave equation. Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel-Gauss and the Airy-Gauss beams, which are of strong interest to researchers and practitioners in various fields.

Self-focusing collapse distance in ultrashort pulses and measurement of nonlinear index.

We analyze the method of moving focus to determine the critical power for self-focusing by means of numerical simulation and a semianalytical model. It is shown that the original interpretation of a moving focus experiment does not hold in general and that inclusion of defocusing effects due to free electrons is necessary to relate the measured data to critical power.

Coherent beam transformations using multimode waveguides.

Physical insights and characteristics of beam transformations based on multimode interference (MMI) in multimode waveguides are illuminated and analyzed. Our calculations show that, utilizing a short piece of cylindrical multimode waveguide, an input Gaussian beam can be readily transformed to frequently desired beams including top-hat, donut-shaped, taper-shaped, and Bessel-like beams in the Fresnel or the Fraunhofer diffraction range, or even in both ranges. This is a consequence of diffractive propagation of the field exiting the waveguide. The performance of the beam shaper based on MMI can be controlled via tailoring the dimensions of the multimode waveguide or changing the signal wavelength. This beam shaping technique is investigated experimentally using monolithic fiber devices consisting of a short piece of multimode fiber (approximately 10 mm long) and a single-mode signal delivery fiber.

Femtosecond filamentation in air and higher-order nonlinearities.

According to a recent experiment, the instantaneous electronic Kerr effect in air exhibits a strong intensity dependence, the nonlinear refractive index switching sign and crossing over from a self-focusing to a defocusing nonlinearity. A subsequent theoretical work has demonstrated that this has paradigm-changing consequences for the understanding of filamentation in air, so it is important to subject the idea of higher-order nonlinearities to stringent tests. Here we use numerical modeling to propose an experiment capable of discriminating between the standard and the new intensity-dependent Kerr-effect models.

On the higher-order Kerr effect in femtosecond filaments.

A recent experiment probing the electronic nonlinearity in the femtosecond filament indicated that the optical Kerr effect not only saturates but even changes its sign at high intensities and thus switches from self-focusing to a strongly defocusing regime. Here we examine, through simulations and experiment, some implications of such a behavior. We perform comparative simulations based on the standard model on one hand and on a model implementing the intensity-dependent Kerr effect on the other. Comparison with an experiment provides a strong indication that of these two Kerr-effect models the standard model is better in capturing the observed length of the filament. However, neither of the models can reproduce length and filament radius. Possible implications are discussed.

Plasmonic nano-structures for optical data storage.

We propose a method of optical data storage that exploits the small dimensions of metallic nano-particles and/or nano-structures to achieve high storage densities. The resonant behavior of these particles (both individually and in small clusters) in the presence of ultraviolet, visible, and near-infrared light may be used to retrieve pre-recorded information by far-field spectroscopic optical detection. In plasmonic data storage, a very short (approximately few femtoseconds) laser pulse is focused to a diffraction-limited spot over a small region of an optical disk containing metallic nano-structures. The digital data stored in each bit-cell, comprising multiple bits of information, modifies the spectrum of the incident light pulse. This spectrum is subsequently detected, upon reflection/transmission, with the aid of an optical spectrum analyzer. We present theoretical as well as preliminary experimental results that confirm the potential of plasmonic nano-structures for high-density optical data storage applications.