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.

Nonlinearity and ionization in Xe: experiment-based calibration of a numerical model.

Recently proposed universality of the nonlinear response is put to the test and used to improve a previously designed model for xenon. Utilizing accurate measurements resolving the nonlinear polarization and ionization in time and space, we calibrate the scaling parameters of the model and demonstrate agreement with several experiments spanning the intensity range relevant for applications in nonlinear optics at near-infrared and mid-infrared wavelengths. Applications to other species including small molecules are discussed, suggesting a self-consistent way to calibrate light-matter interaction models.

Universal long-wavelength nonlinear optical response of noble gases.

We demonstrate numerically that the long-wavelength nonlinear dipole moment and ionization rate versus electric field strength F for different noble gases can be scaled onto each other, revealing universal functions that characterize the form of the nonlinear response. We elucidate the physical origin of the universality by using a metastable state analysis of the light-atom interaction in combination with a scaling analysis. Our results also provide a powerful new means of characterizing the nonlinear response in the mid-infrared and long-wave infrared for optical filamentation studies.

Accelerated nonlinear interactions in graded-index multimode fibers.

Multimode optical fibers have recently reemerged as a viable platform for addressing a number of long-standing issues associated with information bandwidth requirements and power-handling capabilities. As shown in recent studies, the complex nature of such heavily multimoded systems can be effectively exploited to observe altogether novel physical effects arising from spatiotemporal and intermodal linear and nonlinear processes. Here, we study for the first time, accelerated nonlinear intermodal interactions in core-diameter decreasing multimode fibers. We demonstrate that in the anomalous dispersion region, this spatiotemporal acceleration can lead to relatively blue-shifted multimode solitons and blue-drifting dispersive wave combs, while in the normal domain, to a notably flat and uniform supercontinuum, extending over 2.5 octaves. Our results pave the way towards a deeper understanding of the physics and complexity of nonlinear, heavily multimoded optical systems, and could lead to highly tunable optical sources with very high spectral densities.

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.

True versus effective Kerr nonlinear response in optical filamentation.

The optical Kerr effect, and the nonlinear polarization in general, represents an important light-matter interaction governing many regimes encountered in the nonlinear optics. We reason that in the context of optical filamentation one should distinguish the third-order Kerr effect occurring at relatively low light intensities from the effective Kerr nonlinearity relevant to higher intensity. While many properties of filaments can be captured well with a third-order nonlinear polarization model with a nonlinear index chosen somewhat higher than the true nonlinear index operative at low intensities, our comparative simulations indicate that some filamentation aspects carry significant signatures from the higher-order nonlinearity.

Bound-Electron Nonlinearity Beyond the Ionization Threshold.

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

On the manifestation of higher-order nonlinearities in a noble gas medium undergoing strong ionization.

While there is a consensus that higher-order effects beyond χ(3) are present also in high-intensity light-matter interactions, when and how they become apparent needs further study. The central question addressed in this Letter is whether it is possible to design a situation in which they show up before being completely masked by the electrons freed by a high-intensity field. The second question we attempt to answer is how much such observations, if and when feasible, can reveal about the nature of the nonlinear polarization. We answer the first question in the affirmative, but our comparative simulations indicate that distinguishing the higher-order nonlinearity from the third-order polarization can be extremely challenging. We also briefly discuss the implications for the interpretation of the measured values of the nonlinear index.

Versatile supercontinuum generation in parabolic multimode optical fibers.

We demonstrate that the pump's spatial input profile can provide additional degrees of freedom in tailoring at will the nonlinear dynamics and the ensuing spectral content of supercontinuum generation in highly multimoded optical fibers. Experiments and simulations carried out at 1550 nm indicate that the modal composition of the input beam can substantially alter the soliton fission process as well as the resulting Raman and dispersive wave generation that eventually lead to supercontinuum in such a multimode environment. Given the multitude of conceivable initial conditions, our results suggest that it is possible to pre-engineer the supercontinuum spectral content in a versatile manner.

Tailoring frequency generation in uniform and concatenated multimode fibers.

We demonstrate that frequency generation in multimode parabolic-index fibers can be precisely engineered through appropriate fiber design. This is accomplished by exploiting the onset of a geometric parametric instability that arises from resonant spatiotemporal compression. By launching the output of an amplified Q-switched microchip laser delivering 400 ps pulses at 1064 nm, we observe a series of intense frequency sidebands that strongly depend on the fiber core size. The nonlinear frequency generation is analyzed in three fiber samples with 50 µm, 60 µm, and 80 µm core diameters. We further demonstrate that by cascading fibers of different core sizes, a desired frequency band can be generated from the frequency lines parametrically produced in each section. The observed frequency shifts are in good agreement with analytical predictions and numerical simulations. Our results suggest that core scaling and fiber concatenation can provide a viable avenue in designing optical sources with tailored output frequencies.

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.

Numerical investigation of enhanced femtosecond supercontinuum via a weak seed in noble gases.

Numerical simulations are employed to elucidate the physics underlying the enhanced femtosecond supercontinuum generation previously observed during optical filamentation in noble gases and in the presence of a weak seed pulse. Simulations based on the metastable electronic state approach are shown not only to capture the qualitative features of the experiment, but also reveal the relation of the observed enhancement to recent developments in the area of sub-cycle engineering of filaments.

Carrier-wave shape effects in optical filamentation.

Strong-field ionization in optical filaments created by ultrashort pulses with sub-cycle engineered waveforms is studied theoretically. To elucidate the physics of the recently demonstrated enhanced ionization yield and spatial control of the optical filament core in two color pulses, we employ two types of quantum models integrated into spatially resolved pulse-propagation simulations. We show that the dependence of the ionization on the shape of the excitation carrier is adiabatic in nature, and is driven by local temporal peaks of the electric field. Implications for the modeling of light-matter interactions in multicolor optical fields are also discussed.

Assessment of the metastable electronic state approach as a microscopically self-consistent description for the nonlinear response of atoms.

This Letter presents the first quantitative assessment of the recently proposed metastable electronic state approach (MESA) for calculation of the nonlinear optical response of noble gas atoms. Based on the single active electron potentials for several atomic species, Stark resonant states are used to extract the nonlinear polarization and ionization rates free of any additional fitting parameters. It is shown that even the simplest version of the method provides a viable, first-principle-based, and self-consistent alternative to the standard model commonly used for simulations in the field of extreme nonlinear optics.

Spatial effects in supercontinuum generation in waveguides.

An economic, space- and time-resolved method to model ultra-short, intense pulse propagation in waveguides is described. Simulations of supercontinuum generation on a chip demonstrate the utility of the approach. Comparisons with the generalized nonlinear Schrödinger equation elucidate spatial effects, which influence pulse dynamics and the generation of new spectral components.

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.

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.

Raman effect in self-focusing of few-cycle laser pulses in air.

Self-focusing of ultrashort pulses in air is investigated by means of numerical simulations. The role of the vibrational Raman effect and its dependence on pulse chirp is studied, with results shedding new light on the interpretation of the measurements of the critical self-focusing power. We also discuss computational modeling issues important specifically for few-cycle pulses.

Midinfrared femtosecond laser pulse filamentation in hollow waveguides: a comparison of simulation methods.

This work compares computational methods for laser pulse propagation in hollow waveguides filled with rare gases at high pressures, with applications in extreme nonlinear optics in the midinfrared wavelength region. As the wavelength of light λ=2π/k increases with respect to the transverse size R of a leaky waveguide, the loss of light out of the waveguide upon propagation, in general, increases. The now standard numerical approach for studying such structures is based on expansion of the propagating field into approximate leaky waveguide modes. We compare this approach to an improved method that resolves the electric field in real space and correctly captures the energy loss through the waveguide wall. The comparison reveals that the expansion-based approach overestimates losses that occur in nonlinearly reshaped pulsed waveforms. For a modest increase in computational effort, the alternate method offers a physically more accurate model to describe phenomena (e.g., extreme pulse-selfcompression) in waveguides with smaller values of kR.

Dressed optical filaments.

In this Letter we show that by appropriately providing an auxiliary "dress" beam one can extend the longevity of an optical filament by almost one order of magnitude. These optical dressed filaments can propagate substantially further by judiciously harnessing energy from their secondary beam reservoir. This possibility is theoretically investigated in air when the filament is dressed with a conically convergent annular Gaussian beam.