Femtosecond filamentation in transparent media

Nonlinear photonic chips can generate and process signals all-optically with far superior performance to that possible electronically — particularly with respect to speed. Although silicon-on-insulator has been the leading platform for nonlinear optics, its high two-photon absorption at telecommunication wavelengths poses a fundamental limitation. We review recent progress in non-silicon CMOS-compatible platforms for nonlinear optics, with a focus on Si3N4 and Hydex®. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation and ultrafast optical pulse generation and measurement. We highlight their potential future impact as well as the challenges to achieving practical solutions for many key applications. This article reviews recent progress in the use of silicon nitride and Hydex as non-silicon-based CMOS-compatible platforms for nonlinear optics. New capabilities such as on-chip optical frequency comb generation, ultrafast optical pulse generation and measurement using these materials, and their potential future impact and challenges are covered.

New CMOS-compatible platforms based on silicon nitride and hydex for nonlinear optics

Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration and peak powers exceeding several terawatt (TW). When such pulses propagate through optically transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid on the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. The dynamics of single filaments created over laboratory scales in various materials such as noble gases, liquids and dielectrics reveal new perspectives in pulse shortening techniques. Far-field spectra provide promising diagnostics. Attention is also paid to the multifilamentation instability of broad beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy and the possibility of guiding electric discharges in air are finally addressed on the basis of experimental results.

https://iopscience.iop.org/article/10.1088/0034-4885/70/10/R03/pdf

Ultrashort filaments of light in weakly ionized, optically transparent media

Self-similar propagation of ultrashort, parabolic pulses in a laser resonator is observed theoretically and experimentally. This constitutes a new type of pulse shaping in mode-locked lasers: in contrast to the well-known static (solitonlike) and breathing (dispersion-managed soliton) pulse evolutions, asymptotic solutions to the nonlinear wave equation that governs pulse propagation in most of the laser cavity are observed. Stable self-similar pulses exist with energies much greater than can be tolerated in solitonlike pulse shaping, and this has implications for practical lasers.

https://arxiv.org/pdf/physics/0402013.pdf

Self-similar evolution of parabolic pulses in a laser.

In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

https://iopscience.iop.org/article/10.1088/1464-4266/7/5/R02/pdf

Spatiotemporal optical solitons

A qualitative as well as quantitative investigation is made of the conditions for avoiding wave breaking during pulse propagation in optical fibers. In particular, it is shown that pulses having a parabolic intensity variation are approximate wave-breaking-free solutions of the nonlinear Schrodinger equation in the high-intensity limit. A simple expression for the compression factor of a fiber-grating compressor based on parabolic pulses is also derived.

Wave-breaking-free pulses in nonlinear-optical fibers

We analyze the structure of the first azimuthal stationary state for a nonlinear medium presenting simultaneously a cubic (focusing) and a quintic (defocusing) dependence with the light intensity in the refractive index. This solution takes the form of a dark vortex of light hosted in a compact light beam. The existence of these modes is guaranteed if the flux exceeds a certain minimum threshold and if the modes are extremely stable for fluxes larger than a critical value that we calculated. We verified the robust nature of this solution inducing internal oscillations by an initial phase chirp. Using the variational method, we obtain an approximate picture for the beam internal dynamics. We also studied numerically the interactions between two near-vortex solutions, finding that for a wide combination of beam parameters they show elastic collisions.

Stable azimuthal stationary state in quintic nonlinear optical media

An analytical investigation is made of the interplay between dispersion and nonlinearity in the creation of wave breaking in optical fibers. Wave breaking is found to involve two independent processes: (a) overtaking of different parts of the pulse and (b) nonlinear generation of new frequencies during overtaking. Analytical predictions for the distance of wave breaking are obtained and found to be in good agreement with numerical results.

Wave breaking in nonlinear-optical fibers

We show that a laser beam which propagates through a cubic-quintic nonlinear optical material may reach, for a given power, a condensed state with a collisional dynamics resembling a liquid drop. We qualitatively describe the analogies between this system and the usual fluids and show them by simulating numerically total reflections of these beams with planar boundaries and localized defects. We use the analogy ''liquid light'' to stress the connections with the dynamics of quantum fluids, including Bose-Einstein condensates. If a laser beam is regarded as a gas of photons, two inter- esting questions can be formulated: Would it be possible to produce something like a state of liquid light? and what physical properties will this peculiar state show? We will demonstrate in the present paper that high-power laser beams and pulses which propagate through certain nonlinear optical materials, may reach a condensed state with physical behav- ior resembling a ~coherent! liquid droplet. We have per- formed a numerical exploration of the properties of these ''light droplets,'' inspired by the physical picture of the sur- face tension of the usual liquids. Our numerical simulations reveal that the collisions of light ''streams'' ~i.e., laser beams! and droplets ~i.e., laser pulsed beams! against bound- aries and localized inhomogeneities show interesting analo- gies with fluid mechanics. The calculations also demonstrate that our theoretical predictions can be tested in the frame of current experiments with realistic materials. Thus, we will begin by recalling some well-known effects of laser beam propagation in cubic-quintic nonlinear media, which are the simplest optical materials where light conden- sates can be obtained. Next, we will analyze in detail the peculiar shape of the stationary states of the system and for- mulate two simple ideal experiments to detect properties of ''light streams'' and ''light droplets'' analogous to the surface tension of liquids. Finally, we performed the numerical implementation of these ideas and found that light conden- sates do exhibit surface tension properties. We calculated the main parameters involved for realistic materials, in order to stimulate the experimental test of our predictions.

Liquid light condensates

A nonlinear fiber with a gain that has symmetric lateral frequency bands is found to generate a stable train of bright or dark pulses with a well-defined repetition rate. The pulse train is generated from noise; the pulses are unchirped, and their amplitude and repetition rate are determined by the parameters of the system. The underlying mechanism for this pulse formation is recognized as dissipative four-wave mixing in which only two frequencies are nonnegligible; one near the maximum gain transmits energy by wave mixing to its third harmonic, which is in the region of negative gain. An implicit analytical expression for the pulse train solution is derived. It is demonstrated that dissipative four-wave mixing can be employed to yield passive mode locking in a fiber ring laser consisting of only a filter and an active fiber. The resulting train of pulses is shown to have a high soliton content.

M. L. Quiroga-Teixeiro

Papers

Wave-breaking-free pulses in nonlinear-optical fibers

Stable azimuthal stationary state in quintic nonlinear optical media

Wave breaking in nonlinear-optical fibers

Liquid light condensates

Passive mode locking by dissipative four-wave mixing