Paolo Di Trapani

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

We present an overview of nonlinear phenomena related to optical quadratic solitons—intrinsically multicomponent localized states of light, which can exist in media without inversion symmetry at the molecular level. Starting with presentation of a few derivation schemes of basic equations describing three-wave parametric wave mixing in di7ractive and=or dispersive quadratic media, we discuss their continuous wave solutions and modulational instability phenomena, and then move to the classi8cation and stability analysis of the parametric solitary waves. Not limiting ourselves to the simplest spatial and temporal quadratic solitons we also overview results related to the spatio-temporal solitons (light bullets), higher order quadratic solitons, solitons due to competing nonlinearities, dark solitons, gap solitons, cavity solitons and vortices. Special attention is paid to a comprehensive discussion of the recent experimental demonstrations of the parametric solitons including their interactions and switching. We also discuss connections of quadratic solitons with other types of solitons in optics and their interdisciplinary signi8cance. c

Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses.

The precise observation of the angle-frequency spectrum of light filaments in water reveals a scenario incompatible with current models of conical emission (CE). Its description in terms of linear X-wave modes leads us to understand filamentation dynamics requiring a phase- and group-matched, Kerr-driven four-wave-mixing process that involves two highly localized pumps and two X waves. CE and temporal splitting arise naturally as two manifestations of this process.

Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses

Nonlinear losses accompanying self-focusing substantially impact the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D + 1 nonlinear Schrödinger equation, which are stable against radial collapse. These are featured by linear, conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as a strong attractor for the self-focusing dynamics in Kerr media.

Generation of extended plasma channels in air using femtosecond Bessel beams

Extending the longitudinal range of plasma channels created by ultrashort laser pulses in atmosphere is important in practical applications of laser-induced plasma such as remote spectroscopy and lightning control. Weakly focused femtosecond Gaussian beams that are commonly used for generating plasma channels offer only a limited control of filamentation. Increasing the pulse energy in this case typically results in creation of multiple filaments and does not appreciably extend the longitudinal range of filamentation. Bessel beams with their extended linear foci intuitively appear to be better suited for generation of long plasma channels. We report experimental results on creating extended filaments in air using femtosecond Bessel beams. By probing the linear plasma density along the filament, we show that apertured Bessel beams produce stable single plasma channels that span the entire extent of the linear focus of the beam. We further show that by temporally chirping the pulse, the plasma channel can be longitudinally shifted beyond the linear-focus zone, an important effect that may potentially offer additional means of controlling filament formation.

Time-resolved refractive index and absorption mapping of light-plasma filaments in water

By means of a quantitative shadowgraphic method, we performed a space-time characterization of the refractive index variation and transient absorption induced by a light-plasma filament generated by a 120 fs laser pulse in water. The formation and evolution of the plasma channel in the proximity of the nonlinear focus were observed with a 23 fs time resolution.

Far-field spectral characterization of conical emission and filamentation in Kerr media

By use of an imaging spectrometer we map the far-field (theta-lambda) spectra of 200-fs optical pulses that have undergone beam collapse and filamentation in a Kerr medium. By studying the evolution of the spectra with increasing input power and by using a model based on an asymptotic linear superposition of stationary wave modes (rather than the exact instantaneous solution), we are able to trace a consistent model of optical beam collapse highlighting the interplay between conical emission, multiple pulse splitting, and other effects such as spatial chirp.

Ultrashort laser pulse filamentation from spontaneous X Wave formation in air

The description of ultrashort laser pulse filamentation in condensed media as a spontaneous formation of X waves is shown to apply also to filaments generated in air. Within this framework, a simple explanation is brought for several features of the filament such as the subdiffractive propagation and the energy flux from the weakly localized tails of the X-waves to the intense core.

Localized and stationary light wave modes in dispersive media

In recent experiments, localized and stationary optical wave packets have been generated in second-order nonlinear processes with femtosecond pulses, whose asymptotic features relate to those of nondiffracting and nondispersing polychromatic Bessel beams in linear dispersive media. We investigate the nature of these linear waves and show that they can be identified with the X-shaped (O-shaped) modes of the hyperbolic (elliptic) wave equation in media with normal (anomalous) dispersion. Depending on the relative strengths of mode phase mismatch, group velocity mismatch with respect to a plane pulse, and the defeated group velocity dispersion, these modes can adopt the form of pulsed Bessel beams, focus wave modes, and X waves (O waves), respectively.

Bessel X waves in two- and three-dimensional bidispersive optical systems

We show that new families of two- and three-dimensional nondiffracting Bessel X waves are possible in linear bidispersive optical systems. These X waves can be observed in both bulk and waveguide configurations as well as in photonic crystal lattices that simultaneously exhibit normal and anomalous dispersive-diffractive properties in different spatial or spatiotemporal coordinates.

Spiraling zero-order Bessel beam

The question that we are addressing concerns the possibility of creating a zeroth-order Bessel-like beam that spirals around the axis of propagation. The analytical features of the beam propagation are studied theoretically. Approximations to such a light field can be experimentally realized by using an axicon and a hologram. The beam potentially can attract interest in microfabrication applications.