Miguel A. Porras

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.

Complex beam parameter and ABCD law for non-Gaussian and nonspherical light beams

We define the width, divergence, and curvature radius for non-Gaussian and nonspherical light beams. A complex beam parameter is also defined as a function of the three previous ones. We then prove that the ABCD law remains valid for transforming the new complex beam parameter when a non-Gaussian and nonspherical, orthogonal, or cylindrical symmetric laser beam passes through a real ABCD optical system. The product of the minimum width multiplied by the divergence of the beam is invariant under ABCD transformations. Some examples are given.

Non-paraxial vectorial moment theory of light beam propagation

Abstract The cross sections of arbitrary-shaped non-paraxial light beams are characterized by the zero, first and second order moments of the energy flux spatial distribution. On the basis of the Maxwell equations and a plane wave spectrum representation of electromagnetic fields, the laws governing the change of these moments upon free beam propagation are found. In particular, the change of the second-moment-based width is found to be hyperbolic. The moment-based parameters are calculated and the hyperbolic law applied to some particular non-paraxial beam-like electromagnetic field models to show some new features that arise from this non-paraxial vectorial theory.

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.

Diffraction-free and dispersion-free pulsed beam propagation in dispersive media.

The diffraction of pulsed beams of light is formulated as an anomalously dispersive phenomenon. In a dispersive material, the effects of material group-velocity dispersion and diffraction on pulsed beam propagation can mutually cancel if the transverse profile of the pulse is suitably chosen.

Relationship between elegant Laguerre–Gauss and Bessel–Gauss beams

We show that the elegant Laguerre-Gauss light beams of high radial order n are asymptotically equal to Bessel-Gauss light beams. The Bessel-Gauss beam equivalent to each elegant Laguerre-Gauss beam is found and shown to have almost identical propagation factors M2. In the limit n-->infinity, elegant Laguerre-Gauss beams can be identified with Durnins Bessel beam. Our results suggest a new experimental procedure for generating light beams with nondiffractinglike properties directly from the output of a stable resonator.

Self-reconstruction of light filaments.

By observing how a light filament generated in water reconstructs itself after hitting a beam stopper in the presence and in the absence of a nonlinear medium, we describe the occurrence of an important linear contribution to reconstruction that is associated with the conical nature of the wave. A possible scenario by which conical wave components are generated inside the medium by the distributed stopper or reflector created by nonlinear losses or plasma is presented.

High localization, focal depth and contrast by means of nonlinear Bessel Beams

We show an experimental and computational comparison between the resolution power, the contrast and the focal depth of a nonlinearly propagated diffraction-free beam and of other beams (a linear and a nonlinearly propagated Gaussian pulse): launching a nondiffractive Bessel pulse in a solution of Coumarine 120 in methanol creates a high contrast, 40 mm long, 10 microm width fluorescence channel excited by 3-photon absorption process. This fluorescence channel exhibits the same contrast and resolution of a tightly focused Gaussian pulse, but reaches a focal depth that outclasses by orders of magnitude that reached by an equivalent Gaussian pulse.

Suppression of dispersive broadening of light pulses with Bessel–Gauss beams

Abstract We show that a pulse can travel arbitrarily long distances without significant temporal spreading in a material with normal group velocity dispersion by endowing the pulse with a transversal Bessel–Gauss amplitude profile of suitable characteristics. Contrary to previous works, dispersion suppression is achieved with a finite-energy, transversally limited source, whose radius determines the largest dispersion-free propagation distance.