Fields of a Bessel-Bessel light bullet of arbitrary order in an under-dense plasma

Quasi-Rational Analytic Approximation for the Modified Bessel Function I1(x) with High Accuracy

A new simple and accurate expression to approximate the modified Bessel function of the first kind I1(x) is presented in this work. This new approximation is obtained as an improvement of the multi-point quasi-rational approximation technique, MPQA. This method uses the power series of the Bessel function, its asymptotic expansion, and a process of optimization to fit the parameters of a fitting function. The fitting expression is formed by elementary functions combined with rational ones. In the present work, a sum of hyperbolic functions was selected as elementary functions to capture the first two terms of the asymptotic expansion of I1(x), which represents an important improvement with respect to previous research, where just the leading term of the asymptotic series was captured. The new approximation function presents a remarkable agreement with the analytical solution I1(x), decreasing the maximum relative error in more than one order of magnitude with respect to previous similar expressions. Concretely, the relative error was reduced from 10−2 to 4×10−4, opening the possibility of applying the new improved method to other Bessel functions. It is also remarkable that the new approximation is valid for all positive and negative values of the argument.

Long-range quasi-non-diffracting Gauss-Bessel beams in a few-cycle laser field

Many applications ranging from nonlinear optics to material processing would benefit from pulsed ultrashort (quasi-)non-diffracting Gauss-Bessel beams (GBBs). Here we demonstrate a straightforward yet efficient method for generating such zeroth- and first-order GBBs using a single reflective spatial light modulator. Even in the sub-8-fs range there are no noticeable consequences for the measured pulse duration. The only effect is a weak "coloring" of the outer-lying satellite rings of the beams due to the spectrum spanning over more than 300 nm. The obtained beams have diffraction half-angles below 40 μrad and reach propagation distances in excess of 1.5 m.

Integrated structured light architectures

The structural versatility of light underpins an outstanding collection of optical phenomena where both geometrical and topological states of light can dictate how matter will respond or display. Light possesses multiple degrees of freedom such as amplitude, and linear, spin angular, and orbital angular momenta, but the ability to adaptively engineer the spatio-temporal distribution of all these characteristics is primarily curtailed by technologies used to impose any desired structure to light. We demonstrate a laser architecture based on coherent beam combination offering integrated spatio-temporal field control and programmability, thereby presenting unique opportunities for generating light by design to exploit its topology.

Zeroth- and first-order long range non-diffracting Gauss-Bessel beams generated by annihilating multiple-charged optical vortices

We demonstrate an alternative approach for generating zeroth- and first-order long range non-diffracting Gauss–Bessel beams (GBBs). Starting from a Gaussian beam, the key point is the creation of a bright ring-shaped beam with a large radius-to-width ratio, which is subsequently Fourier-transformed by a thin lens. The phase profile required for creating zeroth-order GBBs is flat and helical for first-order GBBs with unit topological charge (TC). Both the ring-shaped beam and the required phase profile can be realized by creating highly charged optical vortices by a spatial light modulator and annihilating them by using a second modulator of the same type. The generated long-range GBBs are proven to have negligible transverse evolution up to 2 m and can be regarded as non-diffracting. The influences of the charge state of the TCs, the propagation distance behind the focusing lens, and the GBB profiles on the relative intensities of the peak/rings are discussed. The method is much more efficient as compared to this using annular slits in the back focal plane of lenses. Moreover, at large propagation distances the quality of the generated GBBs significantly surpasses this of GBBs created by low angle axicons. The developed analytical model reproduces the experimental data. The presented method is flexible, easily realizable by using a spatial light modulator, does not require any special optical elements and, thus, is accessible in many laboratories.

Velocity and acceleration freely tunable straight-line propagation light bullet

Three-dimensional (3-D) light solitons in space–time, referred to as light bullets, have many novel properties and wide applications. Here we theoretically show how the combination of diffraction-free beam and ultrashort pulse spatiotemporal-coupling enables the creation of a straight-line propagation light bullet with freely tunable velocity and acceleration. This light bullet could propagate with a constant superluminal or subluminal velocity, and it could also counter-propagate with a very fast superluminal velocity (e.g., − 35.6c). Apart from uniform motion, an acceleration or deceleration straight-line propagation light bullet with a tunable instantaneous acceleration could also be produced. The high controllability of the velocity and the acceleration of a straight-line propagation light bullet would enable very specific applications, such as velocity and/or acceleration matched micromanipulation, microscopy, particle acceleration, radiation generation, and so on.

Self-induced periodic interfering behavior of dual Airy beam in strongly nonlocal medium

Based on a reduction of nonlocal nonlinear Schrödinger equation in strongly nonlocal regime, the linear Schrödinger equation with parabolic potential, analytical results describing the evolution of dual Airy beam are presented. The results show that the dual Airy beam in strongly nonlocal medium exhibits a periodic focusing and defocusing behavior, and forms the interference fringes between the focusing and defocusing positions. The analytical results are verified by numerically solving nonlocal nonlinear Schrödinger equation and shown to be reasonable when the characteristic response width is broader than the width of the dual Airy beam. Furthermore, the characteristics of the interference fringes induced by the dual Airy beam are also investigated in detail, and can be used for the measurement of the system parameters. In addition, we propose a scheme to generate dual Airy beam in strongly nonlocal medium.