Diffraction of an optical pulse as an expansion in ultrashort orthogonal Gaussian beam modes

Abstract

The Laguerre-Gaussian (LG) beam expansion is described as a numerical and physical model of paraxial ultrashort pulse diffraction in the time domain. An overview of the dynamics of higher-order ultrashort planar LG modes is given through numerical simulations, and the finite width of these beams is shown to induce a dispersive-like axial broadening of the fields, which creates related variations in the on-axis amplitude of such pulses. The propagation of a pulsed plane wave scattered at an aperture is then illustrated as a finite weighted sum of individual planar LG pulses, which allows for intuitive illustration of the convergence of this expansion technique. By applying such an expansion to diffraction at a hard aperture, the planar pulsed LG beams are described as the paraxial analogs of the Bessel boundary waves typically observed in such situations, with both exhibiting superluminal group velocities along the optical axis. Numerical results of pulse diffraction at an aperture highlight the suitability of the LG expansion method for efficient and practical simulation of ultrashort fields in the paraxial regime.

Femtosecond spatial pulse shaping at the focal plane

“…An alternative method to find the diffraction of optical pulses by hard apertures were proposed recently in [11], in which the diffracted ultrashort pulses are obtained propagating the basis elements of the aperture expansion in terms of LG modes. This procedure were not computational efficient since the analytical expression for the propagation of the LG ultrashort pulses, the pulselets, were undiscovered.…”

“…The expansion of light fields in LG modes is a well known technique used mostly for monochromatic light [9], with the exception of a few works in which this is employed to analyze the dynamics of ultrashort pulses [10,11]. In [10], Liu et al determine the propagation of the ultrashort pulse Laguerre-Gaussian Beam.…”

“…The authors consider non-constant expansion coefficients dependent on space-time variables, whose solutions are found numerically. In [11], Mahon et al use the expansion method to find the diffraction of ultrashort pulses by amplitude modulating transmittances. The procedure in [11] is quite different to that in [10] since the expansion coefficients are taking as constant values, while the expansion elements (the orthonormal basis) are space-time dependent.…”

“…In [11], Mahon et al use the expansion method to find the diffraction of ultrashort pulses by amplitude modulating transmittances. The procedure in [11] is quite different to that in [10] since the expansion coefficients are taking as constant values, while the expansion elements (the orthonormal basis) are space-time dependent. Their results were not computational efficient, as pointed out by the authors, for the reason that the expansion elements were calculated numerically.…”

“…Their results were not computational efficient, as pointed out by the authors, for the reason that the expansion elements were calculated numerically. We extend the procedure described in [11] to determine the diffraction of pulses by complex signals codified in computer generated holograms. Each element of the expansion at the SLM plane is propagated to the focus being univocally associated to its corresponding ultrashort electric field, the "pulselet".…”