Efficiently parallelized modeling of tightly focused, large bandwidth laser pulses

TL;DR

This paper presents a parallelized computational method based on the Stratton-Chu integral representation to efficiently model large bandwidth, tightly focused laser pulses, enabling accurate analysis of their spatio-temporal properties.

Contribution

The authors develop a parallelized algorithm for evaluating Stratton-Chu diffraction integrals that handles arbitrary incident fields, improving computational efficiency for modeling high-intensity laser focusing.

Findings

Efficient quadrature methods can evaluate diffraction integrals without strong oscillations.

Reflection induces ellipticity and longitudinal components in the focused laser field.

Projected laser intensities may reach up to 10^{24} W/cm^2 in future facilities.

Abstract

The Stratton-Chu integral representation of electromagnetic fields is used to study the spatio-temporal properties of large bandwidth laser pulses focused by high numerical aperture mirrors. We review the formal aspects of the derivation of diffraction integrals from the Stratton-Chu representation and discuss the use of the Hadamard finite part in the derivation of the physical optics approximation. By analyzing the formulation we show that, for the specific case of a parabolic mirror, the integrands involved in the description of the reflected field near the focal spot do not possess the strong oscillations characteristic of diffraction integrals. Consequently, the integrals can be evaluated with simple and efficient quadrature methods rather than with specialized, more costly approaches. We report on the development of an efficiently parallelized algorithm that evaluates the Stratton-Chu diffraction integrals for incident fields of arbitrary temporal and spatial dependence. This method has the advantage that its input is the unfocused field coming from the laser chain, which is experimentally known with high accuracy. We use our method to show that the reflection of a linearly polarized Gaussian beam of femtosecond duration off a high numerical aperture parabolic mirror induces ellipticity in the dominant field components and generates strong longitudinal components. We also estimate that future high-power laser facilities may reach intensities of $10^{24}\,\text{W/cm}^2$.