On the localization of the high-intensity region of simultaneous space-time foci

TL;DR

This paper investigates whether simultaneous space-time focusing (SSTF) truly reduces the longitudinal extent of high-intensity regions, using analytical and numerical methods to clarify misconceptions about its localization capabilities.

Contribution

The study provides analytical expressions for SSTF pulse profiles and compares SSTF with equivalent non-SSTF focusing, clarifying misconceptions about intensity localization.

Findings

SSTF does not constrain high-intensity regions more than equivalent non-SSTF focusing.

Analytical methods agree well with numerical calculations for SSTF profiles.

Simplistic intensity calculations can overestimate localization unless spatio-temporal couplings are considered.

Abstract

Simultaneous space-time focusing (SSTF) is sometimes claimed to reduce the longitudinal extent of the high-intensity region near the focus, in contradiction to the original work on this topic. Here we seek to address this confusion by using numerical and analytical methods to investigate the degree of localization of the spatio-temporal intensity of an SSTF pulse. The analytical method is found to be in excellent agreement with numerical calculations and yields, for bi-Gaussian input pulses, expressions for the three-dimensional spatio-temporal intensity profile of the SSTF pulse, and for the on-axis bandwidth, pulse duration, and pulse-front tilt (PFT) of the SSTF pulse. To provide further insight, we propose a method for determining the transverse input profile of a non-SSTF pulse with equivalent spatial focusing. We find that the longitudinal variations of the peak axial intensities of the SSTF and spatially equivalent (SE) pulses are the same, apart from a constant factor, and hence that SSTF does not constrain the region of high intensity more than a non-SSTF pulse with equivalent focusing. We demonstrate that a simplistic method for calculating the pulse intensity exaggerates the degree of intensity localization, unless the spatio-temporal couplings inherent to SSTF pulses are accounted for.