Optimized Computation of Tight Focusing of Short Pulses Using Mapping to Periodic Space

Abstract

When a pulsed, few-cycle electromagnetic wave is focused by optics with f-number smaller than two, the frequency components it contains are focused to different regions of space, building up a complex electromagnetic field structure. Accurate numerical computation of this structure is essential for many applications such as the analysis, diagnostics, and control of high-intensity laser-matter interactions. However, straightforward use of finite-difference methods can impose unacceptably high demands on computational resources, owing to the necessity of resolving far-field and near-field zones at sufficiently high resolution to overcome numerical dispersion effects. Here, we present a procedure for fast computation of tight focusing by mapping a spherically curved far-field region to periodic space, where the field can be advanced by a dispersion-free spectral solver. In many cases of interest, the mapping reduces both run time and memory requirements by a factor of order 10, making it possible to carry out simulations on a desktop machine or a single node of a supercomputer. We provide an open-source C++ implementation with Python bindings and demonstrate its use for a desktop machine, where the routine provides the opportunity to use the resolution sufficient for handling the pulses with spectra spanning over several octaves. The described approach can facilitate the stability analysis of theoretical proposals, the studies based on statistical inferences, as well as the overall development and analysis of experiments with tightly-focused short laser pulses.

Explicit energy-conserving modification of relativistic PIC method

“…where ρ is the charge density and the current J(r) is omitted in accordance with the PIC modification in question. Applying Fourier transform to both sides of equations (63,64) and denoting the representations of functions F(r) and ρ(r) in the basis of wave-vectors k by subscript k, we get:…”

“…To maintain reasonable performance the communication between the data of simulations and Python is arranged using C callbacks provided by Numba package. This approach has been previously developed and used in hi-χ framework [64]. From Python it is possible to call a full cycle over all cells or particles so that for each particle or cell a function defined in Python is called.…”

Towards critical and supercritical electromagnetic fields

“…We advance this field to the vicinity of the focal point using a spectral solver of Maxwell’s equations within the open-source package hi- [ 46 ] . To reduce the amount of needed computational resources we also employ the module of contracting a spherical window that maps the concave region of the pulse to a thin layer of space with periodic boundary conditions [ 47 ] .…”

Towards ML-Based Diagnostics of Laser–Plasma Interactions

“…The data was generated by simulation of the propagation of a tightly focused laser pulse initialized in the far field zone to the focal plane. The modeling was performed by means of the Hi-chi module [21], which uses a spectral method for solving Maxwell's equations. The cumulative energy flux was calculated in the focal plane to be used for the ML-model training.…”

“…In addition, sufficiently intense foregoing laser radiation (prepulse) can cause the formation and spreading of plasma before the arrival of the main laser pulse (preplasma) in a way that affects the experimental results but is hard to diagnose in-situ. It is also advantageous to use tight focusing that presents particular challenges, in particular, due to the broad spectrum of short laser pulses (see, e.g., [22]). As a result, almost all experiments lack information about what actually happens at the focus and this ultimately hampers the realization of promising applications of laser-plasma interactions.…”