Fast algorithm for calculating two-photon absorption spectra

TL;DR

This paper presents a fast numerical algorithm for calculating two-photon absorption spectra by reducing computational complexity through random vector averaging, enabling efficient high-resolution non-linear response calculations.

Contribution

The paper introduces a novel real-time real-space difference method with random vector averaging to efficiently compute two-photon absorption spectra, significantly reducing computational load.

Findings

Reduces computation time to linear response levels.

Efficiently calculates higher-order non-linear response functions.

Achieves high energy resolution in spectra calculations.

Abstract

We report a numerical calculation of the two-photon absorption coefficient of electrons in a binding potential using the real-time real-space higher-order difference method. By introducing random vector averaging for the intermediate state, the task of evaluating the two-dimensional time integral is reduced to calculating two one-dimensional integrals. This allows the reduction of the computation load down to the same order as that for the linear response function. The relative advantage of the method compared to the straightforward multi-dimensional time integration is greater for the calculation of non-linear response functions of higher order at higher energy resolution.