Optimal control under spectral constraints: Enforcing multi-photon absorption pathways

TL;DR

This paper introduces a method using Krotov's optimal control technique to impose spectral constraints on shaped pulses, ensuring physically realistic spectra without losing convergence guarantees, demonstrated through suppressing undesired frequencies.

Contribution

The authors develop a novel approach to incorporate spectral constraints into optimal control algorithms while maintaining monotonic convergence, using positive semi-definite quadratic forms.

Findings

Spectral constraints can be integrated without losing convergence guarantees.

Gaussian filters effectively suppress undesired frequency components.

The method efficiently solves the integral equation for the optimized field.

Abstract

Shaped pulses obtained by optimal control theory often possess unphysically broad spectra. In principle, the spectral width of a pulse can be restricted by an additional constraint in the optimization functional. However, it has so far been impossible to impose spectral constraints while strictly guaranteeing monotonic convergence. Here, we show that Krotov's method allows for simultaneously imposing temporal and spectral constraints without perturbing monotonic convergence, provided the constraints can be expressed as positive semi-definite quadratic forms. The optimized field is given by an integral equation which can be solved efficiently using the method of degenerate kernels. We demonstrate that Gaussian filters suppress undesired frequency components in the control of non-resonant two-photon absorption.