# Optimization of high-order harmonic generation by optimal control theory: Ascending a functional landscape in extreme conditions

## TL;DR

This paper develops a theoretical optimal control method to enhance specific high-order harmonics in HHG by optimizing the driving pulse within physical constraints, demonstrating significant harmonic enhancement in a model system.

## Contribution

It introduces a novel OCT-based optimization framework for HHG that accounts for realistic physical restrictions and employs advanced simulation techniques.

## Key findings

- Significant enhancement of targeted harmonics achieved.
- Controlled ionization probability and minimized pulse energy demonstrated.
- Successful enhancement of even harmonic emission.

## Abstract

A theoretical optimization method of high-harmonic-generation (HHG) is developed in the framework of optimal-control-theory (OCT). The target of optimization is the emission radiation of a particular frequency. The OCT formulation includes restrictions on the frequency band of the driving pulse, the permanent ionization probability and the total energy of the driving pulse. The optimization task requires a highly accurate simulation of the dynamics. Absorbing boundary conditions are employed, where a complex-absorbing-potential is constructed by an optimization scheme for maximization of the absorption. A new highly accurate propagation scheme is employed, which can address explicit time dependence of the driving as well as a non-Hermitian Hamiltonian. The optimization process is performed by a second-order gradient scheme. The method is applied to a simple one-dimensional model system. The results demonstrate a significant enhancement of selected harmonics, with minimized total energy of the driving pulse and controlled permanent ionization probability. A successful enhancement of an even harmonic emission is also demonstrated.