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HL: Fachverband Halbleiterphysik

HL 26: Poster II

HL 26.38: Poster

Mittwoch, 11. März 2026, 09:30–11:30, P1

Predicting nonlinear optical properties from the linear response: Generalized Miller Formulae — •Maximilian Tim Meyer and Arno Schindlmayr — Universität Paderborn, Department Physik, 33095 Paderborn, Germany

Predicting the nonlinear optical response of real materials from first principles remains a major challenge, since quantitative calculations require strong simplifications and large computational resources. As a shortcut, Miller’s rule provides an empirical relation between the linear and second-harmonic coefficients. It can be extended to higher-order nonlinearities and is now accepted as a useful tool for guiding experiments and computational materials discovery. However, its theoretical foundation had long been limited to a simple derivation for the classical Lorentz model with a weak anharmonic perturbation, whose properties differ from those of real quantum-mechanical electrons. We have developed a mathematical framework which enabled us to prove that Miller’s rule is nevertheless equally valid for weakly anharmonic quantum-mechanical oscillators [1]. For three-dimensional anharmonic oscillators, we further derived generalized Miller formulae that express all orders of the nonlinear response to an arbitrary multi-frequency field exactly in terms of the linear optical susceptibility [2]. These generalized formulae are applicable to a much broader range of nonlinear optical processes and systems. The practical implementation is illustrated by means of a numerical example. [1] Meyer and Schindlmayr, J. Phys. B 57, 095001 (2024). [2] Meyer and Schindlmayr, Dynamics 5, 34 (2025).

Keywords: Miller's rule; Generalized Miller Formulae; nonlinear optics; quantum anharmonic oscillator; time-dependent perturbation theory