Numerical Liouville approach: Formulation of third-order nonlinear optical susceptibilities

Abstract

As a continuation of a previous paper [Phys. Rev. A 50, 2989 (1994)], this article develops and describes in detail the new nonperturbative approach to the third-order nonlinear optical susceptibilities χ(3)g(ω) in third-harmonic generation (THG), electric-field-induced second-harmonic generation (EFISH), degenerate four-wave mixing (DFWM), electric-field-induced optical rectification (EFIOR), and electric-field-induced Kerr effect (EFIKE) for N-state quantum systems interacting with intense electric fields. The present method utilizes the Fourier transformation of numerically exact solutions of the Liouville equation, so that it can provide both real and imaginary nonlinear optical spectra valid for arbitrary laser intensities, frequencies, and relaxation. As an application of the method, we investigate the characteristics of nonlinear optical spectra in THG, EFISH, and DFWM for a three-state model that mimics the electronic excited states of t-octatetraene obtained from a full configuration interaction (FCI) calculation using the Pariser–Parr–Pople (PPP) Hamiltonian. Comparisons between the present nonperturbative and the conventional perturbative results are also carried out. The magnitudes of the third-order nonlinear susceptibilities in the off-resonant region show the following trend: χ(3)(THG)≳χ(3)(EFISH)≳χ(3)(DFWM), with χ(3)(THG) exhibiting the largest frequency dispersion.