Nonperturbative prediction of Nonlinear optical properties using Action Lagrangian applied to 1D Harmonic oscillator model.

Nonlinear optical properties are the optical properties of the materials which depend on the intensity of the illuminated light. These properties occur when the polarization induced in the material is not directly proportional to the intensity of light. Nonlinear optical (NLO) properties are intensely studied for their rich fundamental physics and chemistry and because they are central to technologies like spectroscopy, bioimaging, and optical limiting. The primary theoretical approach to predicting NLO properties is through response theory. However, response theory is inherently perturbative and thus may c­­­­onverge slowly for moderate field strengths. Here, we introduce the Action Lagrangian Eigenvalue Problem (ALEP), which will allow us to calculate nonperturbative NLO properties directly at a moderate electric field strength. As an example, we apply the ALEP method to a one-dimensional harmonic oscillator interacting with an electric field of moderate field strength. We will show that for weak and moderate field strengths, NLO properties obtained using i) response theory, ii) quantum dynamics, and iii) the ALEP are all equivalent, thus showing that ALEP is a promising strategy.