A high-order perturbation method for analysing the Dirichlet-Neumann operator for a nonlinear Kerr medium

Area of Science:

• Computational Electromagnetics
• Nonlinear Optics
• Materials Science

Background:

• Intense radiation is not the sole method for achieving nonlinear optical responses.
• Indium Tin Oxide (ITO) exhibits strong nonlinear effects near epsilon-near-zero (ENZ) wavelengths even with moderate fields.

Purpose of the Study:

• To introduce and analyze a novel formulation for the Capretti experiment.
• To develop robust and accurate numerical simulations for nonlinear optical phenomena.
• To explore surface methods as an alternative to volumetric algorithms for specific geometries.

Main Methods:

• Development of a surface-based approach utilizing Dirichlet-Neumann operators (DNOs).
• Analysis of the DNO for a nonlinear Kerr medium layer.
• Perturbative proof methods to establish DNO properties.

Main Results:

• The Dirichlet-Neumann operator is well-defined and analytic for nonlinear Kerr media layers.
• Surface methods offer optimal performance for piecewise homogeneous geometries.
• The perturbative approach suggests avenues for stable numerical simulations.

Conclusions:

• The proposed interfacial approach using DNOs provides an efficient and accurate method for simulating nonlinear optical responses in ENZ materials.
• This work opens new possibilities for incorporating interface deformations into theoretical and numerical models.
• The findings contribute to advancements in computationally grounded full-wave methods.