Abstract
A modal method for the study of second harmonic (SH) generation in nanostructures is depicted both for plane waves and focused beam illumination. It is based on the B-spline modal method, and relies on the undepleted pump approximation. The nonlinear polarization induced by an incident plane wave or a focused beam generates a source term at the doubled frequency. The latter is divided into a finite number of sub-sources, and the SH field is subsequently computed by integration of these sub-source contributions.
Highlights
In the near- and the mid-infrared, nanostructured devices are giving promising results for controlling the localization of the electric field and for strong intensity field enhancement [1,2,3,4]
Numerical simulations are performed in the case of Maker fringes in a 110 crystalline GaAs membrane, where a square sine function at a spatial frequency Δk k2ω − 2kω
2n2ω − nω ω∕c is expected in the direction z of the incident plane wave [24,26]
Summary
Numerical examples are described and the convergence of the method is investigated. In the near- and the mid-infrared, nanostructured devices are giving promising results for controlling the localization of the electric field and for strong intensity field enhancement [1,2,3,4]. Since nonlinear optics processes benefit from a large enhancement of the local electric field, such nanostructures are very promising [5,6,7,8]. Their design and optimization need fast numerical simulation tools. We adapt the BMM to map the SH field throughout periodic nanostructured layers for plane waves (of arbitrary incident angle) under the undepleted pump approximation. The theoretical method to compute the generated SH field in periodic nanostructures is detailed first for a single plane wave of frequency ω, and is generalized to a focused beam
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