Simulating the focusing of light onto 1D nanostructures with a B-spline modal method

Focusing the light onto nanostructures thanks to spherical lenses is a first step to enhance the field, and is widely used in applications, in particular for enhancing non-linear effects like the second harmonic generation. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam can not be described by the simple ray tracing formalism. Here, we present a method to compute the response to a focused beam, based on the B-spline modal method. The simulation of a gaussian focused beam is obtained thanks to a truncated decomposition on plane waves computed on a single period, which limits the computation burden.