Optical simulators for a miniwasp eye (mwaspbie)

_images/mwasp.pdf

miniwaspbie is a package for solving time harmonic Maxwell equations dielectric problems specialized to the geometries arising in the eyes of miniwasps. The electric permitivity in each component of the eye is assumed to be a piecewise constant, and has dependencies on FMM3D and fmm3dbie. The library is written in Fortran and has wrappers for Python. As an example, suppose that we are given a component of the eye denoted by \(\Omega_{-} \in \mathbb{R}^{3}\) whose boundary is \(\Gamma\), an incoming electric field \(E^{\textrm{inc}}\), and incoming magnetic field \(H^{\textrm{inc}}\). Let \(\Omega_{+} = \mathbb{R}^{3} \setminus \Omega_{-}\), denote the exterior of \(\Omega_{-}\). Let \(E_{-},H_{-}\) denote the electric and magnetic fields inside \(\Omega\), and \(E^{+}, H_{+}\) denote the electric and magnetic fields outisde \(\Omega\). Let \(\varepsilon_{\pm}\) denote the electric permitivities in the interior and exterior domains respectively, and \(\mu_{\pm}\) denote the magnetic permeabilities in the interior and exterior domains respectively. Let \(\omega\) denote the wave number of the incoming wave. Then the electric and magnetic fields satisfy the interface problem for time harmonic Maxwell equations given by

\[\begin{split}\nabla \times E_{\pm} &= i\omega \mu_{\pm} H_{\pm} \quad \mbox{ in } \Omega_{\pm} \, , \\ \nabla \times H_{pm} &= -i \omega \varepsilon_{\pm} E_{\pm} \quad \mbox{ in } \Omega_{\pm} \, , \\ n \times (E_{+} - E_{-}) &= -n \times E^{\textrm{inc}} \quad \mbox { on } \Gamma \, , \\ n \times (H_{+} - H_{-}) &= -n \times H^{\textrm{inc}} \quad \mbox { on } \Gamma \, , \\\end{split}\]

The library currently supports high order triangulations of surfaces stored in the .go3 format. In this setup each map from the standard right triangle is stored at order \(p\) Vioreanu-Rokhlin nodes. The input format currently assumes that each patch is discretized using the same order nodes. Upcoming support will be provided for triangulations stored in .gmsh format, and .step format, and quadrilaterizations in all of the above formats.