{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Differential/Radar Cross Section\n", "\n", "As an extension of the [Mie scattering example](https://meep.readthedocs.io/en/latest/Python_Tutorials/Basics/#mie-scattering-of-a-lossless-dielectric-sphere) which involved computing the *scattering* cross section ($\\sigma_{scat}$), we will compute the *differential* cross section ($\\sigma_{diff}$) which is proportional to the [radar cross section](https://en.wikipedia.org/wiki/Radar_cross-section). Computing $\\sigma_{diff}$ in a given direction involves three steps: (1) solve for the [near fields](https://meep.readthedocs.io/en/latest/Python_User_Interface/#near-to-far-field-spectra) on a closed box surrounding the object, (2) from the near fields, compute the far fields at a single point a large distance away (i.e., $R$ ≫ object diameter), and (3) calculate the Poynting flux of the far fields in the outward direction: $F = \\hat{r}\\cdot\\Re[E^* \\times H]$. The differential cross section in that direction is $R^2F$ divided by the incident intensity. The radar cross section is simply $\\sigma_{diff}$ in the \"backwards\" direction (i.e., backscattering) multiplied by 4π.\n", "\n", "The scattering cross section can be obtained by integrating the differential cross section over all [spherical angles](https://en.wikipedia.org/wiki/Spherical_coordinate_system):\n", "\n", "