Adjoint optimization of the extraction efficiency of a disc in cylindrical coordinates

[oskooi]

With the recent addition of Tutorial/Extraction Efficiency of a Collection of Dipoles in a Disc, it would be nice to demonstrate the adjoint optimization of a texture or coating applied to the top surface of the disc. The objective function is the extraction efficiency within an angular cone computed using the radiation pattern of a collection of stochastic dipoles.

For each "forward" simulation of the Fourier-series expansion in the azimuthal dependence $e^{im\phi}$ of the fields given a dipole at $r > 0$, we would need to perform one "backward" simulation. The adjoint sources would be defined at the near-field monitors and computed by backpropagating the far fields. This is similar to the metalens tutorial. The adjoint gradients computed for each $m$-simulation would then be summed in post processing similar to the summation of the radiation patterns $P_m(\theta)$.

It would be good to start with just a single dipole and then extend this to a collection of dipoles.