Make the EigenmodeCoefficient adjont solver accept a DiffractedPlanewave object

[mawc2019]

The mode argument of the EigenmodeCoefficient adjont solver cannot be a DiffractedPlanewave object. This PR allows this mode argument to be a DiffractedPlanewave object.

[oskooi]

Note that #2054 (unfinished) is identical to this PR. Unfortunately, enabling this feature requires more than simply modifying the API for EigenmodeCoefficient as explained in this comment.

[mawc2019]

I see. Is there a temporary expedient for the DiffractedPlanewave adjoint solver? The Metagrating3D optimization problem would need the DiffractedPlanewave adjoint solver.

[oskooi]

Is there a temporary expedient for the DiffractedPlanewave adjoint solver?

The workaround is to specify the wavevector of the diffracted order manually using the kpoint_func parameter of the EigenmodeCoefficient object. See the example in #2235(comment). This also requires the hack in mpb.cpp in #2285.

[mawc2019]

I specified the wave vector of the diffracted order manually using kpoint_func and used the hack in #2285, but the results given by get_eigenmode_coefficients or the forward run of the EigenmodeCoefficient adjoint solver is different from that given by the DiffractedPlanewave object. For example, at resolution=20, using device1.csv in Metagrating3D, the deflection efficiency given by DiffractedPlanewave is 83% while the result given by get_eigenmode_coefficients is only 51%. (Without the hack in #2285, the result given by get_eigenmode_coefficients is only 3%.)
Did you compare this get_eigenmode_coefficients approach mentioned above with the DiffractedPlanewave approach?

[oskooi]

Did you compare this get_eigenmode_coefficients approach mentioned above with the DiffractedPlanewave approach?

We already have a unit test (test_diffracted_planewave.py) which verifies, using a 2d binary grating, that get_eigenmode_coefficients produces the same result when called with either a band_num/eig_parity (but not kpoint_func) or DiffractedPlanewave object. Once #2285 is resolved, I was planning to add a separate test involving kpoint_func.

Anyhow, since the 2d metagrating is a 3d simulation, you need to be careful about specifying the correct symmetry of the mode. I think it should be: eig_parity = mp.EVEN_Y if P_pol else mp.ODD_Y.