How to modify Metagrating-Topology-Optimization to optimize 2D DOE beam splitter with cross polarization orders?

[Samson-Ming]

I hope to modify the Metagrating-Topology-Optimization to optimize 2D DOE Damman grating, say a 3×3 beam beam splitter. But I failed to make it when there are cross polarization diffraction orders, so how to deal with the adjoint field and gradient of these cross polarization orders? Thank you.

P.S. I have adopt the C4v symmetry to reduce the compution cost.

[Jackcheng1]

hello,do you have an idea now

[Samson-Ming]

Not yet