Why do we add 1 extra pixel to material grid while doing adjoint optimization?

[satadrudas]

In many of the tutorial I see that the material grid pixels are added with 1, lin in the Splitter example. Why is this done?

Also, if I set my resolution to 100, for a 1um long device, does the resolution stay 100/1um or 101/um?

Nx = int(design_region_resolution * design_region_width) + 1
Ny = int(design_region_resolution * design_region_height) + 1

Also, in the splitter example, won't there be pixel misalignments with the background waveguides?

On issue I am facing is even when I am applying a mask(for a waveguide of 0.5um) in the design region, the mask width become 0.51um at the end of the optimization. Is is to be expected?

[stevengj]

It's a fencepost problem: if you have N intervals, they are bounded by N+1 points.

[satadrudas]

Oh, I see. The Nx+1, Ny+1 are "pixel boundaries", not the pixel centre. But, what does it mean when we say these Nx,Ny grid points have a value, say 1? Is it the weighted average of it's surrounding pixels?

How do I get the Nx, Ny pixel values (not the boundary points)

[stevengj]

The material grid, by definition, is bilinearly interpolated onto your simulation. So the degrees of freedom are defined as the pixel boundaries.

Give these values, you can of course interpolate it yourself onto whatever grid you want.