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As discussed in #2002, it might be nice to write a new tutorial that shows how to design a simple 2D grating coupler using the adjoint solver. This particular design problem easily illustrates the many advantages of our new hybrid density-levelset approach. Specifically, the tutorial could cover the following scenarios:
A simple density-based approach where the DOF are just the MaterialGrid variables themselves. The grating evolution consists of just two or three betas, where the last beta goes to infinity for levelset (i.e. shape) optimization (e.g. β=8, β=32, β=∞). This is the most straightforward way to design a GC using the current framework.
A parameterized version (perhaps using a signed distance function) that abstracts fundamental parameters like grating period, duty cycle, etc using a simple autograd function mapping (as described here). There isn't as much flexibility with this "parameterization", but it illustrates many important applications (e.g. fabrication sensitivity analysis). β=∞ throughout the entire process.
A combination of approaches 1 and 2, where the degrees of freedom are the individual grating widths and gaps themselves. This means that after each optimization iteration, a new MaterialGrid object and geometry must be generated (and consequently, a simulation object too) as the individual lengths continually rescale the "design region". This is similar to the "remeshing" step that often takes place with various differentiate-then-discretize schemes. Practically, this relaxes an implicit constraint placed by idea 1 above, where the grating length itself cannot change. The new constraint is that the number of grating "teeth" cannot change. β=∞ throughout the entire process.
As discussed in #2002, it might be nice to write a new tutorial that shows how to design a simple 2D grating coupler using the adjoint solver. This particular design problem easily illustrates the many advantages of our new hybrid density-levelset approach. Specifically, the tutorial could cover the following scenarios:
MaterialGrid
variables themselves. The grating evolution consists of just two or three betas, where the last beta goes to infinity for levelset (i.e. shape) optimization (e.g. β=8, β=32, β=∞). This is the most straightforward way to design a GC using the current framework.autograd
function mapping (as described here). There isn't as much flexibility with this "parameterization", but it illustrates many important applications (e.g. fabrication sensitivity analysis). β=∞ throughout the entire process.MaterialGrid
object andgeometry
must be generated (and consequently, asimulation
object too) as the individual lengths continually rescale the "design region". This is similar to the "remeshing" step that often takes place with various differentiate-then-discretize schemes. Practically, this relaxes an implicit constraint placed by idea 1 above, where the grating length itself cannot change. The new constraint is that the number of grating "teeth" cannot change. β=∞ throughout the entire process.(cc @oskooi)
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