Parameterized level set optimization of PEC structure

[Guizhixing]

Hi Tidy3D Team,

I have been studying the "Parameterized level set optimization of a y-branch" example and found the integration of JAX with level set optimization highly impressive. To better understand the underlying physics and implementation, I have a few specific questions:

1. Modeling of Curved Structures
   In the Y-branch model, is the curved boundary modeled using effective permittivity (sub-pixel smoothing)?

2. Derivative of the Objective Function & JAX’s Role
   How is the derivative of the objective function with respect to the boundary variations obtained by AVM? What specific role does JAX’s automatic differentiation play here? Does JAX handle the "chain rule" between the objective function J and the level set parameters?

3. Applicability to PEC Structures
   It is my understanding that standard material averaging (equivalent permittivity) methods in FDTD are generally not applicable to PEC structures due to the discontinuous nature of the fields at the boundary. Does the level-set methodology used in this example support PEC shape optimization?

I look forward to your insights!