From 0fc477bd913baba5aa3533271b6e01e004af1d9b Mon Sep 17 00:00:00 2001 From: "Steven G. Johnson" Date: Fri, 9 Aug 2024 15:13:59 -0400 Subject: [PATCH] Update doc/docs/Python_Tutorials/Adjoint_Solver.md --- doc/docs/Python_Tutorials/Adjoint_Solver.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/docs/Python_Tutorials/Adjoint_Solver.md b/doc/docs/Python_Tutorials/Adjoint_Solver.md index 8cb41c69a..f8aa1d877 100644 --- a/doc/docs/Python_Tutorials/Adjoint_Solver.md +++ b/doc/docs/Python_Tutorials/Adjoint_Solver.md @@ -1193,7 +1193,7 @@ if __name__ == "__main__": Shape Optimization of a Multilayer Stack ---------------------------------------- -We extend the demonstration of the shape derivative from the previous tutorial to perform shape optimization of a multilayer stack over a broad bandwidth. The 1D design problem is shown in the schematic below and involves finding the layer thicknesses for a fixed number of layers (9) which minimize the largest transmittance (or alternatively, maximize the smallest reflectance) at two wavelengths: $\lambda_1$ = 0.95 μm and $\lambda_2$ = 1.05 μm. However, rather than use the transmittance as the objective function, we use the *field decay* via (the logarithm of) the integral of the fields in the stack ($\int |E_x|^2$). This provides more information to the optimizer which should produce better results. +We extend the demonstration of the shape derivative from the previous tutorial to perform shape optimization of a multilayer stack over a broad bandwidth. The 1D design problem is shown in the schematic below and involves finding the layer thicknesses for a fixed number of layers (9) which minimize the integrated field intensity $\int |E_x|^2$, which demonstrates a `FourierFields` objective function. (This is equivalent to minimizing absorption if $\varepsilon$ had a small imaginary part, and is related but not precisely equivalent to minimizing transmission or maximizing reflection.) In particular, we minimize the worst case (largest) of the intensities at two wavelengths: $\lambda_1$ = 0.95 μm and $\lambda_2$ = 1.05 μm, to roughly emulate a broadband problem. The stack consists of two materials of alternating refractive index $n_A$ = 1.3 and $n_B$ = 1.0. The layers are arranged as $n_A$, $n_B$, $n_A$, $n_B$, ..., $n_A$. The semi-infinite regions to the left and right of the stack are vacuum.