Forward-Mode Differentiation of Maxwell's Equations
| Autor: | Hughes, Tyler W, Williamson, Ian A D, Minkov, Momchil, Fan, Shanhui |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | ACS Photonics, vol. 6, no. 11, pp. 3010-3016, Oct. 2019 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1021/acsphotonics.9b01238 |
| Popis: | We present a previously unexplored forward-mode differentiation method for Maxwell's equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable method, but provides a significant improvement in both memory and speed scaling for problems involving several output parameters, as we analyze in the context of finite-difference time-domain (FDTD) simulations. Furthermore, it provides an exact alternative to numerical derivative methods, based on finite-difference approximations. To demonstrate the usefulness of the method, we perform sensitivity analysis of two problems. First we compute how the spatial near-field intensity distribution of a scatterer changes with respect to its dielectric constant. Then, we compute how the spectral power and coupling efficiency of a surface grating coupler changes with respect to its fill factor. Comment: 13 pages, 4 figures |
| Databáze: | arXiv |
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