Euler–Lagrange equations for full topology optimization of the Q-factor in leaky cavities

  title={Euler–Lagrange equations for full topology optimization of the Q-factor in leaky cavities},
  author={Matthias Eller and Illya M. Karabash},
  journal={2021 Days on Diffraction (DD)},
We derive Euler–Lagrange equations for the structural optimization of exponential decay rate of standing waves in 3-D leaky optical cavities. This leads to a new class of time-harmonic differential or integro-differential equations, which can be written as nonlinear Maxwell equations with switching functions of special types. Our approach is based on the notion of Pareto optimal frontier and on the multi-parameter perturbation theory for eigenvalues. 

M-dissipative boundary conditions and boundary tuples for Maxwell operators



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