Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavities
This provides a theoretical framework for optimizing Q-factor in leaky cavities, relevant to photonics and optical device design.
The authors derive Euler-Lagrange equations for topology optimization of decay rate in 3D lossy optical cavities, leading to nonlinear Maxwell systems with switching functions. The approach uses Pareto optimality and multi-parameter perturbation theory.
We derive Euler-Lagrange equations for the topology optimization of decay rate in 3-d lossy optical cavities. This leads to a new class of time-harmonic differential or integro-differential equations, which can be written as nonlinear Maxwell systems 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 eigenfrequencies. Parallels with optimal control theory are discussed.