Topology optimization of photonics based on variational principles
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Topology optimization in photonics typically assumes rigid, non-deforming structures. In response to this limitation, the present work introduces an action functional that incorporates thermomechanical and electrodynamic contributions together with a design variable representing the density distribution. Applying Hamilton's principle yields a fully coupled system of equations and ensures thermodynamic consistency. Combined with Betti's reciprocal theorem, this framework enables topology optimization problems that manipulate light propagation through thermomechanical loads and the resulting deformation. The applicability of the procedure is demonstrated through benchmark simulations, including a metalens and a demultiplexer, where deformations are not considered. Subsequently, a thermomechanical switch is introduced, in which thermal or mechanical loads deform the design domain and alter the output of an incoming light beam. In summary, the results establish a thermodynamically consistent topology optimization framework for coupled electrodynamics and thermomechanics, demonstrating its potential for designing mechanically actuated optical devices.
