Optimization of a Multiphysics Problem in Semiconductor Laser Design

A multimaterial topology optimization framework using phase fields is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. The technique provides a means of determining the cross section of the material alignments needed to create a sufficiently large strain profile within an optically active region of a photonic device. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed in the form of a linear elliptic partial differential equation (elasticity) coupled via the underlying topology to an eigenvalue problem of Helmholtz type (optics). The differential sensitivity of the displacement and eigenfunctions with respect to the changes in the underlying topology is investigated. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a Ge-on-Si microbridge are...