Topology Optimization Approaches for Nanophotonic Applications

This thesis is dedicated to implementing and developing topology optimization approaches for the inverse design of novel nanophotonic devices that address operational requirements through different objectives and fabrication constraints specific to their nanophotonic and optoelectronic applications.

Topology optimization is utilized as an inverse design tool to explore the attainable figure of merits for light-matter interactions in nanocavities. The Purcell factor refers to enhancement in light-matter interactions, and it scales with light
confinement in space (mode volume) and time (quality factor). In this optimization problem, Purcell enhancement is maximized under practical conditions, such as small device footprints and fabrication limitations. By incorporating the mentioned geometric constraints, the nanocavity optimization set aims to grasp the trade-off between quality factor and mode volume, shedding light on the limiting factors for Purcell enhancement.

High Purcell enhancement nanocavities may offer remarkable benefits in various applications, including optical switches. However, a further advantage can be gained by targeting carrier dynamics in optimization rather than solely prioritizing Purcell enhancement. The inverse design of carrier diffusion requires a computationally demanding transient optimization approach; as a substitute, a harmonic assumption-based optimization approach is introduced to reduce the associated computation cost. The proposed harmonic optimization approach is validated by a heat diffusion example, showing comparable performance to transient optimization but with a remarkable 20-fold acceleration in computation speed. Furthermore, this approach can be extended to optimizing carrier dynamics with appropriate adjustments, as thermal partial differential equations govern both problems. A discussion on the adaptability of harmonic formulation to carrier diffusion and the advantages of targeting carrier dynamic is presented.

Finally, the explored and developed tools find practical application in the design of nanostructures, considering cutting-edge fabrication techniques in the optimization process. Specifically, this study concentrates on template-assisted selective epitaxy (TASE), a technique that enables the high-quality in-plane growth of III-V semiconductors on silicon. The advantages of TASE are exploited in a topology optimization scheme to design efficient photodetectors and nanolasers tailored for optical interconnects. The performance of both designs is investigated by numerical means; additionally, the fabricated designs for the photodetector study are presented. Finally, another novel fabrication method that utilizes Casimir’s force to allow controllable and extremely small features within the light-confining region is considered. A topology optimization approach is proposed to capture the fabrication process of Casimir collapsed nanocavities, and their advantageous usability for strong optical confinement is discussed.