Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory

Area of Science:

• Photonics and optical engineering
• Computational physics
• Materials science

Background:

• The quality factor (Q) of photonic resonators is crucial for applications like sensing and lasing.
• Optimizing Q in engineered cavities is well-understood, but less so for disordered media like Anderson-localized modes.
• Quasinormal modes (QNMs) offer a theoretical framework for analyzing such systems.

Purpose of the Study:

• To demonstrate the utility of QNM theory and complex eigensolvers for automated Q-factor optimization.
• To apply this framework to both ordered (L3 cavities) and disordered (Anderson-localized modes) photonic environments.
• To achieve significant Q-factor enhancements and explore resulting modal properties.

Main Methods:

• Utilized quasinormal modes (QNMs) as a non-Hermitian perturbation theory.
• Employed a finite-element complex eigensolver for mode analysis.
• Performed automated shape optimization by adjusting hole positions in dielectric slabs.
• Benchmarked the QNM perturbation formula for accuracy.

Main Results:

• Successfully optimized the Q-factor of fundamental modes in L3 cavities, accounting for all loss mechanisms.
• Achieved a 3 order of magnitude increase in the Q-factor for an Anderson-localized mode.
• Demonstrated a threefold reduction in mode volume and altered spatial localization for the optimized Anderson-localized mode.
• Showcased minor modifications to modal structure in L3 cavities.

Conclusions:

• QNMs combined with complex eigensolvers provide a powerful, automated tool for Q-factor optimization in photonic resonators.
• This method is effective for both ordered and disordered photonic media.
• Significant Q-factor enhancements are achievable, leading to improved device performance and novel modal behaviors.