Modelling of active semiconductor photonic crystal waveguides and robust designs based on topology optimization

In this paper, we present a theoretical analysis of slow-light enhanced light amplification in an active semiconductor photonic crystal line defect waveguide. The impact of enhanced light-matter interactions on propagation effects and local carrier dynamics are investigated in the framework of the Lorentz reciprocity theorem. We highlight topology optimization as a systematic and robust design methodology considering manufacturing imperfections in optimizing active photonic crystal device performances, and compare the performance of standard photonic crystal waveguides with optimized structures.