Probabilistic Markov Chain model of photonic crystal surface emitting lasers

Semiconductor lasers face a fundamental trade-off between high output power and high-quality single-lobe beams. Photonic crystal surface-emitting lasers (PCSELs) have emerged as a promising platform that overcomes this limitation by enabling scalable, single-mode, vertical emission. However, their design is hindered by complex interactions between microscopic scattering and macroscopic losses—especially in-plane loss (α//), which is critical yet difficult to measure experimentally. This thesis introduces a computationally efficient Probabilistic Markov Chain (PMC) model to bridge microscopic physics and device performance. By treating light propagation as a stochastic process, the model translates coupling coefficients into directional scattering probabilities, enabling rapid simulation of finite-sized PCSELs without directly solving Maxwell’s equations. The PMC model is quantitatively and qualitatively validated by predicting the performance (e.g. loss, slope efficiency and near-field pattern) of PCSEL devices (GaN-based PCSEL, GaAs-based PCSEL and InP-based PCSEL) from references and against experimental PCSEL and resonator-embedded PCSEL (REPCSEL) data. The predicted result has excellent agreements (e.g. < 1 cm-1 difference in loss) with those reported in references and experimental. Through parametric studies, it quantifies the impact of in-plane coupling and integrated mirrors on α// and mode control. Furthermore, the model reveals an interdependence between in-plane and internal loss in designs with unpumped boundaries, challenging conventional design assumptions. Finally, three novel high-efficiency PCSEL architectures are proposed and evaluated—incorporating butt-coupled passive sections, selective area intermixing, and dual contacts—to minimize parasitic losses and maximize power conversion efficiency. In summary, this work establishes the PMC model as a versatile design tool that provides fundamental insight into PCSEL loss mechanisms and opens new pathways toward highperformance, scalable semiconductor lasers.