A synergistic approach to optical modeling of PCSELs through rigorous methods and the coupled-wave theory

Abstract

A wide range of numerical and semi-analytical approaches has been developed for optical modeling of photonic-crystal surface-emitting lasers (PCSELs). However, a systematic framework for comparing their predictive capabilities and identifying their respective validity limits remains largely unexplored. In this work, we introduce a comparative methodology in which four representative methods - including rigorous numerical and effective-index-based approaches - are analyzed and partially hybridized within a coupled-wave-theory framework. Using single-lattice and double-lattice PCSELs as representative models, we demonstrate that this approach not only reveals fundamental differences between predictions of rigorous numerical methods and the coupled-wave-theory framework, but also captures a qualitative phase transition and a symmetry-broken phase of quasi-bound states in the continuum (quasi-BICs) relevant for laser operation.

Figures (15)

• Figure 1: Refractive-index profile of a unit cell of the single-lattice (left) and double-lattice (right) photonic crystals. White regions correspond to air holes, while black regions denote bulk GaN.
• Figure 2: (a) PhC confinement factors based on three methods as functions of the hole filling factor in the Type I PCSEL. 3D-CWT, unlike other methods, assumes a common vertical electric-field profile for all four modes, and thus $\Gamma_{\text{PhC}}$. $t_{\text{PhC}}$ is fixed to 100 nm. (b) Effective indices as functions of $ff$, obtained as $\lambda_{\text{A,B}}/a$ for each corresponding method. The photonic-crystal thickness $t_{\text{PhC}}$ is fixed at 100 nm.
• Figure 3: (a) PhC confinement factors as functions of the PhC thickness, obtained by 3D-CWT, FEM, and I-EIM. $ff$ is fixed to 10 %. (b) Effective indices as functions of $t_{\text{PhC}}$, obtained as $\lambda_{\text{A,B}}/a$ for each corresponding method. $ff$ is fixed to 10 %.
• Figure 4: (a) Radiation constants of the fundamental A,B,C and D modes, plotted in different scales (left and right y axes) as functions of the $ff$. $\alpha_{\text{C,D}}$ is not plotted at $ff=20\%$ due to a strong spectral overlap of degenerate modes C, D with modes A and B. The PhC thickness is set to 100 nm. (b) Radiation constants of C and D modes, varying with PhC thickness. $ff$ is fixed to $10 \%$. Radiation constants of modes A and B are negligible and therefore omitted from the plot.
• Figure 5: Radiation constants $\alpha_{A,B}$ derived from FEM (black curves) and their CWT-compliant counterparts (cyan curves) as functions of $ff$. The error $\delta$ is shown in red.