Finite-size effects in photonic-crystal surface-emitting lasers: critical discussion of different approximations

We present a comparative study of vertical and lateral loss estimation in photonic-crystal surface-emitting lasers (PCSELs), focusing on how finite-size effects depend on the choice of infinite-structure band model. To analyze these effects, we introduce a k-space weighted loss estimation (kSWLE) framework that can be applied to any infinite-structure band model, and we contrast its predictions with those of finite coupled-wave theory (finite-CWT), which inherently relies on the infinite-CWT bandstructure. The kSWLE approach provides a semi-analytical means of estimating radiative and lateral losses by integrating band-dependent quantities over a Gaussian k-space envelope determined by the device size. We apply kSWLE using both CWT and guided-mode expansion (GME) bandstructure models, enabling a direct comparison of how different infinite-structure descriptions influence the predicted losses and spectral properties. In regimes where the lasing mode is dominated by a single band and has a spectrally compact k-space distribution, kSWLE reproduces similar scaling trends as finite-CWT. However, for small devices or at specific fill factors, the mode has a broader k-space distribution with contributions from multiple bands, leading to ambiguous mode classification and increased deviation between models. These results highlight the strengths and limitations of each modelling strategy and establish kSWLE as a practical tool for evaluating finite-size effects in PCSELs.