Design and numerical analysis of hybrid plasmonic–photonic crystal quantum-dot nanolasers with enhanced spontaneous emission

Hybrid plasmonic–photonic crystal cavities offer an attractive paradigm for achieving both ultra-high quality factors and deep subwavelength mode confinement. However, establishing rigorous design rules that balance Purcell enhancement against parasitic non-radiative quenching remains a critical challenge. In this work, we develop a self-consistent multiscale computational framework, validated against analytical and numerical benchmarks, to investigate six hybrid metallic nanoparticle architectures (gold and silver nanospheres, nanorods, and nanostars) integrated into a GaAs L3 photonic crystal cavity coupled to InAs quantum dots. Multi-solver cross-validation between analytical Mie theory, the boundary element method (BEM), and 3D finite-difference time-domain (FDTD) simulations demonstrates close agreement across resonance wavelengths, cross-sections, and field enhancements. We show that the localized density of states (LDOS) and cavity-mode Purcell factors fundamentally decouple for emitter–metal gap distances below 5 nm, where non-radiative Ohmic absorption dominates over radiative decay. Coupling the electrodynamic cavity parameters into semiclassical four-level laser rate equations predicts lasing threshold reductions of up to 85% under the local-response approximation (and over 82% under generalized nonlocal optical response hydrodynamic analysis) for the silver nanorod geometry, driven by optimal longitudinal plasmon resonance alignment at the 900 nm emission wavelength and strong near-field concentration ( | E / E 0 | 2 ≈ 300 ). This work provides quantitative design guidelines and operational boundaries for developing high-efficiency, subwavelength hybrid quantum-dot nanolasers.