Two-Dimensional Coupled Wave Theory for Triangular Lattice TM-Polarised Photonic Crystal Surface Emitting Lasers

This paper presents a coupled-wave analysis of triangular-lattice photonic crystal surface emitting lasers (PCSELs) with transverse magnetic polarization. Six plane waves coupled by Bragg diffraction describe the two-dimensional optical coupling. Resonant mode frequencies are calculated for a lattice of circular holes at various fill factors and compared to the plane-wave expansion method. Analytical equations for coupling constants and mode frequencies are derived, and mode degeneracy as a function of fill factor is examined. Comparison to a square lattice TM mode PCSEL shows improved in-plane 2D coupling. The general equations for arbitrary unit cell dielectric functions are discussed, with predictions of the lasing mode supported by finite device calculations.