Fig. 1: Device concept and simulation.

a Spatial dependence of the effective refractive index induced by one-dimensional patterns of open slits defined following the 8th-order Octonacci sequence, with geometric parameters L_A = 11.6 µm and L_B = 8.7 µm that generate a quasi-periodicity of Λ = 2L_A + L_B = 31.9 µm. b Enlarged section of the refractive index spatial modulation induced by the Octonacci grating, showing the characteristic length L_B associated with the open slit and the length L_A associated with the metal-covered regions. c Fourier space representation of the grating wavevectors, highlighting the main Bragg peaks contributing to the photon scattering inside the photonic quasi-crystal laser. d Device schematics. A fully three-dimensional device simulation is performed through a finite element method (FEM) to extract the resonating modes via Maxwell’s equations. The laser active material is modelled with a refractive index n₁ = 3.6, while the external border of the ridge covered by a 7-nm-thick Cr layer is described by the effective complex value n₂ = 4.43 + i0.31, accounting for the optical losses induced by chromium. The laser is surrounded by a volume of air with n_Air = 1. The top and bottom metal claddings of the laser are described by perfect electric conductor (PEC) conditions. The far-field polar coordinates are defined as follows: φ is in the x-z plane, and ϑ is in the y-z plane. e Plot of the quality factor as a function of the resonance frequency calculated for a three-dimensional model of a device with a ridge width of W = 160 µm, slit length of L = 1.9 µm, and quasi-period of Λ = 31.9 µm. The light blue areas indicate the photonic pseudo-bandgap associated with the Octonacci quasi-crystal. f SEM image of a prototypical device with a ridge width of W = 160 µm and length of 2.9 mm, featuring the Octonacci grating on the laser top surface with a slit length of L = 3.5 µm