Fig. 4: Model and simulations for the vertical localization of emitters within the waveguide.

a Conditional probability model for estimating the vertical localization of the emitters. b Comparison of the normalized carbon concentration (orange line) measured via SIMS, with a peak value of 3.3 × 10¹⁸ atoms/cm³, and the derived concentration of G-centers (yellow area) within the waveguide, shown on the left, as a function of vertical position within the waveguide. The emitters' vertical localization probability distributions for the most likely scenario are depicted on the right. c Schematic of the cantilever waveguide with the coordinate axes used in the analysis. Both the setup framework axis and the crystal framework are shown. The cantilever is oriented along the [\(\overline{1}10\)] direction. d Colormap showing the strain distribution along the cantilever and its displacement, extracted from FEM simulations at an applied voltage of 35 V. e Spectral shift for four emitters as a function of voltage applied to the cantilever. Dots represent the Lorentzian fit centers of the emission peaks, while the line shows the fitted curve derived from the FEM voltage-strain model used to determine the vertical positions of the emitters. f Coupling to the quasi-TE fundamental waveguide mode for three different equivalent classes of emitter orientations as a function of vertical and lateral position in the waveguide.