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J. Eur. Opt. Society-Rapid Publ. 22, 56( 2026)
Fig
. 5. a) Schematic illustration of the two beams emitted from the GC, corresponding to orthogonal TE and TM polarizations. b) Top-view optical microscope image of the fabricated Si 3 N 4 / SiO 2 GC.( c, e) Simulated far-field intensity distributions as a function of emission angle, evaluated in a plane 100 lm above the chip surface, for TE and TM polarizations, respectively.( d, f) Experimental intensity maps acquired from 25 lm to 150 lm above the chip surface were fitted to reconstruct the emission profiles of the GC for TE and TM polarizations, respectively.
analyzed by determining the position of maximum intensity. This maximum was taken as the beam position in the transverse plane. By repeating this procedure for all measured z- slices, we obtained a set of beam-center coordinates along the propagation direction. The emission angle was then extracted by performing a linear fit to these beam-center positions. The resulting angles for both polarizations were then compared with simulations, as shown in Figures 5c – 5f. The measured emission angle of( �52.0 ± 0.4)° for TE polarization, agrees well with the simulated value of �52.0 °. For TM polarization, the measured angle of( �62.8 ± 0.4)° shows a larger deviation from the simulated value of �58.8 °. This discrepancy may be attributed to the increased sensitivity of steeper emission angles to fabrication tolerances. The measurement uncertainty accounts for the individual angle fit error per measurement(± 0.1 ° for both TE and TM), the uncertainty in the z-translation calibration of the microscope system(± 0.3 ° for both TE and TM) and the chip-tilt uncertainty(± 0.2 °). Angles are reported with respect to the surface normal to ensure consistency between simulations and the experimental analysis. Negative angles correspond to a backward-emitting GC.
A detailed comparison between the simulated and measured far-field beam profiles presented in Figure 6, whereall data sets were analyzed using the elliptical contour method and 1D Gaussian fits along the principal axes. The ellipsebased method provides a geometric estimate of the beam diameters along the principal axes of the far-field spot, while the Gaussian model fitting yields beam waists with onestandard-deviation uncertainties. The TE beam exhibits simulated waists of( 7.96 ± 0.01) lm( 13.09 ± 0.01) lm, compared to measured values of( 9.07 ± 0.24) lm( 10.79 ± 0.24) lm. For the TM polarization, the simulated beam waists are( 12.29 ± 0.01) lm( 19.17 ± 0.01) lm and the measured waists of( 15.47 ± 0.24) lm( 17.59 ± 0.24) lm. The simulated grating-coupler efficiencies are �3.61 dB for TE polarization and �8.79 dB for TM polarization. These values are in good agreement with the experimentally measured efficiencies of( �3.55 ± 0.58) dB for TE and( �9.02 ± 0.69) dB for TM, which were obtained by measuring the emitted free-space power relative to the power after the fiber array and subtracting the losses of the remaining PIC components.
4 Discussion
4.1 Propagation losses
Both TE- and TM-polarized light were guided in the fabricated Si 3 N 4 waveguides. The measured propagation loss is 0.86 ± 0.38 dB / cm higher for the TE polarization than for the TM polarization. This behavior indicates that the propagation loss is dominated by sidewall roughness, as the TE mode exhibits a larger modal overlap with etched sidewalls. The measured losses remain higher than stateof-the-art Si 3 N 4 waveguides of similar thickness, where values as low as 2 dB at 729 nm have been demonstrated [ 10 ]. This indicates that further optimization of the fabrication process is required. The TM propagation loss may be attributed to leakage into the ground plane or substrate, since their larger vertical mode extent demands sufficiently thick