J. Eur. Opt. Society-Rapid Publ. 22, 1( 2026) 5
Figure 6. 2D maps efficiencies as a function of the grating depth d and waveguide thickness Wg for h L = 56.44 °:( a) 0th order,( b) �1st order.
( Fig. 6b), respectively, for given couples values( Wg, d), which indicates a maximum energy transfer between the two orders. The white line in Figures 6a and 6b corresponds to the total thickness d + Wg = 337 nm and its intersection with minimum for the 0th order and maximum for the �1st order provides the optimal couple values d = 47nm, Wg = 290 nm( white point) for the energy transfer.
3.2.3
Angular response of the optimized structure
Using the optimized structure with a TE-polarized light excitation at wavelength 980 nm, on an angular range between 0 ° < h s < 90 ° into the BK7 substrate and between 0 ° < h wg < 25 ° into the a-Si: H layer, the diffraction efficiencies are plotted in the Figure 7 where both orders 0 and �1 are represented in black and red line, respectively. Points of interest are also represented, especially the resonances at positions A and B corresponding to 5.2 ° and 33.4 ° angles. Then, the efficiency curves intersect each other at C and E corresponding to 44.1 ° and 76.2 ° angles, which are relevant for further sensing measurements. Position D corresponds to the Littrow’ sangleh L = 56.44 °. Above44 °( position C), the energy transfer between the 0th and �1stordersisobtained and at the Littrow angle specifically, their respective efficiencies reach 0( minimum for the 0th order) and 0.9( maximum for the �1st order).
Knowing the optimal values allowing a good energy transfer between the 0th and �1st orders, the grating fabrication process can now be carried out as described in the next section.
3.3. Gratings fabrication
After deposition of a-Si: H on the BK7 substrate, the gratings are formed by a combination of e-beam lithography and plasma etching, performed at 3IT. Nano facilities, Sherbrooke, QC, Canada.
3.3.1 E-beam
A layer of 150 nm-thick positive electroresist( Zep520A) is spun onto the sample, followed by a thin metallic layer evaporated on the resist to evacuate charges and to adjust focus during exposure. The patterns are exposed using an EBPG e-beam lithography tool from Raith operating at 100 kV. The design corresponds to a 10 10 mm 2 grating
Figure 7. Computed efficiencies in TE-polarization of the �1st( red curve) and the 0th( black curve) orders versus incident angle for a square grating of 390 nm period, 0.5 duty cycle, 47 nm depth and 290 nm waveguide thickness: h s angular position into the BK7 substrate( black axis values) and h wg into the a-Si: H layer( green axis values) with characteristic angles at A, B, C, D and E.
with a period of 390 nm and a line width of 195 nm( see Sect. 3.2). Writing fields of 100 100 lm 2 were used to reduce stitching effects and ensure smoothness along the grating’ s direction. After exposure, the metallic layer is removed by an acidic bath that does not affect the resist. Development is performed in ZED-N50 solution at 4 ° C and dried with a nitrogen jet.
3.3.2 Plasma etching
Following electron-beam lithography, the resulting patterns are transferred into the amorphous silicon( a-Si: H) layer via plasma etching using a CF 4 / H 2 / He gas mixture in an Advanced Oxide Etcher( AOE) system from SPTS. The etching duration is determined empirically through iterative trials to achieve the targeted etch depth of approximately 47 nm. Subsequently, residual photoresist is