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J. Eur. Opt. Society-Rapid Publ. 22, 1( 2026)
Figure 8.( a) Photograph of the grating etched with e-beam with( b) SEM surface characterization( c) AFM image.
removed by O 2 plasma treatment performed within the same etching tool. Finally, the sample undergoes ultrasonic cleaning in isopropyl alcohol for 10 min, followed by thorough rinsing with deionized water and drying with a nitrogen jet.
3.3.3 Characterization of manufactured samples
After etching, morphological characterizations by AFM and SEM are carried out to precisely determine the grating geometry( Fig. 8). These measurements reveal an average period of K = 390nm, adepthd = 69nm( Wg = 268nm) and a duty cycle( 1�f) = 0.57, values which slightly differ from the optimized parameters found previously( K = 390 nm, d = 47nm, Wg = 290nm, 1�f = 0.5). Despite this discrepancy attributed to the fabrication deviations, the following section will present how the structure behaves for energy transfer between the �1st and 0th orders with the real geometry of the manufactured grating.
4 Results and discussion
4.1 Simulated optical response of the fabricated structure
The actual grating dimensions have been input in the modeling software to verify that the optical energy transfer is still obtained between the two orders above the incident angle h s > 40 ° in the BK7 layer. Figure 9 shows that even though the amplitudes efficiencies difference of the 0th and the �1st orders is smaller than those of the optimized structure for the Littrow angle, the actual structure still provides an optical energy transfer between angles 40 ° and 90 °. Despite the difference between the optimized and the real structure, the energy transfer can still theoretically be exploited, as demonstrated in the experimental part below.
For each relevant incident angles, A, B, C and E, Figure 10 illustrates the incident and the reflected beams propagation in the direct space as well as in the reciprocal space( Ewald’ s sphere) and the electrical field distribution in the resonant structure to identify respective guided modes. To do this, an angle conversion from the substrate to the a-Si: H layer is necessary. Figures 10a and 10b show three reflected diffracted orders( 0, �1 and + 1) inside the
Figure
9. Comparison between the computed �1st( red curves) and the 0th( black curves) orders efficiencies in TE-polarization versus incident angle h s into the BK7 substrate for a square grating of 390 nm period. Full line: depth d = 47 nm, waveguide thickness Wg = 290 nm and duty cycle f = 0.5; dotted line: d = 69 nm, Wg = 268 nm, f = 0.57. For A, B, C and E, h s( h wg into the a-Si: H layer) are mentioned in black( green).
a-Si: H layer. For point A( h s = 2.8 °), the 0th order is transmitted in the superstrate( air) and the + 1st order excites the TE 1 mode that propagates in the guide with an effective index n e = 2.59 as seen in the Ewald sphere in the Figure 10a and visible on the electric field E y amplitude map. The reflected �1st order cannot escape from the a-Si: H layer and is not transmitted back into the substrate. For point B( h s = 32.7 °), the 0th order is partially reflected into the a-Si: H layer and transmitted in the substrate( BK7) and the + 1st order excites the TE 0 mode that propagates in the guide with an effective index n e = 3.33( Fig. 10b). The reflected �1st order can still not come out of the a-Si: H layer and is not transmitted into the substrate. For the first and the second crossing points C( h s = 46.8 °, Fig. 10c) andE( h s = 69.5 °, Fig. 10d), there is no phase matching between the diffracted evanescent orders and the propagating modes in the waveguide but the electric field is partially present in the superstrate above