## 3 Results  
A schematic view of a BSW-supporting photonic device is presented in Figure 3a. It consisted of coupling and decoupling diffraction gratings, focusing and defocusing triangles, and a waveguide part. A diffraction grating coupling scheme provides efficient and compact excitation of BSW. The period of gratings (1340 nm) fulfilled wavevector-matching condition to guide incident radiation into the second diffraction order. Focusing and defocusing triangles enhance the efficiency of coupling [38]. The waveguide part is the main element of the device. Its geometry defines the mode structure of propagating radiation. We fixed the lateral size and the period of gratings, the size of triangles and waveguide length, while the height of the waveguide was varied in the range of 170-220 nm and the width of the waveguide was varied in the range of 1400-2000 nm. We fabricated four samples: sample 1 (height = 200 \(\pm\) 10 nm, width = 1800 \(\pm\) 100 nm), sample 2 (height = 200 \(\pm\) 10 nm, width = 1400 \(\pm\) 100 nm), sample 3 (height = 170 \(\pm\) 10 nm, width = 1800 \(\pm\) 100 nm), and sample 4 (height = 215 \(\pm\) 10 nm, width = 2000 \(\pm\) 100 nm). The quality and geometrical parameters of nanostructures were measured by atomic force microscopy (AFM) in contact mode regime. The AFM image of sample 2 is presented in Figure 3b. Non-square form of the cross-section (Figure 3c) may be attributed to the finite size of AFM probe. Figure 4a shows a direct plane image of the device under illumination of the coupling (left) grating by focused radiation with transverse electric (TE)-polarisation (perpendicular to the waveguide) or transverse magnetic (TM)-polarisation (parallel to the waveguide). There is no mode propagation for TM-polarised light, only a bright spot of incident radiation scattered from the coupling diffraction grating may be observed (Figure 4a, top). Change in the polarisation results in the appearance of a bright grating-shaped reflex at the right end of the waveguide (Figure 4a, bottom) attributed to radiation emitted from decoupling grating. This experimentally observed polarisation sensitivity is consistent with the results found in literature for photonic crystals with similar geometry [19] as well as preliminary calculations made by transfer matrix approach. Figure 2: The scheme of a leakage radiation microscopy experiment with a schematical intensity map of a back focal plane image. The Bloch surface wave (BSW) modes appear as sharp narrow vertical stripes. To perform more accurate analysis, an image of the BFP was recorded. To make BFP images more clear, the intense radiation transmitted through the coupling grating was eliminated by a vertical block mounted in the intermediate direct plane image. Figure 4b,c shows two BFP images of sample 4 illuminated by TE-polarised incident light. Corresponding direct plane images and schematic views of the device are presented in the inset for comparison. One can see a central bright circle corresponding to the transmitted scattered radiation, an oval-shape reflex at the right side of the circle (Figure 4b), and a set of weak vertical stripes that is related to different BSW modes propagating in the waveguide of the device. Closing the decoupling diffraction grating in the intermediate direct plane image results in disappearance of the oval-shape reflex in the BFP image (Figure 4c). Thus, it can be attributed to the first diffraction order of the decoupling grating. Using the BFP images, the effective refractive indices of BSW waveguide modes can be determined. Figure 5 depicts the BFP image of sample 3 and the circles defined the numerical aperture of the collecting objective and the light cone. The waveguide of the sample 3 supports only two BSW-modes. From the known NA = 1.3 of the objective and the position of the intersecting point of the \(X\)-axis and every stripe, the effective refractive index for distinctive modes may be calculated as \(n_{eff}=k_{x}/k_{0}\). Stripe width defines the experimental error.