We calculated the dependence of the reflectance on the incident angle using the rigorous coupled-wave analysis (RCWA) method for the case of a metal diffraction grating. The simulation model is illustrated in Figure 1, and the simulation conditions were as follows: a metal diffraction grating period of 600 nm, a duty ratio of 0.5, an Au thickness of 40 nm, a light source wavelength of 635 nm, and polarized light in the TM wave. The refractive index of the glass substrate was n_g = 1.45 and the dielectric constant of the Au film was N_Au = 0.18 - 3.51i. Four media with refractive indices n = 1.660, 1.676, 1.686, and 1.700 were simulated.

The metal diffraction grating used in this study was fabricated using electron beam lithography and sputtering on a glass substrate. The resist was applied on a glass substrate and the pattern was formed via irradiation with an electron beam. Then, metal (Au) was sputtered and a one-layer metal diffraction grating was formed via removing the resist with a lift-off process. The metal thickness, period, and duty ratio of the diffraction grating fabricated in this study were 40 nm, 600 nm, and 0.5, respectively. Prior to electron beam lithography, the Au thickness is measured using spectroscopic ellipsometry (UVISEL, HORIBA) and a non-contact film thickness meter (FR-pOrtable, Theta Metrisis). By using various thickness samples, the thickness of Au is determined to be 40 nm. The size of the sample was 1.5 × 1.5 mm². The scanning electron microscopy (SEM) image of the surface of the structure in Figure 1 is presented in Figure 2, showing that the sample was fabricated as designed.

The method to measure the reflectance is illustrated in Figure 3. A red laser with a wavelength of 635 nm was used as the light source, and the TM polarized light entered the sample through a polarizer. The liquid medium was placed in a transparent quartz cell, the metal side of the sample was in contact with the liquid, and the light was irradiated from the side of the glass substrate. The reflection intensity was measured for different incident angles of light to investigate the dependence of the reflectance on the incident angle.

Figure 4 shows a graph of the dependence of the reflectance on the incident angle obtained in our numerical simulations. For all refractive index values, a sharp decline in the reflectance was observed at a certain angle. Based on results from previous studies of surface plasmon sensors, it is thought that this angle is the surface plasmon polariton (SPP) excitation angle [7] . Further inspection of Figure 4 shows that the SPP excitation angles are shifted to higher values with the increasing refractive index of the medium. These results show that the fabricated structure displays the characteristics of an effective sensor because the SPP excitation angles clearly change with minute changes in the refractive index and exhibit a sharp decline in the reflectance.

Figure 5 shows the experimental measurement results of the dependence of the reflectance on the incident

angle in the case of the refractive index n = 1.700. Due to the limitation of the measurement system, the experiment is conducted between 15˚ and 30˚. The simulation results are shown by the black curve and the experimental measurement results are shown by the red curve. Experimentally, a sharp decline in the reflectance was observed at an angle of 25.6˚. This value is essentially equal to the excitation angle (26.2˚) expected from the simulation. It is speculated that the mismatch between experimental and numerical data is caused by the subtle difference between the simulation model and the actual structure. Moreover, further measurements using three other media showed declines in the reflectance at nearly the same angles as those predicted by the simulations. The four experimentally discovered excitation angles are shown in Figure 6 together with the simulation results. Even though the measured results are shifted slightly to the lower angle side compared to the simulation results, it was confirmed that the excitation angles change with the change in the refractive index. If the simulation model can be close to the actual structure, the simulation results can be improved so as to better match the experimental data. Furthermore, from the results of [5] , we can continue to observe this type of match between the experimental data and simulation.

The magnetic field distribution at the SPP excitation angle for a medium with n = 1.700 is shown in Figure 7. The incident angle is 25.6˚. The magnetic field is concentrated at the interface between the Au and the medium. This is the origin of the surface plasmon polariton. It combines with the transmitted light in the medium, and then, a strong transmitted light can be obtained. An inspection of Figure 7 confirms that the light entering the medium from the glass substrate is transmitted strongly in the medium via the extraordinary transmission by SPR. The dependences of the reflectance and transmittance on the incident angle in the medium with n = 1.700 are shown in Figure 8, and a sharp decline in the reflection and a sharp increase in the transmittance at the SPP excitation angle are observed. These results suggest that the highly efficient light transmission through the metal diffraction grating is enabled by the coupling of the propagating SPP excited at the interface between the Au and the medium with the light propagating through the medium [10] [11] .