## 3 Results and Discussion
When introducing tilt angle \(\alpha\), the middle of the mirror plane is fixed. It is observable that the peak intensity is increased by \(\sim\)4% for \(\alpha\) equal to 5\({}^{\circ}\), and slowly decreases with the further increase in \(\alpha\). The reason for the initial increase in peak intensity may be an additional phase accumulation during reflection at the Au layer, which changes the phase matching condition. To summarize, there is a quite tight tolerance of Au mirror positioning with respect to the center of the grating bar, while other fabrication tolerances for the mirror trenches are relatively relaxed. The performance of a designed practical device was tested by applying 3D FDTD simulations on a high-performance computer server. During simulations, similar x- and z-axis grid sizes were applied in 2D, while y-axis grid was set to 50 nm. The width w of the RWG structure was found to have a negligible influence on the spectral response, and was thus set to be 15 \(\upmu\)m. The results for sensor reflectance are presented in Figure 6a. The peak mode reflectance (blue curve) is \(\sim\)73.3%, which is about 93% that of total reflectance (green curve), showing that, with the assistance of the FP cavity, most of the reflected energy can be collected and coupled into the back-propagating fiber mode. In addition, the peak mode reflectance is at a similar level as that of the 2D result (green dashed curve), with only a slight wavelength shift, showing a good agreement between the 2D and 3D simulation results. The background reflectance is below 3% on both sides of the resonant peak, showing that the designed RWG exhibits a high extinction ratio. The peak mode reflectance is about three times that (\(\sim\)27.1%) for a uniform grating, showing a remarkable enhancement. At the same time, the FWHM is reduced from 23.5 nm to 14.3 nm by employment of the FP cavity. Figure 5: (**a**) Mode reflectance for the designed fiber-tip RWG for different off-center x-axis alignment errors (blue, circles) and for different depths of the mirrors’ trenches (red, squares); (**b**) Mode reflectance for different inclinations \(\alpha\) of the sidewalls of the mirrors’ trenches. The sensing performance of the designed FP cavity-assisted fiber-tip RWG was investigated by applying 3D FDTD as well. The results are presented in Figure 6b. During simulations, three different ambient refractive indices were used. As the refractive index increases, the resonant peak experiences a linear red shift in the used index range from 1.33 to 1.43. The sensor sensitivity was calculated to be \(\sim\)158 nm/RIU, like that reported in References [15; 20]. The figure of merit (FOM) for resonance type fiber sensors can be defined as the ratio of its sensitivity to FWHM of the resonance peak [27]. It was found that the FOM of the designed RWG sensor was improved by \(\sim\)64% compared to the uniform grating scenario, mainly due to FWHM narrowing. At the same time, the length of the required grating structure is reduced by approximately one order of magnitude as compared to these recent works, with the grating covering only a small region over the fiber core. With an increase in the ambient medium refractive index, slight reduction in peak intensity is observed, which could be attributed to a reduction of confinement of the guided mode in the RWG layer.