I. Introduction
Recently, tilted fiber Bragg gratings (TFBGs) have been considered as the important components in novel fiber sensors [1]–[6] because they have the sensing characteristics of both uniform fiber Bragg gratings (FBGs) and long period fiber gratings (LPFGs) [7]. In the TFBGs, light coupling occurs not only between the forward and backward core modes but also between the forward core mode and backward cladding modes and even radiation modes [8]. The conventional method to fabricate FBGs is using an ultraviolet (UV) excimer laser source [1]–[7]. The UV-written gratings are dependent on the fiber intrinsic photosensitivity and the induced refractive index (RI) modulation is limited by the saturation effect. In addition, the regular grating structures are easy to erase when temperature is higher than 400° C [9] unless a high temperature annealing regenerated process is applied to the gratings [10]. To solve these problems, the femtosecond (fs) laser microfabrication technique has been adopted in recent years [11], [12]. The grating formation result from the permanent breakage of the covalent bonds due to the strong nonlinear interaction between the glass and fs laser. In this case, photosensitization, including hydrogen-loading or increasing germanium-doing level, is no more needed and the grating structures are high temperature stable. Furthermore, the nonlinear light absorption induces a relative strong local RI modulation, which will increase additional propagation loss, but ensures that the length of the fs-written FBG is short, a smaller grating length reduces the spatial averaging of surrounding RI, which could increase the measurement accuracy, making it an ideal fiber sensor in fixed point measurement. However, to the best of our knowledge, the fabrication of fiber gratings by fs laser has only been studied in uniform- [11]–[14], chirped- [15], [16], sampled- [17], [18], and phase shifted-FBGs [18] and LPFGs [19], [20]. To date, there have no reports on the fs-written TFBGs.