## 1 Introduction  
Microfibers have a diameter of dozens of microns or even several hundred nanometers [1], as well as some outstanding properties, such as high transmission efficiency (>90%), low noise (0.2-0.5 dB), and small signal loss (<1 dB/m) [2; 3; 4]. By combining microfiber and fiber Bragg grating (FBG) technologies, a microfiber Bragg grating (MFBG) can be developed to detect physical qualities (such as temperature [5], stress [6], pressure [7], etc.) with high sensitivity and can be applied in structural health monitoring [8], medical diagnosis [9], biosensing [10], environmental monitoring [7], etc.  
MFBGs are prepared by reducing the diameters of common FBGs to the micron- or even nanometer level using methods such as chemical corrosion and taper pulling [5; 11]. Conventional FBGs are insensitive to the external environment because all of the light signals are tightly confined near the fiber core [12], so the FBGs cannot detect a refractive index outside the fiber structure. If the cladding diameter of the FBG is reduced to tens of microns or nanometers, a strong evanescent field will be launched and transmitted along the core's surface [13; 14], where the change in the refractive index in the external environment can be monitored in a timely manner. Based on this mechanism, FBGs can be used for the detection of the refractive index. MFBGs combine the evanescent field characteristics of microfibers with the wavelength selection characteristics of traditional FBGs. The evanescent field characteristics of microfibers can effectively enhance the refractive index sensitivity of FBGs [15] and offer the ability to perform wavelength selection [16].  
MFBGs have higher sensitivity or accuracy regarding the refractive index and stress than ordinary FBGs [10; 17; 18]. [PERSON] used a 193 nm excimer laser to fabricate MFBGs [19]. They presented the Bragg gratings in microfibers with different diameters and studied their refractive index-sensing characteristics. The smaller diameters of the MFBGs made them more sensitive to changes in the external environment [20].  
Compared to other types of FBGs, a tilted FBG (TFBG) has a unique structure in which its grating plane has a certain angle with respect to the axial direction of the optical fiber [21]. Therefore, in addition to the characteristics of FBGs, TFBGs have their own unique advantages [22]. Some optical fiber sensors have been developed by reducing the cladding diameter of the TFBG. [PERSON] et al. studied the influence of the fiber core and cladding diameter of TFBGs on the simultaneous measurement of the liquid refractive index and temperature [23]. In order to improve the measurement accuracy, it is necessary to balance the diameters of the fiber core and cladding. [PERSON] analyzed the influence of the cladding diameter on the sensing accuracy of a TFBG using the spectral envelope method [24]. The results showed that the sensor's accuracy will decrease with a decrease in the fiber cladding diameter, but the extinction ratio of the spectrum will increase.  
The motive of this study is to design and demonstrate a tilted microfiber Bragg grating (TMFBG) with a uniform diameter distribution along the fiber. In previous works, in order to obtain a microstructural TFBG, the material was completely immersed in hydrofluoric acid. The obtained TMFBG is a biconical structure with a long conical transition region and two tapering regions on both ends. It is difficult to accurately analyze its optical properties and sensing performance. At the same time, there is no theoretical simulation model for reference. In this study, the theoretical model of a TMFBG was constructed with OptiFDTD, and the influence of its structural parameters on the spectral characteristics was studied. Based on the capillary protection (as a sacrificial layer) method, the selective corrosion of the TFBG region was realized, and a TMFBG with a uniform outer diameter was obtained.