## 1 Introduction  
The surface plasmon resonance (SPR) technique has been widely used in biosensing due to its high sensitivity and rapid response [1, 2]. The key to improve the sensitivity of optical fiber SPR sensors is to enhance the intensity of the interaction between the evanescent wave and the metal film [3]. Compared with the fundamental mode, the higher-order modes (the LP\({}_{11}\) and LP\({}_{21}\) modes) easily leak to the fiber cladding due to a greater angle of incidence, leading to much more power remaining in the cladding [4]. Given this, when the evanescent wave to excite the SPR in sensing is used, the sensitivity can be improved by higher-order modes. Therefore, several methods have been proposed to excite higher-order modes to enhance the sensitivity of fiber SPR sensors, such as D-shaped structures [5], tilted fiber Bragg gratings (TFBGs) [6], and lens illumination [7]. Although the existing studies can improve the sensitivity of SPR sensors using higher-order modes, the power proportion of higher-order modes used to excite SPR is unknown due to the mixing with the fundamental mode. If the proportion of the fundamental mode can be reduced to the minimum, or even to zero, along the optical fiber, the sensitivity of the SPR fiber sensors could be further improved.  
Utilizing higher-order modes to improve the sensitivity of fiber SPR sensors has been explored by many researchers [7, 8, 9, 10]. For instance, using a Bessel-Gauss beam as a light source, a sensor with a high sensitivity of 11,928.25 dB/RIU is obtained, which is 10 times that of a Gaussian beam [7]. The higher-order modes in the cladding can be generated by TFBGs with different angles, which provides a sensitivity of around 500 nm/RIU [8]. Moreover, a biosensor shows a detection limit of \(1.5\times 10^{3}\) colony-forming units (CFU)/mL, using a U-shaped fiber to tilt the incident angle to generate higher-order modes [9]. Meanwhile, these higher-order modes can be generated by changing the mode field using a mismatched junction between two fibers, which improves the performance of the sensor with a sensitivity of 4816.092 nm/RIU [10]. However, these approaches fail to further improve their sensitivity because the mixing of higher-order modes with the fundamental mode is inevitable, and the fundamental mode dominates in the optical fiber. In particular, the latter is the main reason preventing the enhancement of the sensitivity of fiber SPR sensors. Hence, if we want to further improve the sensing performance of SPR sensors, it is reasonable to consider using relatively pure higher-order modes. However, it is difficult to excite the pure higher-order modes according to the existing methods. In 2020, [PERSON] et al. [11] fabricated a visible mode selective coupler (MSC), generating the LP\({}_{11}\) mode at a specific wavelength range (480-540 nm), almost without the fundamental mode. The presented approach gives us a new practical way to apply this MSC to excite the pure higher-order mode (not just the LP\({}_{11}\) mode) after slight modifications. With this method, we can intensify the SPR on the surface of the core by generating relatively pure higher-order modes.  
In this paper, we propose a SPR sensor with a designed MSC to obtain a pure higher-order mode for sensitivity improvement. Section 2 describes the mechanism of the sensor for the refractive index (RI) measurement using higher-order modes. Then, in Section 3, we calculate the power proportion of different modes in the cladding and design an MSC, using two optical fibers. Finally, the parameters of the MSC are optimized to produce a pure higher-order mode for RI measuring, and simulations of the designed SPR sensor are shown in Section 4, proving that this sensor is an effective device to achieve highly sensitive RI measuring.