## 1 Introduction  
Recently, perfect absorbers (PAs) have attracted great attention because they have a variety of potential applications. PAs with a broad operating bandwidth are useful in photonic detection [1] and light energy acquisition [2], whereas PAs with a narrow operating bandwidth are advantageous for sensing [3], filtering [4], and selective thermal emitting [5]. In particular, narrowband PA-based refractive index sensors are very promising due to their simple structure and high-throughput detection [6]. Researchers have presented this type of sensor which exhibits good performance [7; 8]. Furthermore, thermo-optical sensing can also be achieved by narrowband PAs operating in the terahertz spectral region [9].  
To achieve narrowband PAs, many researchers have investigated the use of all-metal structures or tri-/multi-layer metal-insulator-metal (MIM) structures [10; 11; 12; 13; 14]. However, fabrication of these structures is costly due to their incompatibility with complementary metal oxide semiconductor (CMOS) fabrication processes [15]. For this reason, there has been an increasing interest in realizing narrowband PAs by dielectric structure on metal systems [16; 17; 18]. In comparison with metallic PAs, this type of absorber can save the fabrication cost [19]. Such absorbers typically have one or more dielectric waveguide layer between the grating and the metallic substrate. They can generate ultra-narrow absorption peaks, but their structures are relatively complex. To simplify the structure, a dielectric grating can be placed on top of a metallic substrate/film directly [20; 21; 22; 23; 24; 25; 26]. For example, in 2004, [PERSON] et al. theoretically studied the resonance absorption of a usual dielectric grating on a metal system [25]. In 2017, [PERSON] et al. numerically presented a narrowband PA constructed by a usual and a compound dielectric grating on a metallic substrate [26; 27]. These absorbers can also provide ultra-narrow absorption bandwidths.  
Most of the structures above used low-index dielectric gratings, thus showing obvious disadvantages. For example, the grating grooves could have large depth-width ratios (\(>\)10) and were difficult to fabricate. The designed peaks could disappear in high-index surroundings, which limited their practical applications in refractive index sensing. Moreover, they mainly operated in the visible and near-infrared spectral region.  
However, such narrowband PAs operating in the mid-infrared (mid-IR) spectral region are particularly useful, as in the mid-IR spectral region there are various molecular fingerprint spectra [28]. When used with diode lasers and quantum cascade lasers, these narrowband PAs can be very promising in a number of applications, including spectroscopic sensing and gas detection [29; 30].  
In this work, we proposed a mid-IR narrowband PA for sensing applications. The PA was achieved by placing a fine-structured silicon grating on a gold film. The silicon grating consisted of two narrow silicon strips in each unit cell, which enabled the excited resonance mode to be low-loss. Thus, the absorber provided a narrow absorption peak at a wavelength of 4.071 \(\upmu\)m with a high absorption rate. The absorber is useful for the spectral control of mid-IR signals. When used as a refractive index sensor, it has the advantage of still being effective in high-index surroundings. The proposed absorber is very simple and is fully compatible with current CMOS fabrication processes.