## 1 Introduction  
Optical absorbers are an essential optical component that can be fabricated by using various materials and structures [1; 2; 3; 4; 5]. Absorbing structures have been used in a number of diverse applications, including solar-energy harvesting [6; 7; 8; 9; 10], light modulation [11; 12; 13; 14; 15], and optical sensing and detection [16; 17; 18; 19]. There are several principles and methods used to fabricate electromagnetic wave absorbers, such as stacked metal-dielectric-metal (MIM) structures [20; 21; 22; 23], metamaterials and metasurfaces [1; 2; 3; 4; 10; 24; 25; 26; 27; 28; 29; 30], asymmetric Fabry-Perot (FP) cavities with ultrathin high-absorption dielectric layers [31; 12; 32], and subwavelength metallic gratings [1; 9; 14; 15; 17; 18; 33; 34; 35; 36; 37]. Among them, reflection-type subwavelength metallic gratings have been widely adopted due to their relatively simple geometry and practical applicability. It is interesting that visible light can be strongly confined in deep-subwavelength scale grating grooves with width and depth of a few nanometers [34]. Incident waves are absorbed due to coupling in the metallic grating as a gap surface plasmon (GSP) mode [1; 18; 33; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45]. Light is subsequently trapped within the grating cavity, thereby being absorbed due to metallic Ohmic loss. These types of structures have advantages in that they are capable of perfect absorption, and they are robust in terms of their angular dependence. For these reasons, many studies have focused on effective use of these structures in specific frequency ranges. In addition to absorber applications, it was recently shown that reflection-type spatial light modulation can be implemented by using appropriately designed subwavelength gratings and tunable materials [14; 15]. In this paper, we numerically studied the absorption properties of a subwavelength metallic grating coated with a lossy dielectric layer. The roles of the grating and coated dielectric in overall absorbance are analyzed by regarding the subwavelength grating as a homogeneous semi-infinite effective medium. Moreover, we show that subwavelength grating reflectors can be used to create critically coupled perfect absorption conditions. Although these kinds of grating-related structures have been actively studied, detailed numerical studies on the absorption characteristics of lossy dielectric coated subwavelength metallic gratings have not been reported to the best of our knowledge. The presented results can provide a useful platform for understanding and designing structures that include reflective subwavelength gratings. Absorption Characteristics of a Subwavelength Metallic Grating Covered with a Lossy Dielectric Layer  
A subwavelength metallic grating covered with a dielectric layer is illustrated in Figure 1a. This structure contains stacked dielectric resonant cavity, metallic subwavelength grating, and metal substrate layers. Since the subwavelength grating reflects light without generating higher-order diffraction peaks, the grating and substrate can be equivalently replaced by a semi-infinite effective medium substrate, as shown in Figure 1b. In this model, which is an asymmetric FP resonant cavity, the reflection coefficient between the dielectric resonant cavity and effective medium substrate can be obtained by numerically calculating the modulated amplitude and phase profiles created by the grating. We note that the magnitude of the reflection coefficient is associated with absorption due to localized GSP modes within the grating cavities. Calculation of the reflection coefficient for the semi-infinite effective medium can be implemented with the model shown in Figure 2a. The one-dimensional grating in this model is periodic along the \(x\)-axis and is embedded in a background dielectric medium. The period and thickness of the grating are labelled \(p\) and \(t_{\text{g}}\), respectively, and \(w\) is the width of the grating cavity.