# Quasi-BIC-Based High-Q Perfect Absorber with Decoupled Resonant Wavelength and Q Factor

^{1}

^{2}

^{*}

## Abstract

**:**

^{5}is designed. This work proposes a method to tune the quasi-BIC mode, thereby introducing a new paradigm for the design of a high-Q perfect absorber.

## 1. Introduction

^{5}is designed by using this method.

## 2. Methods

_{11}, and absorptivity can be obtained by 1−R since there is no transmission in the system.

## 3. Results and Discussion

#### 3.1. Scheme of the Quasi-BIC-Based High-Q Perfect Absorber

_{2}spacer, and a Si layer from bottom to top, with gratings engraved on top of the Si layer (left panel in Figure 1). In this structure, BIC originated from the coupling between a guided mode and an FP mode. The guided mode horizontally propagates inside the Si layer (since the refractive index of Si is higher than that of SiO

_{2}), while the FP mode vertically oscillates between the Si and SiO

_{2}layers (right panel in Figure 1). The Au substrate serves as a bottom mirror to prevent transmission and absorb the incident light. The SiO

_{2}layer is used to separate the guided mode from the Au substrate to reduce the resistive loss. The resonance of the guided mode is determined by the period of gratings and the thickness of the Si layer, while that of the FP mode is determined by the thickness of both Si and SiO

_{2}layers. Since the factors affecting the resonance of both modes slightly differ from each other, it is possible to tune one mode while maintaining the other. Thus, it is feasible to independently tune the resonant wavelength and the Q factor of the quasi-BIC mode. The cross-section of a single period is demonstrated in the middle panel of Figure 1, where w represents the width of the grating; p is the period; h

_{0}is the grating thickness; h

_{1}is the Si layer thickness; h

_{2}is the SiO

_{2}layer thickness, and h

_{3}is the thickness of the Au substrate.

#### 3.2. Characterization of the BIC Mode

_{2}layer thickness h

_{2}was simulated for the structures with different periods p = 430 nm, 450 nm, and 470 nm (Figure 2a–c). Other structure parameters were set as h

_{0}= 30 nm, h

_{1}= 670 nm, h

_{3}= 200 nm, and w = p/2. The track of the guided mode is parallel to the h

_{2}axis, while that of the FP mode is almost an oblique straight line (Figure 2a–c). The resonance of the FP mode experiences a redshift with increasing h

_{2}, while the guided mode maintains the same resonant wavelength. On the other hand, the track of the FP mode maintains the same position, while that of the guided mode redshifts with increasing p. Thus, the resonances of the guided mode and the FP mode can be independently tuned by either changing p or h

_{2}.

_{2}values of each BIC point are about 480 nm, 560 nm, and 660 nm corresponding to p = 430 nm, 450 nm, and 470 nm, respectively. By comparing Figure 2a–c, it is noted that the resonant wavelength of the quasi-BIC mode is relevant to the period p and is hardly influenced by the thickness of SiO

_{2}layer h

_{2}.

_{2}on the quasi-BIC modes, five absorptivity curves (Figure 2d–f) were plotted for the quasi-BIC modes in the orange dashed areas of Figure 2a–c, with the interval of h

_{2}as 10 nm. For all the periods, the difference between the resonant wavelengths is within 1 nm against the change of h

_{2}. Especially for p = 470 nm, the quasi-BIC modes resonate at the same wavelength of 1356 nm (Figure 2f), showing that the resonant wavelength is hardly influenced by h

_{2}. However, the resonant wavelength changes by nearly 40 nm when p changes by 20 nm. The resonant wavelengths are near 1275 nm, 1312 nm, and 1356 nm for p = 430 nm, 450 nm, and 470 nm, respectively (Figure 2d–f), indicating that the period is a key factor to change the resonant wavelength.

_{2}is tuned from 410 nm to 450 nm (Figure 2d); for p = 470 nm, the peak absorptivity decreases when h

_{2}is tuned from 610 nm to 650 nm (Figure 2f). These results suggest that h

_{2}cannot be used to tune the resonant wavelength, but it can help to tune the Q factor (or the bandwidth) and the peak absorptivity.

_{2}layer thickness h

_{2}.

#### 3.3. Analysis of Q Factor and Peak Absorptivity

_{2}, h

_{0}+ h

_{1}, etc.) influence the coupling between the guided mode and the FP mode in a similar way, i.e., by tuning the phase difference between these two modes. Since the period p was used to determine the resonant wavelength and the SiO

_{2}layer thickness h

_{2}was used to tune the coupling, h

_{2}was set as the only variable in the following simulation, with other structure parameters as h

_{0}= 30 nm, h

_{1}= 670 nm, h

_{3}= 200 nm, p = 450 nm, and w = 225 nm (Figure 3a). When h

_{2}is changed from 510 nm to 600 nm (the BIC point is within this range), the damping rate of resistive loss maintains the magnitude of 10

^{10}s

^{−1}, while that of radiative loss experiences a huge change from 10

^{7}s

^{−1}to 10

^{10}s

^{−1}(Figure 3b). This indicates that h

_{2}mainly influences the radiative loss and slightly influences the resistive loss. The change of resonant wavelength stays within 1 nm during the tuning of h

_{2}(Figure 3e). For h

_{2}= 550 nm (near the BIC point), the damping rate of resistive loss is nearly three orders higher than that of the radiative loss. According to the coupled mode theory [38], resistive and radiative losses serve key roles in tuning the Q factor and the peak absorptivity. Thus, the mechanism behind the Q factor and peak absorptivity tuning is that h

_{2}can change the radiative loss.

_{tot}, Q

_{res}, and Q

_{rad}represent the total Q factor, resistive Q factor, and radiative Q factor, respectively). Thus, unlike dielectric BIC structures (without resistive loss), the total Q factor of the BIC mode in this work is limited by the resistive loss and cannot approach infinity. The resistive loss in this structure is mainly from the bottom Au substrate (Figure 3d). Moreover, the dissipation mainly happens within the top 50 nm of the Au substrate, which suggests that as long as the thickness of the Au substrate is larger than 50 nm, there will be no light transmission, and the absorption will be the same.

_{2}from 510 nm to 600 nm; i.e., the highest total Q factor corresponds to the lowest peak absorptivity. Thus, there is a tradeoff between the total Q factor and the peak absorptivity for this design of the quasi-BIC high-Q absorbers presented in this work.

#### 3.4. Realizing Higher Q Factor While Maintaining High Peak Absorptivity

_{2}layer thickness h

_{2}, one idea to simultaneously realize a higher Q factor and high peak absorptivity in the quasi-BIC mode is to decrease the damping rate of resistive loss at first and then tune that of radiative loss to the same magnitude as the resistive loss by changing h

_{2}. Thus, it is critical to find a way to lower the damping rate of resistive loss in the quasi-BIC mode.

_{0}is found to have the capability to change the damping rate of resistive loss. Simulations are conducted for the structure with parameters h

_{0}+ h

_{1}= 700 nm, h

_{2}= 530 nm, h

_{3}= 200 nm, p = 450 nm, and w = 225 nm (Figure 4a). The damping rate of resistive loss increases by two orders—from 10

^{9}s

^{−1}to 10

^{11}s

^{−1}when h

_{0}is changed from 5 nm to 70 nm (Figure 4b). The damping rate of radiative loss decreases to 10

^{6}s

^{−1}at first and then increases rapidly to 10

^{11}s

^{−1}, suggesting that the resonance evolves to a BIC mode during the progress.

_{0}was set as 5 nm to decrease the damping rate of resistive loss as much as possible, and the next step was to tune the damping rate of radiative loss to the magnitude of resistive loss (Figure 4c,d). Setting h

_{0}as 5 nm and keeping other structure parameters fixed, damping rates were simulated for different h

_{2}values (from 510 nm to 600 nm). The damping rates of resistive loss and radiative loss almost equal to each other when h

_{2}= 580 nm (green circled data in Figure 4d).

_{0}= 5 nm, h

_{1}= 695 nm, h

_{2}= 580 nm, h

_{3}= 200 nm, p = 450 nm, and w = 225 nm. The absorptivity curve is shown in Figure 4e. The structure has a peak at 1323.375 nm (the electric field distribution is shown in the inset), and the peak absorptivity is unity. The FWHM (full width at half maximum) of the peak is as narrow as 2.58 × 10

^{−3}nm, corresponding to a high Q factor of 5.13 × 10

^{5}.

#### 3.5. General Steps to Design a Quasi-BIC-Based High-Q Perfect Absorber

_{0}; last, make the damping rate of radiative loss approximately equal to that of resistive loss by tuning the SiO

_{2}layer thickness h

_{2}.

## 4. Conclusions

^{5}is designed. First, the design in this work is versatile such that it can be easily scaled to different operating wavelengths, e.g., mid-IR for sensing or high-Q emitter. Second, the mechanism of decoupling the resonant wavelength and the Q factor can used on other structures with two resonances that can be independently tuned. Third, by replacing the SiO

_{2}layer with a dielectric elastomer actuator [39] (thickness could be varied dynamically), it could be possible to dynamically tune the Q factor while maintaining the resonant wavelength. Lastly, the structure proposed in this work can serve as a platform for cutting-edge technologies [40,41,42,43,44,45,46], including ultrasensitive biosensing [47], high-harmonic generations [48], and coherent and quantum light generations [49].

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematic of the quasi-BIC based high-Q perfect absorber (

**left panel**), the cross-section of a single period (

**middle panel**), and electric field distributions of the guided mode and the FP mode (

**right panel**).

**Figure 2.**Simulation results of absorptivity. (

**a**–

**c**) Dispersion relation of absorptivity versus wavelength and the SiO

_{2}layer thickness for the period p values of 430 nm, 450 nm, and 470 nm, respectively. Insets show electric field distributions in (

**a**) corresponding to the guided mode and the FP mode (the red stars) and the BIC point (the white point). Red circled area represents the avoided crossing. (

**d**–

**f**) The absorptivity curves for different SiO

_{2}layer thicknesses h

_{2}(with the interval of 10 nm), corresponding to the indicated orange dashed area of (

**a**–

**c**), respectively.

**Figure 3.**Analysis of Q factor and peak absorptivity. (

**a**) Schematic of the simulated structure. The only variable parameter is the SiO

_{2}layer thickness h

_{2}. Plots of (

**b**) damping rates and (

**c**) Q factors versus h

_{2}. Red and blue dots represent resistive and radiative losses, respectively. (

**d**) Distribution of electric field (left) and resistive loss (right) for h

_{2}= 550 nm. (

**e**) The resonant wavelength versus h

_{2}plots. (

**f**) Peak absorptivity (red dots) and total Q factor (blue dots) versus h

_{2}plots. For all the above cases, h

_{2}is tuned from 510 nm to 610 nm, with an interval of 10 nm.

**Figure 4.**Design for increasing Q factor. (

**a**) Schematic of the structure (grating thickness h

_{0}is the variable parameter). (

**b**) Damping rates versus h

_{0}plots. Red and blue dots represent resistive and radiative losses, respectively. Grating thickness h

_{0}is varied from 5 nm to 70 nm, with an interval of 5 nm. (

**c**) Schematic of the structure (h

_{0}is set as 5 nm, and the SiO

_{2}layer thickness h

_{2}is varied). (

**d**) Damping rates versus h

_{2}plots. SiO

_{2}layer thickness h

_{2}is changed from 510 nm to 600 nm, with an interval of 10 nm. (

**e**) Absorptivity curve for the green circled structure parameter in (

**d**). Inset represents the electric field distribution at the peak, λ

_{0}= 1323.375 nm.

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**MDPI and ACS Style**

Zha, W.; Huang, Y.; Ghosh, P.; Li, Q.
Quasi-BIC-Based High-Q Perfect Absorber with Decoupled Resonant Wavelength and Q Factor. *Electronics* **2022**, *11*, 2313.
https://doi.org/10.3390/electronics11152313

**AMA Style**

Zha W, Huang Y, Ghosh P, Li Q.
Quasi-BIC-Based High-Q Perfect Absorber with Decoupled Resonant Wavelength and Q Factor. *Electronics*. 2022; 11(15):2313.
https://doi.org/10.3390/electronics11152313

**Chicago/Turabian Style**

Zha, Weiyi, Yun Huang, Pintu Ghosh, and Qiang Li.
2022. "Quasi-BIC-Based High-Q Perfect Absorber with Decoupled Resonant Wavelength and Q Factor" *Electronics* 11, no. 15: 2313.
https://doi.org/10.3390/electronics11152313