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Abstract
A high-performance optical sensor with a vertical cavity structure comprising high-contrast gratings (HCGs) and a distributed Bragg reflector was designed. The structure has two peaks with different mechanisms, among which the first peak is formed by breaking the symmetry of the structure and coupling between the incident wave and the symmetric protection mode. The joint action of the HCG resonance and Fabry–Perot resonance formed a second peak. Moreover, changing the structural parameters, such as the grating width, period, and cavity length, can tune the spectral reflection dips. The sensitivity of the designed structure was as high as 674 nm/RIU, and the corresponding figure of merit was approximately 34741. The presented gas sensor provides a method for applying a vertical cavity structure to the sensing domain.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical gas sensors can provide real-time and accurate detection and have various applications in health care, safety and environmental monitoring [1,2]. Many gas sensors have been reported to exhibit different physical mechanisms, such as guided mode resonance (GMR), surface plasma, and Tamm plasmas [3–6]. The GMR-based gas sensors have attracted considerable attention owing to their narrow linewidths. Deng et al. introduced a vertical resonant cavity based on the GMR that utilizes light–gas interactions to realize gas sensing [7]. Although such sensing can have outstanding sensing performance, the leaky waves resulting from the mode cannot be ideally confined. In 2021, a double high-contrast grating (HCG) [8] resonant structure was proposed by Zhang et al. to address the problem of mode leakage [9]. Here, the light field can be trapped in the grating region using the quasi-continuous bound-state (BIC) mode [10,11], thereby increasing the local electric field intensity and decreasing the line width. Thus, achieving high-performance optical sensing [12–15] using a BIC mode with excellent spectral properties, such as high sensitivity, is highly desirable.
Based on the formation mechanism, BIC can be classified as symmetry-protected BICs, generated at the Brillouin zone center $(\mathrm{\Gamma }$ point) due to different distributions of the outgoing wave and mode fields [16–21], and as accidental BICs generated at the off-$\mathrm{\Gamma }$ point due to destructive interference [22–24]. An actual BIC state with an infinite radiative Q-factor and vanishing resonance peaks is an ideal state that is difficult to realize in practice. The BIC is transformed into a quasi-BIC using external radiation. The quasi-BIC has a finite Q-value and narrow linewidth. The narrow-linewidth spectrum is sensitive to the refractive index of the surrounding environment medium, imparting the designed sensor with a good sensitivity (S)and an excellent figure of merit (FOM) value. Recently, multimode BICs have been attracted and considered promising for multiband sensing [25–27]. Consequently, this provides a new path for achieving a high-performance sensor with a multiband channel. In 2022, Shi et al. demonstrated a double-layer symmetric grating that could control dual-band resonance by adjusting the grating gap [28]. However, the reflection spectrum and field intensity were significantly affected by adjusting the grating gap. Furthermore, the preparation of the double-symmetric grating is relatively complex compared to that of the HCG-distributed Bragg reflector (DBR) vertical cavity. Therefore, the DBR can be used instead of a grating layer in the double-layer gratings to achieve double-peak sensing.
In this study, we propose a vertical cavity structure combining a compound HCG (HCCG) and a DBR that supports symmetry-protected BIC and Fabry–Perot (F–P) resonance. A symmetry-protected BIC is induced by adjusting the widths of the two HCGs. In addition, the cavity length and structural period can be adjusted to control the grating and DBR coupling states. Finally, we implemented a dual-wavelength resonant cavity for gas sensing, which provides an effective method for realizing multiwavelength sensing.
2. Structure and theory
Figure 1 shows a schematic of the HCCG-DBR sensor under transverse magnetic (TM)-polarized plane-wave illumination at an incidence angle of 4°. The structure consists of a compound HCG, an air-filled cavity, and a DBR with 13 pairs of SiO2/Si3N4 alternating layers. The thicknesses of the SiO2 (${n_{\textrm{Si}{\textrm{O}_2}}} = 1.45$) and Si3N4 (${n_{\textrm{S}{\textrm{i}_3}{\textrm{N}_4}}} = 2$) in the DBR were L1 and L2, respectively. The thickness of the air cavity (${n_{\textrm{air}}} = 1$) was denoted as L, and the period of the structure was represented by P. The HCGs, made of Si (${n_{\textrm{Si}}} = 3.5$), had widths of W1 and W2, and their thicknesses were expressed as Tg. To study the effect of the resonance characteristic with symmetric and asymmetric gratings, the adjacent HCG widths were regulated and a new dimensionless parameter was defined as ${\alpha _w} = \; |{{W_1} - {W_2}} |/({{W_1} + {W_2}} )$ to measure the “degree of asymmetry” in the grating width.
Fig. 1. Schematic of the sensor based on the compound high-contrast grating(HCCG)-distributed Bragg reflector (DBR) structure.
S and the FOM are used to quantify the sensing performance, and are expressed as follows [29]
where Δλres is the resonant wavelength shift, Δnc is the change in the gas index during the analysis, and Δλ is the full width at half maximum (FWHM).Recently, an HCG-based vertical cavity structure was reported in the experiment [30]. As reported from previous studies, a feasible fabrication process can be initiated using the Si substrate, following which the Si3N4/SiO2 DBRs can be fabricated via plasmas-enhanced chemical vapor deposition. Previously, electron-beam lithography was used to define the grating pattern to fabricate the HCG-based cavity [31].
3. Results and discussion
First, we calculated the reflection spectra of the solitary compound HCG and HCCG-DBR structures at incidence angles of 0° and 4°. The reflection spectra of the solitary compound and the HCCG-DBR structure were calculated using the rigorous coupled-wave analysis (RCWA) method [32,33], as shown in Fig. 2(a) and (b). The following parameters were set for the simulations: $P = 1351\; $nm, ${T_g} = 240\; $nm, ${W_1} = 560.5\; $nm, ${W_2} = 439.5$ nm (${\alpha _w } = 0.121$), $L = 1080\; $nm, ${L_1} = 284.48\; \textrm{nm}$, and ${L_2} = 206.25\; $nm. The sum of the adjacent HCG widths was 1000 nm. Figure 2(a) and (b) show that when the light is normally incident with a TM-polarized plane wave, the solitary HCGs and HCCG-DBR structures exhibit only one peak at ${\lambda _{\textrm{quasi} - \textrm{BIC}}} = 1762.8$ nm and ${\lambda _{\textrm{quasi} - \textrm{BIC}}} = 1763.4\; \textrm{nm}$, respectively. The figures show the FWHM of the two structures with FWHM of 6.7 and 0.02 nm, respectively. We set the asymmetric parameter ${\alpha _w} = 0.121$ to break the symmetry of the gratings, which resulted in a narrow FWHM [17]. The magnetic-field profile at the peak wavelength shows that most of the energy is confined within the grating, with only a minor amount leaking into free space, as depicted in Fig. 2(c) and (e). The line width was obviously reduced with DBR compared to that without DBR. The DBR can enhance the magnetic field intensity and improve the Q-factor, which is very favorable to the formation of BIC.
Fig. 2. Reflection spectra for (a) HCGs and (b) HCCG-DBR. Magnetic field profile of HCGs with (c) normal incidence angle and (d) oblique incidence angle of 4°. Magnetic field profile of the HCCG-DBR with (e) normal incidence angle. Magnetic field profile of the HCCG-DBR structure with an oblique incidence angle of 4° for the (f) first and (g) second peaks.
Moreover, the reflection spectra, produced by a 4° oblique incidence and based on the aforementioned structural parameters, is represented using the red lines in Fig. 2(a) and (b). In the case of solitary HCGs, the oblique incidence resulted in a resonance peak shift and a narrower FWHM, suggesting that more energy was concentrated within the HCGs, as indicated by the magnetic field profile in Fig. 2(d). For the HCCG-DBR structure with an oblique incidence of 4°, two resonance peaks were observed. The formation mechanism of the first peak was similar to that of the peak generated at normal incidence. The symmetry of the HCCG-DBR structure was broken by designing an oblique incident and asymmetric grating results in the transformation of an ideal BIC into a quasi-BIC. Most of the energy was bounded by the HCGs, as depicted in Fig. 2(f). Most of the energy was focused within the gratings, with a small portion leaking into the DBR, as shown in Fig. 2(g). This is because the F–P mode may cause mode leakage, whereas the HCG resonance enhances the bound energy.
Next, we analyze the influence of asymmetry parameter αw on the HCCG-DBR structure for the normal and oblique incident light. The reflection spectrum as function of αw for the normal incident light is illustrated in Fig. 3(a). For the BIC, a vanishing linewidth was observed at ${\alpha _w} = 0$. Through the finite element method, the complex eigenfrequency $\omega = {\omega _0} + i\gamma $ can be obtained, where ${\omega _0}$ is the central resonant frequency, and γ is the radiative loss of the leaky mode [34]. The radiative Q-factor can be calculated as $Q = {\omega _0}/2\gamma $ to predict the dependence of Q on the asymmetry parameters. Theoretically, the Q-factor is inversely proportional to the square of the asymmetry parameter ($Q \propto \alpha _w^{ - 2}$) [19]. As αw decreases, the Q-factor sharply increases, as shown in Fig. 3(b). As seen from Fig. 3(c) and (d), two peaks are observed for oblique incidence at 4°. As αw decreases, the linewidth of the resonance also decreases until ${\alpha _w} = 0$, after which the linewidth vanishes. The calculated resonance frequencies at two peaks are 169.94 THz and 160.24 + 2.0513i THz, respectively. For the first peak, no radiative loss of the leaky mode was observed at ${\alpha _w} = 0$ during the forming of an ideal BIC. The ideal BIC can be transformed into a quasi-BIC by adjusting the asymmetry parameter αw. For the second peak, the leaky mode still exists for ${\alpha _w} = 0$. This is because the second peak was affected by the HCG and F–P resonances. Figure 3(e) shows that the reflectance at the resonance will gradually away from 0 with αw decreasing from 0.121 to 0.04 for the first peak. For the second peak, we can observe that the reflectance does not change when αw decreases from 0.121 to 0.08; however, when αw decreases to 0.04, the reflectance dramatically increases. Figure 3(f) illustrates the relationship between S (black line) and FOM (red line) under different asymmetry parameters αw. The sensitivity of the two peaks does not have the same trend with increasing αw. On the contrary, the FOM value of both peaks decreases with the increase in αw. Considering the reflectance of resonance peaks with different αw and the variation trend of S and FOM, we choose αw as 0.121.
Fig. 3. (a) Reflection spectra for different values of αw for a normal incidence angle. (b) Radiative Q-factor versus the asymmetry parameter αw. (c) Reflection spectra with respect to different values of αw for an oblique incidence angle. (d) Spectrograms for different αw values, using transverse magnetic (TM) polarization. (e) Reflection spectra for different αw. (f) S and FOM for different αw values.
Subsequently, we investigated the influence of period P on the reflection spectrum of the proposed structure. Figure 4(a) illustrates the redshift of the two resonance peaks as P increases from 1341 nm to 1361 nm. As P increased, both resonances displayed a significant shift, with the shift in the second resonance becoming more pronounced. Figure 4(b), (c), and (d) depict the magnetic field of the first resonance of P at 1346, 1351, and 1356 nm, respectively. The loss of the reflection spectrum was minimal at $P = 1351$ nm, and more energy was generated in the HCG. Figure 4(e), (f), and (g) show the magnetic fields of the second resonances for P at 1346, 1351, and 1356 nm, respectively. At $P = 1346$ nm, the coupling effect of the HCG and DBR was optimal, and the energy within the HCG was at its highest. As P increases, the loss increases, resulting in a reduced energy intensity in the grating. For the combined effect of the HCG and F–P resonance, most of the energy is well confined to the HCG, and the energy leakage in the DBR gradually decays [35].
Fig. 4. (a) Reflection spectra for different periods P.(b) Magnetic field at the first peak for $P = 1346\; $nm, (c) $P = 1351\; $nm, and (d) $ P = 1356\; $nm. (e) Magnetic field at the second peak for $P = 1346\; $nm, (f) $P = 1351\; $nm, and (g) $P = 1356\; $nm.
To explore the role of the air cavities in the HCCG-DBR structure, we analyzed the effect of L on the reflection spectrum. As displayed in Fig. 5(a), as the thickness of the air cavity increased by 20 nm, the first peak exhibited a significant redshift. In contrast, the second resonance peak showed a subtle blue shift, demonstrating greater tolerance. The first resonance peak is due to the HCG resonance, where the DBR can be observed as a homogeneous layer. The second resonance was formed by the joint action of the HCG and DBR. Figure 5(b) illustrates the S and the FOM for the two peaks with different L. S1 and S2 are the sensitivity for the first and second peaks, respectively. FOM1 and FOM2 are the corresponding FOM value. As L increases, S1 and S2 decrease. Specifically, FOM1 reaches its maximum at $L = 1080\; $nm, whereas FOM2 peaks at $L = 1100\; $nm. Hence, considering the sensing characteristics at different L values, a value of 1080 nm was selected.
Fig. 5. (a) Reflection spectra for different L values. (b) FWHM and reflection dip for different L values.
We analyzed the effects of different structural parameters on the reflection spectrum and FWHM. To evaluate the sensing performance, we utilized the functional relationship between the gas refractive index nc and the S and FOM. Figure 6(a) demonstrates that as the refractive index of the external environment changed from 1 to 1.01, the resonance wavelength underwent a corresponding redshift. Figure 6(b) displays a strong linear relationship between the position of the resonance peak and changes in the refractive index of the external environment. Based on these findings, the S and FOM for the two resonance peaks were determined as ${S_1} = 674$ nm/RIU and ${S_2} = 244$ nm/RIU, and $\textrm{FO}{\textrm{M}_1} = 34741$ and $\textrm{FO}{\textrm{M}_2} = 58050$, respectively.
Fig. 6. (a) Reflection spectra for different refractive indices (nc) values. (b) Resonance wavelengths versus nc.
4. Conclusion
We proposed an HCCG-DBR-based gas sensor to realize dual resonance. The two resonances originate from distinct mechanisms: one from the HCG resonance and the other from a combination of the HCG and F–P resonances. We investigated the resonant characteristics of adjacent HCGs under asymmetric conditions. By disrupting the symmetry of the HCGs, an ideal symmetrically protected BIC was converted into a quasi-BIC. We also examined the effect of the air-cavity thickness and structural period on the reflection spectrum and observed the variations in the magnetic field with different values of L and P. The proposed structure demonstrated excellent optical sensing capabilities, with an S of 674 nm/RIU and an FOM value of 34741 for the first resonance peak and an S of 244 nm/RIU and an FOM value of 58050 for the second resonance peak.
Funding
National Natural Science Foundation of China (61905060); Funded By Science and Technology Project of Hebei Education Department (ZD2021019).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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