Objective High-performance micro-nano integrated optical sensors are widely used for various applications including biomedical sensing. These sensors have several advantages, such as no need of fluorescent labeling, ease of integration, and real-time detection capability. Integrated optical sensors usually include several fundamental components: micro-ring waveguide resonator, photonic crystal waveguide, and guided mode resonance (GMR) grating. Design and implementation of integrated sensors with high figure of merit (FOM) in waveguide-type resonators seem to be complicated due to relatively higher mode volume and mode mismatch. Leaky resonant grating mode can be excited with an input light-wave under certain conditions. The major problem is a trade-off between the quality factor (Q) and sensitivity (S) of optical biosensors integrated with resonant gratings. To tackle this problem, we designed and implemented concave grating micro-structure. The structure was introduced in each unit of periodic gratings and allowed to enhance interaction between light field and test liquid. Moreover, it improved the quality factor and had no negative effect on sensitivity. Thus, a high-performance integrated sensor with high FOM was obtained using concave resonant grating.

Methods In this study, the proposed integrated sensor was composed of Si₃N₄ grating and SiO₂ layer (Fig.1). In order to design this structure, we calculated transmission spectrum of the concave resonant grating using rigorous coupled-wave analysis (RCWA) algorithm. Both reflection spectrum of concave grating and distribution of electric field at resonance were observed (Fig.2). To clarify resonant mechanism of the structure, we investigated its single unit using finite element method (FEM). According to the simulation results, the eigenmode of the structure varied with depth D_r. The sensitivity and full width at half maximum(FWHM) of the structure were both described as the functions of D_r. Eigen mode numerical values agreed well with the RCWA results. Additionally, we analyzed the relationship between other structural parameters (e.g., grating depth D_r and groove width coefficient f_b).

Results and Discussions Reflection spectrum and electric field distribution at resonant wavelength were obtained using RCWA algorithm (Fig.2). Simulation results demonstrated that optical resonance was significantly enhanced with concave resonant grating structure. In particular, sharp resonant peak was observed (Fig.2a). To clarify resonant mechanism of proposed structure with different depth D_r and groove width coefficient f_b, we calculated its eigen mode using FEM (Table 1 and Table 2). Interestingly, we found that the eigenvalue changed with the increase of D_rand width coefficient f_b. By these means, resonant wavelength and Q-factor for each mode can be easily restored. Thus, we can predict the characteristics of the transmission spectra with the change of critical parameters such as the depth and width of grating groove. We further optimized FOM of the proposed sensor using RCWA algorithm. We found that the resonant wavelength also followed blue shift trend as the groove width increased. At the same time, groove depth optimal value was found at 60 nm (Fig.3 and Fig. 4). In addition, we used the same method to study optical spectra when varying width coefficients f_b (Fig.5). As a result, ultra-high FOM can be achieved at 6562.5, while the sensitivity of the concave GMR is kept at 196.875 nm/RIU.

Conclusions A new-type refractive index sensor based on concave resonant grating has been developed. The concave micro-structure is used to enhance the interaction between optical field and cover grating structure. When introduced in unit cell, it allows optimization FOM. Integrated sensor has been optimized using rigorous coupled-wave analysis. The physical mechanism can be easily understood from calculated eigen mode of the resonant structure. As a result, the ultra-high FOM can be achieved. This provides a basis for the development of high-performance optical sensors integrated with micro-nano structure.