On-Chip Refractive Index Sensor With Ultra-High Sensitivity Based on Sub-Wavelength Grating Racetrack Microring Resonators and Vernier Effect

An approach to optimize the sensitivity and the limit of detection of on-chip refractive index sensor is proposed and demonstrated based on sub-wavelength grating racetrack microring resonator and Vernier effect. The sub-wavelength grating waveguide can reduce the structure limitation of the light field, which is beneficial to enhancing the interaction between the photon and analyte. By optimizing the parameters of the sub-wavelength grating racetrack microring resonator, the sensitivity of the sensor could be significantly improved to 664 nm/RIU. Subsequently, capitalizing the Vernier effect, a two cascaded microring-based refractive index sensor is designed. Owing to the Vernier effect, the wavelength spacings among the overlapped peaks could be effectively amplified more than ten times, leading to a high performance. The results demonstrate that an ultra-high sensitivity of 7061 nm/RIU and a low limit of detection of 1.74 × 10−5 RIU. With the advantages of ultra-high sensitivity and low limit of detection, the integrated device has important value in the fields of environmental monitoring and biosensors.

The sub-wavelength grating (SWG) waveguide microrings [26], [27], [28] is a new type of silicon waveguide ring, which consists of periodic silicon pillars with a period smaller than the operating wavelength. As the contact area between the analytes and the waveguide ring is enlarged, it is very beneficial to enhance the interaction between the analyzed solution and photons. Consequently, the sensitivity could be improved. An SWG waveguide microring resonator (SWGMRR) realizes a sensitivity of 520 nm/RIU [29]. In the SWGMRR, effective sensing region includes not only the top and side of the waveguide, but also the space between the silicon pillars on the light propagation path, which is beneficial to enhancing the contact between light and medium. Another SWGMRR scheme based on the Fano resonance demonstrates a sensitivity of 366 nm/RIU [30]. A trapezoidal sub-wavelength grating waveguide microring resonator (T-SWGMRR) is proposed and the sensitivity of 440 nm/RIU is realized [31]. Considering the requirements of high-precision detection in biomedical science and environmental monitoring, it is still highly desirable to achieve a refractive index sensor with high sensitivity.
The Vernier effect has been widely utilized in optical sensors [32], which could effectively improve the sensitivities without requiring high-resolution measurement equipment. As the wavelength shift of the sensing measurement is generally This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Fig. 1. (a) The structural diagram of SWGRMR, and (b) The structural diagram of SWG waveguide. n sub is the index of the substrate, and n 1 and n 2 refer to the indexes of cladding and Si waveguide, respectively. small, a narrow line width tunable laser or a high-resolution optical spectrum analyzer (OSA) is required [32]. In contrast, the Vernier effect is effective to reduce the equipment resolution requirement with maintaining high measurement precision. Even if the wavelength red-shift of the sensing resonance is small, the actual measured wavelength shift could be multiplied under the combined action of the sensing ring and the reference ring (i.e., Vernier effect), which contributes to the effective sensitivity improvement [32], [33], [34]. Consequently, by using the Vernier effect, a high-sensitivity refractive index sensor without requiring a narrow line width tunable laser or a high-resolution OSA could be obtained.
In this paper, a sub-wavelength grating waveguide racetrack microring resonator (SWGRMR) is optimized and further designed as a cascaded double-microring refractive index sensor based on the Vernier effect, which could obtain an ultra-high sensitivity. In this case, the sensitivity and the limit of detection (LOD) are improved to 7061 nm/RIU and 1.74 × 10 −5 RIU, respectively. The high sensitivity is achieved with the solution refractive index ranging from 1.333 to 1.3405.

II. THEORETICAL DESIGN OF THE SWGRMR STRUCTURE
The structure of the SWGRMR is shown in Fig. 1(a), and the light cyan area represents the cladding region. Deionized waters doped with different concentrations of glucose solutions are used as the cladding material. The thick of the top silicon layer and the buried oxide layer are 220 nm and 2 μm, respectively, as shown in Fig. 1(b).
The structural parameters of the SWGRMR are labeled in Fig. 2. The pillar width, the bent waveguide radius, the racetrack length, the coupling gap, grating period and duty cycle of the racetrack microring resonator are denoted as W, R, L c , G, Λ and f, respectively. The radius of the SWGRMR is chosen as R = 10 μm to guarantee low bending loss [35]. To make the SWG waveguide operate in the sub-wavelength regime (λ/Λ > 2n eff , λ = 1550 nm), the period Λ is designed as 250 nm. Consequently, the light could propagate between the voids and the silicon pillars and avoid to be diffracted in the far field [36]. In order to realize the optimal sensing performance, the critical parameters of f, W, G, and L c are analyzed. The simulation conditions are set as follows. The mesh size, the light source, the wavelength range and simulation time are set as at least three, fundamental mode light source, 1500 nm ∼ 1600 nm and 300000 fs, respectively.
The device quality (Q) factor could be denoted by [27] Q = λ res Δλ F W HM (1) where λ res is the resonant wavelength of the cavity, and Δλ FWHM is the full width at half maximum (FWHM) of resonant peak. The sensitivity of the SWGMRR could be expresses as [37] where Δn c is the refractive index change of the cladding solution, and Δλ res is the red-shifts of resonant wavelength. Fig. 3(a) shows the transmission spectrum of the designed sensor with a duty cycle of 0.6. The free spectrum range (FSR) is 13.3 nm. The sensitivities of the SWGRMR refractive index sensor with different duty cycles are illustrated in Fig. 3(b). Deionized water was used as the initial cladding. The electric field distribution diagrams of SWG waveguide under different duty cycles are shown in Fig. 3(c)-(e). The refractive index of the glucose solution is ranging from 1.333 to 1.343 with a changing step of 0.0025. By varying the refractive index of the surrounding liquid, the shifts of the resonance peaks at different refractive indices could be measured to derive the sensitivity of the SWG ring. When the duty cycle is decreased from f = 0.8 to f = 0.6, the overlap region between the analyte and the light becomes larger, resulting in a stronger light-matter interaction. That is to say it is an effective method to improve the sensitivity of the sensor by reducing the duty cycle of SWG waveguide. It can be predicted that reducing the duty cycle will further improve the sensitivity. However, the larger propagation loss is caused by small duty cycle, which leads to the reduction of Q factor and the deterioration of LOD. Consequently, the duty cycle is designed as 0.6 to get a trade-off between the sensitivity and LOD.
The SWG waveguide width is also a key parameter affecting the sensitivity. The sensitivity (the blue line) and the Q factor  (the red line) of the device under different widths are illustrated in Fig. 4. With the same SWG waveguide period and duty cycle, the waveguide width is optimized to simultaneously obtain a high sensitivity and a low LOD. With decreasing the waveguide width, the light limitation of the SWGRMR would be weaker, leading to a higher sensitivity and a lower Q factor. Hence the waveguide width W is chosen as 400 nm to balance the device sensitivity and LOD.
To investigate the relationship between the coupling gap G and the performance, the gaps are analyzed as follows.   shows the sensitivity (the blue line) and extinction ratio (ER) (the red line) under different gaps. With adjusting the gaps, the fluctuation range of the sensitivity could be neglected. On the contrary, when the gap G is set as 260 nm, the SWGRMR can realize the critical coupling and obtain the maximum ER, which is beneficial for the sensing measurement. Fig. 6 illustrates the Q factor of the SWGRMR under different racetrack lengths (i.e., L c = 5.25 μm, 5.5 μm, 5.75 μm, 6 μm, 6.25 μm, 6.5 μm, 6.75 μm). When L c is chosen as 6.0 μm, the Q factor could realize the maximum value. In this case, the corresponding resonant wavelength is 1542.29 nm.

III. SENSING SCHEMES AND RESULT
A. Single-SWGRMR Sensor Fig. 7 shows the initial transmission spectrum of the device in deionized water cladding. There are three resonance peaks (i.e.,1529.14 nm, 1542.29 nm, and 1555.73 nm). The ER of the peak at 1542.29 nm could realize 20 dB. As the Q factors corresponding to the three resonant peaks are 12190, 15918 and 10087 respectively, the resonant peak of 1542.29 nm (the red  dashed box) is chosen to verify the performance. As the effective refractive indices related to different wavelengths are not the same [29], the resonance FWHMs are different. According to the formula (1), the Q values corresponding to different wavelengths are different. The initial cladding structure was deionized water at 25°C. To explore the performance of the device in refractive index sensing, the cladding substance is selected as glucose solutions with different concentrations, whose refractive indexes at 25°C are shown in Table I. The glucose solution is convenient to prepare a solution with a low refractive index change step. Moreover, it has no corrosive effect on the device, which would not affect the experimental results. By adjusting the concentration from 0g/100ml to 8g/100ml, the refractive index of the solutions could be tuned from 1.333 to 1.343.
The LOD of the sensor can be calculated by [38] where λ res is the wavelength of resonance peak.  (1) and (2), the sensitivity and LOD of the device are 664 nm/RIU (as shown in Fig. 8(b)) and 1.43×10 -4 RIU, respectively. The three-dimensional finitedifference time-domain (3D-FDTD) method is used to verify the performance of the single ring sensor, and the difference compared with the MODE simulation results is acceptable, whose influence on the following sensor design incorporating with the Vernier effect is tolerable.
Moreover, the sensitivity in ref. [39] is very high, but our proposed sensor has some advantages. Firstly, the required fabrication precision of the subwavelength grating double slot waveguide resonator (GDSWGR) [39] is relatively high, as the two slot widths and the various pillar gaps are required to be 50 nm. Secondly, the maximum ER of the GDSWG is 9.4 dB and the operation wavelength is around 1700 nm. In contrast, the minimum feature size, ER and the operation wavelength of the propose sensor are 100 nm, 20 dB and around 1550 nm, respectively. The designed device structure does not have high requirements on the manufacturing process, which is required processing technology of 100 nm precision. Consequently, the proposed sensor could be fabricated on an SOI platform with fabrication methods compatible with CMOS foundry standards [40]. Furthermore, the proposed SWGRMR has a good manufacture tolerance on the sensing performance [41]. For instance, when the coupling gap of the sensing ring is changed around the optimum value of 30 nm, the sensitivity drops by at most 11%.

B. Cascaded Double-Microring Sensor
Although the sensitivity of the SWGRMR can be higher than 600 nm/RIU, the sensitivity of the single-microring-based refractive index sensor is difficult to exceed the order of 1500 nm/RIU. To solve the above problem, a new refractive index sensor is designed by a cascaded double-microring structure, including a sensing MRR (i.e., SWGRMR) and a reference MRR (a strip waveguide microring), as shown in Fig. 9. The reference ring is chosen as ordinary strip MRR to reduce the fabrication difficulty. The radius and the waveguide width are set as 5 μm and 400 nm, respectively. The coupling gap is designed as 160 nm to achieve a high ER and the racetrack length is chosen as 3 μm to obtain required FSRs and resonant wavelengths. As discussed in part II, the radius, the waveguide width, the grating period, the duty cycle, the coupling gap and the racetrack length of the sensing ring are chosen as 8 μm, 400 nm, 250 nm, 0.6, 260 nm and 6 μm, respectively. The taper length between the silicon waveguide and SWG waveguide is 20 μm. The output waveguide had better to be SWG waveguide to reduce the device loss. For the double-ring device, the FSR of the Vernier effect peaks is 179.89 nm.
During the verification process, the SWGRMR is exposed to a solution sample to detect the change of refractive index in the sensing window (i.e., the light blue box). The reference MRR can provide a stable comb transmission spectrum for the sensing MRR to achieve better sensing performance [32].
To obtain Vernier effect, the reference ring needs to be covered by the cladding and only the sensing ring is in the sensing window. If the reference ring and the sensing ring are simultaneously immersed in the liquid, the resonance peaks of the two rings would be both shifted. In this case, it is difficult to precisely Theoretically, the sensitivity of a microring resonator can be defined as here, λ res is the central wavelength and n eff is the refractive index of the waveguide. In addition, when the cladding index changes, the n eff of the SWG waveguide would be affected, which can be expressed as [34] n ef f = n ef f 0 + Δn ef f = n ef f 0 + Δn c ∂n ef f ∂n c (5) where Δn eff is the change of n eff , due to the cladding index change Δn c , and n eff0 is the initial value at the 25°C. The free spectrum ranges of the sensing MRR (FSR S ) and the reference MRR (FSR R ) are designed to be approximate (FSR S < FSR R ). As shown in Fig. 10(a) and 10(b), when Δn c = 0, the resonant wavelength λ S(i) of the sensing MRR overlaps with the resonant wavelength λ R(i) of the reference MRR. Hence the transmission spectrum of the cascaded double-microring exhibits one peak at λS (Dr(k)) , shown as the green line in Fig. 10(c). When Δn c is adjusted to 0.0025, the resonant wavelength of the sensing MRR would shift Δλ S , which makes the resonant wavelength λ S(i+1) of the sensing MRR overlap with the resonant wavelength λ R(j+1) of the reference MRR. Consequently, the spectrum overlapped peak of the cascaded-microring moves from λ Dr(k) to λ Dr(k+1) . Therefore, when Δn c changes, the wavelength spacing between the two overlapped peaks of the cascaded microring could be denoted by The relationship between the changes of the cladding refractive index and the waveguide effective refractive index can be expressed as Then combining formulas (3)- (6), the whole device sensitivity S D r could be represented by Consequently, the sensitivity of the whole device could be amplified tens of times based on the Vernier effect of cascaded microrings.
The output transmission spectra of the sensor in glucose solutions with different concentrations (n c : 1.333∼1.3405) are shown in Fig. 11. Δn c = 0 corresponds to deionized water (the refractive index is 1.333 at 25°C), and the initial wavelength and Q factor of the overlapped peak are 1494.46 nm and 12500, respectively (the blue line). When the concentrations of the glucose solutions are set as 1.3355 (Δn c = 0.0025), 1.338 (Δn c = 0.005), and 1.3405 (Δn c = 0.0075), the corresponding shifted peak wavelengths are 1511.78 nm (the red line), 1529.41 nm (the cyan line), and 1547.53 nm (the green line), respectively. Consequently, the sensitivity and the LOD of the sensor are 7061 nm/RIU and 1.74 × 10 −5 RIU, respectively, which has distinguished advantages for high-resolution environmental monitoring and biosensor. Generally, the temperature change around the room temperature is relatively weak, thus the induced resonance red-shifts are small. Capitalizing the Vernier effect, the temperature influence on the sensing measurement could be significantly reduced. Moreover, the device temperature could be precisely controlled by utilizing a thermo electric cooler.

IV. CONCLUSION
In summary, we designed and verified an SWG-based refractive index sensor with ultra-high sensitivity and low detection limit. The parameters of the SWGRMR are analyzed and optimized to improve the sensing performance. Consequently, capitalizing the Vernier effect of the cascaded microrings, an ultra-high sensitivity of 7061 nm/RIU and a low LOD of 1.74 × 10 −5 RIU could be simultaneously achieved. The key innovation in this manuscript is combining the designed compact SWGRMR and the Vernier effect, which could dramatically improve the sensitivity from hundreds of nm/RIU to thousands of nm/RIU. To the best of our knowledge, it is the highest sensitivity among the silicon-MRR-based schemes with such a small size, which is competent to be applied in high-resolution environmental monitoring and biosensor directions.