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Abstract
We present the design, fabrication, and characterization of cascaded silicon-on-insulator photonic crystal microring resonators (PhCMRRs) for dual-parameter sensing based on a multiple resonances multiple modes (MRMM) technique. Benefitting from the slow-light effect, the engineered PhCMRRs exhibit unique optical field distributions with different sensitivities via the excitation of dielectric and air modes. The multiple resonances of two distinct modes offer new possibilities for enriching the sensing receptors with additional information about environmental changes while preserving all essential properties of traditional microring resonator based sensors. As a proof of concept, we demonstrate the feasibility of extracting humidity and temperature responses simultaneously with a single spectrum measurement by employing polymethyl methacrylate as the hydrophilic coating, obtaining a relative humidity (RH) sensitivity of 3.36 pm/%RH, 5.57 pm/%RH and a temperature sensitivity of 85.9 pm/°C, 67.1 pm/°C for selected dielectric mode and air mode, respectively. Moreover, the MRMM enriched data further forges the capability to perform mutual cancellation of the measurement error, which improves the sensing performance reflected by the coefficient of determination (R2-value), calculated as 0.97 and 0.99 for RH and temperature sensing results, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The demands for detection and analysis of physical, chemical, and biological parameters have been increasing dramatically in the fields of environmental monitoring, industrial processing, and human health applications. Throughout the past decade, there has been a burst of interest in photonic integrated sensors due to the inherited benefits of optics which are superior to their electrical counterparts, such as large bandwidth, electromagnetic interference (EMI) immunity, and remote sensing capability [1–5]. The CMOS-compatible nature of silicon photonics has further helped miniaturize conventional fiber-based optical sensors and paved the way towards achieving compact and mechanically robust optical sensors. In particular, the attractive use of microresonant cavities [1–4] has demonstrated an unparalleled ability to measure various environmental parameters on a nanoscale level. Consuming significantly less footprint, this has fueled opportunities to measure more than one physico-chemical parameter simultaneously and independently. In systems where cross-parameter sensing is unavoidable, multi-parameter sensing has become a vital requirement as it provides more comprehensive information with improved cross-sensitivity detection.
To achieve multi-parameter sensing, state-of-the-art photonic integrated sensors have implemented distinct resonant modes such as different order modes, dielectric and air modes, and transverse electric (TE) and transverse magnetic (TM) modes, to independently measure spectrum responses in either optical [6–16] or electrical domain [17], where both the optical waveguide structures and the nature of the sensor coating layer play roles in determining the efficacy of the sensor to interact with the environmental perturbations. Sensors based on microring resonator (MRR) [7,15,16], microdisk [6,17], planar photonic crystal (PhC) [8–10], and PhC nanobeam [11–14] have been presented for sensing different parameters, such as gas concentration [7], temperature [6,8–17], humidity [16,17], refractive index (RI) [6,10–15], pressure [10], and magnetic field [9]. For example, in [11], dielectric and air modes from cascaded PhC nanobeam cavities are used in the simultaneous measurement of RI and temperature, obtaining a RI sensitivity of 254.6 nm/RIU (refractive index unit) and a temperature sensitivity of 30.1 pm/°C for air-mode cavity, while a RI sensitivity of 105.5 nm/RIU and a temperature sensitivity of 56.4 pm/°C for dielectric-mode cavity. Alternatively, utilizing a dual-polarization MRR configuration [16], simultaneous sensing has been demonstrated with a temperature sensitivity of 69.0 pm/°C and 30.6 pm/°C for TE and TM polarization, respectively. By using the hydrophilic polyvinyl alcohol (PVA) layer as top cladding, the sensor shows a maximum relative humidity (RH) sensitivity of 97.9 pm/%RH for TE mode and 325.1 pm/%RH for TM mode, in the measuring range of 45%RH to 96.5%RH. Whilst these methods present a wide availability of modes or resonances for spectral sensing, only a small range of optical frequencies have been utilized. The largely untapped spectrums can in fact be re-purposed for the detection and compensation of unwanted interferences. The increase in the number of modes or resonances allows extra sensing information to be encoded, thereby enriching the optical spectrum analysis to discriminate abnormalities in detected signals corrupted by environmental perturbations [18,19].
Recently, hybrid devices such as photonic crystal microring resonators (PhCMRRs), which integrate the periodic PhC lattice along the circumference of a standard MRR, have demonstrated the promising use of dielectric mode [20,21] or air mode [22] with enhanced light-matter interaction for detecting small environmental changes. Offering the unique ability to excite both dielectric and air modes with different sensitivities within the same cavity, this allows the simultaneous sensing of different parameters while preserving the multi-resonance properties of a conventional MRR sensor. More importantly, the PhCMRR gives the flexibility to engineer the frequency locations of the multi-resonance transmission spectrum close to the arbitrary photonic bandgap (PBG) [23]. However, the PBG is typically very large (>100 nm) in the near-infrared region. This thus requires optical measurement equipment such as optical spectrum analyzers (OSAs) and tunable lasers with a wide wavelength range, which is not always practical and increases the cost and complexity [24]. Partial etching of the periodical holes was demonstrated to successfully compress the PBG using a single PhC cavity device, but this sacrifices the slow-light effect and decreases the sensitivities [25].
In this paper, we propose a configuration to overcome the large PBG limitation by employing a pair of engineered PhCMRRs based on silicon-on-insulator (SOI) for dual-parameter sensing. The proposed structure offers a new error-correction method that capitalizes on the presence of different dielectric and air mode profiles at multiple resonances as a mitigation strategy to minimize detection errors caused by external interferences. The mode characteristics and transmission responses of the two distinct PhCMRRs, which combine both whisper-gallery-modes (WGMs) and slow-light effects, were simulated by the three-dimensional finite element method (3D-FEM). The device was fabricated with optimized sensing performance in terms of large sensitivity contrast, high quality (Q) factor, and large extinction ratio (ER). As a proof of concept, simultaneous detection of RH and temperature was carried out with a hydrophilic polymethyl methacrylate (PMMA) coating. Both parameter changes can be obtained by measuring the resonant wavelength shifts at a single time with a RH sensitivity of 3.36 pm/%RH, 5.57 pm/%RH and a temperature sensitivity of 85.9 pm/°C, 67.1 pm/°C for the selected dielectric mode and air mode, respectively. Furthermore, error reduction is achieved by the presented calibration method to effectively utilize the multiple resonances for interference compensation, proved by the enhanced coefficient of determination (${R^2}$-value).
2. Design and principle
2.1 PBG design
Figure 1(a) shows the schematic diagram and geometrical parameters of the proposed dual-parameter sensing configuration consisting of two SOI PhCMRRs to overcome the large PBG limitation in a single cavity. The PBG, which defines the frequency or wavelength spacing between the fundamental dielectric and air modes, can be manipulated via geometrical parameters, such as the air hole radius (${r_{hole}}$), the lattice constant ($a$), and the ring waveguide width (${w_{ring}}$), to achieve closely spaced multiple dielectric and air modes contributed from PhCMRR1 and PhCMRR2, respectively. Other essential parameters related to the spectral responses, such as the free spectral range (FSR) and ER, include the PhCMRR radius (${r_{ring}}$), coupling bus waveguide width (${w_{bus}}$), and edge-to-edge coupling gap ($g$). Figure 1(b) illustrates the cross-sectional structure of the bus waveguide region of this sensing device. A layer of PMMA coating with 500 nm thickness is chosen to prevent nonlinear RI change induced by swelling or shrinking of the film after absorbing or releasing the moisture [26]. The usage of PMMA enables a fast response with sub-second scale rising and falling times [27]. The geometry-dependent PBG is investigated using 3D-FEM (COMSOL Multiphysics) and illustrated in Fig. 2 for a typical range of optical measurement frequencies from 184.5 THz to 195.9 THz, covering the whole C and L spectral bands (i.e., 1530 nm to 1625 nm). For different lattice constants, the fundamental dielectric mode ($F{M_D}$) and air mode ($F{M_A}$) frequencies can be tailored by various ring waveguide widths and air hole radii, compressing the PBG of cascaded PhCMRRs within the desired frequency window by a range of geometries. Meanwhile, to quantitatively analyze the interaction of light with surrounding materials, the fractions of the optical field in PMMA cladding (${f_{clad}}$) [28] are calculated and shown in Fig. 3. Whilst the selection of lattice constant has negligible impact on the optical field distribution, choosing either larger air hole radii or smaller ring waveguide widths contributes to higher ${f_{clad}}$, where the stronger optical evanescent wave penetrates into the cladding and leads to potentially higher environmental sensitivity.
Fig. 1. (a) Schematic diagram of the presented dual-parameter sensor based on cascaded PhCMRRs in a top view, and the geometrical parameters of the PhCMRR structure in a zoom-in view. (b) Cross-section of the waveguide region of the sensing device.
Fig. 2. Frequencies of fundamental dielectric and air modes at different ring waveguide widths versus different air holes radii when lattice constants are (a) 350 nm and (b) 410 nm.
Fig. 3. Optical field fractions in PMMA cladding at different ring waveguide widths versus different air hole radii for fundamental dielectric and air modes, when lattice constants are (a) 350 nm and (b) 410 nm.
To allow high-performance interrogation of different modes within a measurable spectral range, the geometrical parameters of the cascaded PhCMRRs are optimized. For instance, to achieve better sensing range and resolution, the difference between the ${f_{clad}}$ of dielectric and air modes needs to be maximized to provide large sensitivity contrast towards small measurand changes. Thanks to the inherent resonating attributes, each mode also contains multiple resonances, which form the basis of the interference compensation strategy. As the number of resonances showing enhanced group index increases with smaller lattice constants [29], the slow-light enhanced aperiodic FSR and Q factor [23] will enrich the spectrum with more resonances available for mitigating the detecting errors. Thus, relatively small lattice constants within the simulation range are selected as 350 nm for PhCMRR1 and 380 nm for PhCMRR2 to harness the benefits generated from the slow-light effect. Considering the fabrication tolerance [30], the air hole radii are chosen to be 95 nm and 105 nm for PhCMRR1 and PhCMRR2, respectively. The ring waveguide widths are chosen as 460 nm for PhCMRR1 and 690 nm for PhCMRR2, which result in the $F{M_D}$ from PhCMRR1 at 191.3 THz (1567.1 nm) with ${f_{clad}}$=35.6% and the $F{M_A}$ from PhCMRR2 at 194.4 THz (1542.1 nm) with ${f_{clad}}$=52.2%. Both radii of the PhCMRRs are set to around 10 µm to maintain a small device dimension of about 50 µm×20 µm with negligible bending loss, and the corresponding number of identical holes spaced periodically in each PhCMRR are determined to be 160 and 170, respectively. The band diagram of the two PhCMRRs with finalized geometries is displayed in Fig. 4(a), where multiple dielectric and air modes [23] contributed from PhCMRR1 and PhCMRR2, respectively, are located within the C and L bands (shade area) that can be easily covered by standard OSA instruments. The corresponding normalized optical field profiles of PhC unit cells for both modes [22] are depicted in Fig. 4(b) with obviously distinct field distributions. To ensure an efficient coupling between the bus waveguide and the PhCMRRs, the phase match ratio, defined as the $ka/\pi $ by wavenumber k, is used to evaluate the phase match condition, for which the unity value means the perfect phase match that leads to large ER preferred by sensing applications [31]. However, smaller bus waveguide width may bring extra optical leakage loss due to the poor confinement [32]. Figure 4(c) shows the simulated phase match ratio and optical confinement factor in response to ${w_{bus}}$. Considering the trade-off between ER and mode confinement, the bus waveguide widths are selected as 440 nm and 390 nm for PhCMRR1 and PhCMRR2, respectively. All the critical parameters of the cascaded PhCMRRs are summarized and listed in Table 1.
Fig. 4. (a) Band diagram of each PhCMRR with selected structural parameters. A (A’), B (B’), and C (C’) denote the light line, air band, and dielectric band for PhCMRR1 (PhCMRR2). The wavevector is shown in a normalized unit of $2\pi /a$. (b) Simulated optical field profiles of PhC unit cells for corresponding modes. (c) Phase match ratio (solid lines) and optical confinement factor (dashed line) versus bus waveguide width.
Table 1. The geometry parameters of dielectric modes (PhCMRR1) and air modes (PhCMRR2) design
2.2 Sensitivity
As a proof of concept, the dual-parametric sensing performance of the presented device is demonstrated by detecting the simultaneous changes in humidity and temperature. The resonant wavelength shifts of a group of dielectric ($\Delta {\lambda _D}$) and air ($\Delta {\lambda _A}$) modes due to relative humidity change ($\mathrm{\Delta }RH$) and temperature change ($\mathrm{\Delta }T$) can be described as
Fig. 5. Simulated normalized optical field distributions of (a) dielectric mode in PhCMRR1 and (b) air mode in PhCMRR2. Simulated resonant wavelength shifts (circles) for each PhCMRR at (c) 25°C with different RH levels and at (d) 45%RH with different ambient temperature levels. Solid lines are the slopes of the simulated resonance shifts.
2.3 MRMM technique
The benefit of preserving the slow-light effect, which taps into the intrinsic advantage of having more multiple resonances near the PBG, allows the proposed system to incorporate a new calibration strategy capable of correcting for any external disturbances during the sensing process. Since the multiple resonances of both dielectric and air modes carry additional information about the changes introduced to the system, the matrix ${{\boldsymbol S}_{{\boldsymbol {RH}}\& {\boldsymbol T}}}$ in Eq. (1) for a single group of modes is extended to consider the scenario of multiple resonances in the form of a combined matrix as follows
To illustrate the advantage brought by the optical spectrum containing multiple resonances multiple modes (MRMM), the change in the sensitivity ratio is represented by
where ${r_{RH,n}}$ (${r_{T,n}}$) defines the humidity (temperature) sensitivity ratio using the MRMM technique. Using Eqs. (3), (4), the improvement of sensing performance can be described asWe analyze the implementation of the MRMM technique by evaluating the different combinations of possible resonance group selections. For simplicity, we assume that there are no distinct dielectric-mode or air-mode resonances, which are significantly different from the others in sensitivities.
Case 1: Using only air-mode resonances, the modified sensitivity ratio is simplified as ${r_{RH,n}} = {r_{RH,n - 1}}n/({n - 1} )$ and ${r_{T,n}} = {r_{T,n - 1}}({n - 1} )/n$. The total error reductions of humidity and temperature can be respectively determined as
Case 2: Using only dielectric-mode resonances, where ${r_{RH,n}} = {r_{RH,n - 1}}({n - 1} )/n$ and ${r_{T,n}} = {r_{T,n - 1}}n/(n - 1$), the total error reductions are derived as Case 3: Using both air-mode and dielectric-mode resonances, where ${r_{RH,n}} = {r_{RH,n - 1}}$ and ${r_{T,n}} = {r_{T,n - 1}}$, the total error reductions are given byFigures 6(a) and 6(b) show the AEI capability using the MRMM technique by normalizing the humidity and temperature errors calculated from Eqs. (6)–(8) with the reference values of ${\alpha _{RH,1}}$ and ${\alpha _{T,1}}$. The sensitivity ratios of 1.97 and 1.86 for ${r_{RH,1}}$ and ${r_{T,1}}$ as calculated in Section 2.2 are used here. It can be observed that all three cases show progressive error reduction when n increases. This indicates that the MRMM technique intrinsically realizes an error correction mechanism to reduce the detection error and improve the sensing accuracy without the need for external calibration. As the number n exceeds 4, the error reduction process gradually slows down in all three cases. It is noticed that for both Case 1 (circle) and Case 2 (triangular), there is an apparent trade-off in the error reduction between ${\varGamma _{RH}}$ and ${\varGamma _\textrm{T}}$, while Case 3 (square) exhibits a continuous and simultaneous error reduction for both detection parameters regardless of the initial sensitivity ratio. Thus, given the same number n, the incorporation of both mode profiles is more effective in achieving AEI. In a linear regression analysis, ${R^2}$-value evaluates the proportion of variance for a dependent variable [35], where the larger ${\varGamma _{RH}}$ and ${\varGamma _T}$ provided by Case 3 can improve the ${R^2}$-value closest to the best condition (i.e., ${R^2}$=1) by dramatically suppressing the fluctuations of sensing results.
Fig. 6. Simulated normalized (a) humidity and (b) temperature errors with the MRMM technique for Case 1 (circle), Case 2 (triangular), Case 3 (square), assuming the combined resonances have the same sensitivities as the origins.
3. Fabrication and characterization
The proposed dual-parameter sensor was fabricated using an SOI wafer consisting of a 220 nm thick Si waveguide (${n_{si}}$=3.48) on a 2 µm SiO2 insulator layer (${n_{Si{O_2}}}$=1.44) and coated with a layer of hydrophilic PMMA (${n_{PMMA}}$=1.48). The electron-beam lithography was used to define the device patterns, which were then transferred to the silicon waveguides via inductively coupled plasma reactive-ion-etching. In order to achieve efficient coupling between the optical fiber and the chip, grating couplers were also fabricated at the ends of the bus waveguide. Figure 7 shows the scanning electron microscope (SEM) image of the fabricated dual-parameter sensor with inset pictures as the zoom-in view of the two PhCMRR cavities.
Figure 8(a) shows the measurement setup for humidity and temperature sensing. The humidity was controlled in a homemade chamber with two inputs for dry and moist gas, where the RH value can be altered from 10% to 90% [2]. A commercially available electrical hygrometer (IC-Center 317) was placed in the chamber to act as a reference. Meanwhile, the chip temperature was varied between 15°C to 35°C by a temperature controller module (Newport 325). A variable hot plate can be used to provide a broader temperature range [29,36]. To characterize the fabricated dual-parameter sensor, a tunable laser (Keysight, 81960a) was used as the light source in our measurement with TE-polarized incident light to the chip via the polarization controller (PC). The output optical signal from the chip was collected by the optical power meter (Keysight, N7744A), which is synchronized with the tunable laser to measure the optical wavelength spectrum. Figure 8(b) shows the transmission spectrum of the fabricated device measured at 25°C and 46.8%RH, indicating multiple resonant dips in the wavelength range from 1545 to 1585 nm. The fabricated cascaded PhCMRRs successfully achieve both dielectric and air mode resonances in C and L bands. Thanks to the distinct optical field distributions brought by dielectric and air modes, the resonant air modes have a larger scattering loss induced by the sidewall surface roughness [22], thus exhibiting considerably lower Q factors than the dielectric-mode resonances. The normal values of the loaded Q factors of the dielectric mode are around 15,000 with the highest value as 23,200 at the resonance of 1577.9 nm, while the highest Q factor of the air mode was only around 3,600. It is also noted that the variation of the Q factor and ER in different resonances arises from the wavelength-dependent coupling between the linear dispersive straight bus waveguide and the highly dispersive PhC cells [31].
Fig. 8. (a) Experimental setup for the optical transmission spectra measurement at different humidity and temperature levels. (b) Normalized transmission spectrum of the fabricated sensor showing both dielectric and air mode resonances measured at room environment. Circle and asterisk are used to label the dielectric and air modes, respectively. Insets: Comparison between the measured (cross) and simulated (solid line) dielectric and air mode resonances. PC: polarization controller; TEC: thermoelectric cooler.
4. Experiment and results
Before performing the dual-parameter sensing, the individual responses of the presented sensor to humidity and temperature are first investigated. This helps determine the corresponding sensitivities of the resonances in both mode sets, which will be used to apply the error correction mechanism based on the presented MRMM approach. As an example, we chose the dielectric mode at the wavelength of 1575.7 nm and the air mode at the wavelength of 1547.9 nm, as displayed in Fig. 8(b), to show a more detailed analysis by calculating the corresponding ${S_{RH,D}}(1 )$ and ${S_{T,D}}(1 )$, ${S_{RH,A}}(1 )$ and ${S_{T,A}}(1 )$ based on Eq. (2), while keeping other resonances as candidates for the MRMM technique. The measured dielectric and air mode resonances have a good agreement with the simulations obtained via the coupled mode space approach [37]. The offset in the transmission region is primarily caused by the ripple of the vertical grating couplers (VGCs), which can be minimized by reducing the back reflection [38].
4.1 Humidity sensing
The ${S_{RH,D}}(1 )$ and ${S_{RH,A}}(1 )$ were obtained by varying the humidity levels while maintaining the device temperature at 25°C during the measurement. Figures 9(a) and 9(b) show the measured transmission spectra for the selected group of dielectric and air mode resonances when the sensor was placed into the chamber. It can be found that both resonances shift towards longer wavelengths as the ambient RH level increases, which agrees with the theory that the PMMA coating absorbs water molecules from the surrounding environment when the RH level increases, leading to a slight rise in the effective index of the mode and redshift of the resonant wavelength [26]. Moreover, the RH level was also varied in descending order, for which the relationships between RH and resonant wavelength shifts of the dielectric and air modes were extracted and compared with the ascending order measurement, as plotted in Figs. 9(c) and 9(d), respectively. Both ascending and descending order results signify that the total wavelength shift of 0.45 nm for the air mode is much larger than the total wavelength shift of 0.27 nm for the dielectric mode under the same range of humidity variations, which can be explained by the discussion in Section 2.2 that the larger field distribution of air mode in the cladding region causes stronger evanescent field interaction with PMMA-induced RI change. A maximum hysteresis error of 6.2% was observed, which can be reduced by optimizing the coating material [39]. To obtain the sensitivity of humidity sensing performance, further measurements were carried out and the measured wavelength shifts of the two different modes versus RH (%) are linearly fitted, as shown in Figs. 9(e) and 9(f). The two repeated measurement results show good consistency for both dielectric and air mode resonances. 3.36 pm/%RH and 5.57 pm/%RH sensitivity for dielectric-mode and air-mode resonances, respectively, are obtained. Further improvement in humidity sensing can be achieved by increasing the RH sensitivity of the device, which is implemented by replacing the coating material with a larger response to humidity change, such as nafion [40], agarose [41], and PVA [42].
4.2 Temperature sensing
Next, to extract the temperature sensitivities of the two different mode resonances, ${S_{T,D}}(1 )$ and ${S_{T,A}}(1 )$, the chip temperature was varied via the TEC. Figures 10(a) and 10(b) show the measured spectra, indicating both resonant modes shift towards longer wavelengths with the increase in temperature due to the equivalent increase in effective index dominated by the positive TOC of silicon. The device was subjected to a descending temperature gradient, where the resonant wavelength variations under both ascending and descending temperature changes were extracted and respectively shown in Figs. 10(c) and 10(d) for comparison. Regardless of the ascending or descending order of temperature variations, similar trends prove that a total resonant wavelength shift of 0.66 nm for the dielectric mode is larger than the 0.52 nm wavelength shift recorded by the air mode. It can be understood that the dielectric mode is more sensitive to the changes in temperature than the air mode as the majority of the optical field is confined in the silicon dielectric core. The temperature sensing performance was also investigated under the same surrounding environmental conditions. Figures 10(e) and 10(f) demonstrate the repeated measurement results where the dielectric-mode resonance shows good agreement in both attempts and a sensitivity of 85.9 pm/°C, while the air-mode resonance also displays consistent performance with a sensitivity of 67.1 pm/°C.
Fig. 9. Measured normalized transmission spectra of selected (a) PhCMRR1 dielectric-mode resonance and (b) PhCMRR2 air-mode resonance at an increased RH level and 25°C. Measured resonant wavelength shifts versus RH change in ascending (solid circle) or descending (solid square) order at 25°C for the (c) dielectric mode and (d) air mode. 1st (solid circle), 2nd (solid square) measurement and slope of experimental data (solid line) versus RH change at 25°C for (e) dielectric-mode and (f) air-mode resonance shifts.
Fig. 10. Measured normalized transmission spectra of selected (a) PhCMRR1 dielectric-mode resonance and (b) PhCMRR2 air-mode resonance at an increased temperature and 45%RH. Measured resonant wavelength shifts versus temperature change in ascending (solid circle) or descending (solid square) order at 45%RH for the (c) dielectric mode and (d) air mode. 1st (solid circle), 2nd (solid square) measurement and slope of experimental data (solid line) versus temperature change at 45%RH for (e) dielectric-mode and (f) air-mode resonance shifts.
4.3 Simultaneous sensing
Next, we experimentally demonstrate the feasibility of simultaneous detection for RH and temperature variations with the proposed device and compare the sensing results with and without the MRMM technique. ${R^2}$ statistics, which accounts for all sensing deviations related to the measurand reference levels [35], is used to quantitatively evaluate the sensing errors. By using one dielectric-mode resonance from PhCMRR1 and one air-mode resonance from PhCMRR2, the obtained ${{\boldsymbol S}_{{\boldsymbol {RH}}\& {\boldsymbol T}}}$ is given by
Correspondingly, the wavelength shifts of these resonances due to relative humidity change ($\mathrm{\Delta }RH$) and temperature change ($\mathrm{\Delta }T$) can be calculated based on Eq. (1), and the results are shown in Fig. 11(a). It can be seen that all the measured points fall within the vicinity of the predicted surface planes for each PhCMRR, proving the effectiveness of the model. Moreover, dual-parameter sensing can be obtained based on solving Eq. (1), and the sensing results are shown in Figs. 11(b) and 11(c), indicating a good agreement between the measurements and reference levels in response to humidity and temperature changes. This proves the feasibility of our sensor for the simultaneous measurement of dual parameters. Note the ${R^2}$-values of humidity and temperature sensings are 0.8593 and 0.973, respectively, primarily caused by the difference in Q factors of dielectric and air mode resonances.
Fig. 11. (a) Measured (solid circles) and predicted resonant wavelength shifts (solod lines forming transparent planes) without the MRMM technique (n=1) for a single group of dielectric (blue) and air (red) mode resonances under different humidity and temperature conditions. Measured sensing results (vacant circles) without the MRMM technique (n=1) for different (b) humidity (five points at the same level) and (c) temperature (four points at the same level). Solid lines are for reference to reflect the estimated measurand.
By leveraging the MRMM approach, the effect on combined resonant wavelength shifts and mutually calibrated simultaneous sensing results are further analyzed to verify the error correction ability of the presented system. As a proof of concept demonstration, two dielectric-mode resonances at wavelengths of 1575.71 nm and 1574.80 nm from PhCMRR1 and two air-mode resonances at wavelengths of 1547.87 nm and 1580.80 nm from PhCMRR2 measured at the room environment were used in the MRMM sensing. When the MRMM technique based on Case 3 at $n$ = 2 is applied, the relationship between resonance shifts and the temperature and RH changes is given by
Figure 12(a) shows the enhanced resonant wavelength shifts for both measurement and prediction with the MRMM technique enabled. The higher slopes indicate an improved ability to resolve the small changes in simultaneous sensing due to the almost doubled sensitivities for both measurands in comparison with the results displayed in Fig. 11(a). The sensing results with the MRMM technique are extracted in a similar way to Figs. 11(b) and 11(c), shown in Figs. 12(b) and 12(c) as a comparison. The increment in ${R^2}$-values (i.e., 0.9699 for humidity and 0.9877 for temperature) proves the fewer variations between measured and reference values. This demonstrates that both sensing errors can be dramatically compensated by the MRMM technique, which improves the accuracy of the overall sensing system. Moreover, we also obtained the ${R^2}$ statistics of the MRMM technique in other cases at $n$=2. The results are 0.9622 (Case 1) and 0.8842 (Case 2) for RH sensing and 0.9849 (Case 1) and 0.9829 (Case 2) for temperature sensing, which are lower than the ${R^2}$ statistics of MRMM technique based on Case 3. Note that the ${R^2}$ statistics with the MRMM technique in any cases are larger than that without using the MRMM technique, which firmly verifies the enhancement of sensing performance brought by adopting multiple resonances in optical sensing. The concept of the proposed MRMM technique works to complement the operation of the presented optical sensor scheme by demonstrating its role in reducing the measurement error and improving the measurement accuracy of the system. As such, this concept can also be generalized and extended to other existing optical sensors based on resonant structures on any platform, thus providing a universal technique for sensitivity enhancement and correction of measurement error.
Fig. 12. (a) Measured (solid circles) and predicted resonant wavelength shifts (solid lines forming transparent planes) with the MRMM technique (Case 3, n=2) for multiple groups of dielectric (blue) and air (red) mode resonances under different humidity and temperature conditions. Measured sensing results (vacant circle) with the MRMM technique (Case 3, n=2) for different (b) humidity (five points at the same level) and (c) temperature (four points at the same level). Solid lines are for reference to reflect the estimated measurand.
5. Conclusion
In summary, we have proposed and demonstrated dual-parameter sensing based on an engineered pair of cascaded PhCMRRs, where the usage of different dielectric and air mode profiles at multiple resonances as a mitigation strategy reduces the detection errors. Experimental demonstration of SOI PhCMRRs shows the feasibility of simultaneously sensing humidity and temperature responses with a single spectrum measurement by employing PMMA coating. The dual PhCMRRs enable the measurement of changes in both parameters by monitoring the resonant wavelength shifts at a single time. Moreover, the MRMM technique is capable of efficiently compensating for external interferences and reducing detection errors. With the advantages of distinct sensitivities, compatibility with existing platforms for dense integration, and capability to perform mutual calibration for error correction, the structure has excellent potential to be employed for large-scale on-chip multiparametric sensing applications.
Funding
Department of Defence, Australian Government; Australian Research Council (Discovery Project).
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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