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Abstract
We propose a new type of self-referencing and multiplexed refractive index (RI) sensor based on a compound optical microresonator structure consisting of Fabry-Pérot (FP) resonators coupled with microring resonators. The transmission spectra shows resonant features that are superimposed on a background defined by FP oscillations. The resonances have asymmetric Fano-like non-Lorentzian shapes, which are used as sensing peaks, while the FP oscillations are used as reference peaks for internal self-referencing. The sensing peaks shift linearly with the increased RI of the cladding in the microring resonator, while FP peaks stay constant. When the temperature is increased, both the FP peaks and the Fano resonances shift linearly at the same rate, which eliminates the temperature effect on RI measurements. We theoretically analyzed that the two-mirror FP resonator coupled with a single microring resonator and optimized its sensing performance through finite-difference time-domain simulations. A sensitivity value of 220 nm/RIU and a maximum figure of merit of 4400 RIU-1 were achieved. We also proposed two possible multiplexing schemes consisting of two-mirror and three-mirror FP resonators coupled with two microring resonators of different radii. The proposed sensor concept is simple, easy-to-fabricate, self-calibrating and can be used for simultaneous measurements of different samples.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical refractive index (RI) sensors are becoming promising tools in bio-sensing, environmental monitoring and medical diagnostics [1–5]. For their wider deployment, the future lab-on-a-chip RI sensors would have multi-channel operation, low-cost production and an internal calibration mechanism. Integrated-optical RI sensors are in particular very attractive by being compact, low-cost and rugged, which are also partially addressing above-mentioned requirements. Their small footprint enables multiplex array format, which not only improves the sensitivity of the detection, but also allows the simultaneous detection of an array of samples using the same sensor chip. Several integrated-optical RI sensing schemes have been investigated so far, including Mach-Zehnder interferometer configurations [5,6], microcavity resonators [7–12] and subwavelength grating waveguides [13,14]. Among them, microcavity resonators have the advantage of high quality factors and small mode volumes. However, optical sensors are in general prone to adverse effects, and their detection limit and sensitivity are limited by the environmental noise caused by temperature fluctuations and variations in the bulk refractive index of the sample. Different techniques have been proposed and implemented to reduce the effect of above-mentioned noise sources [15–21]. However, most of them require advanced manufacturing technologies, which would reduce their reproducibility and mass production potential. On the other hand, there are only a few examples in the literature that demonstrated the multiplexed sensing operation for integrated-optical sensors [22–24].
In this paper, we propose a new type of self-referencing and multiplexed integrated-optical RI sensor that is comprised of Fabry-Pérot (FP) microcavity resonators evanescently coupled with microring resonators. An optical microring resonator is a cavity that is known to be an excellent transducer for optical sensing due to its interferometric nature [11]. On the other hand, FP resonators are simple to form on a microchip by using the end-facet reflections [25] or an offset waveguide [26]. A big advantage of coupled cavities is the generation of asymmetric Fano-like resonances, due to the complex interference effect. The sharp slope in Fano resonance provides more sensitive detection of small changes in resonance. Here, we form the on-chip FP resonator by using Sagnac loop mirrors, which makes the resonator design more flexible and easy to optimize in contrast to using end-facet reflections. Figure 1 shows the schematic of the two-mirror based compound resonator. The transmission spectra of the proposed structure consist of Fano resonances that are superimposed on a background defined by the FP oscillations. When the refractive index of the cladding layer of the microring resonator is increased, the Fano resonances shift linearly while FP oscillations stay unchanged, which are then used as the reference peaks for the self-referencing operation. We theoretically analyzed this compound resonator structure and through 2.5D variational finite-difference time-domain (varFDTD) simulations we optimized the sensitivity of the RI sensor. For the two-mirror FP cavity resonator coupled to a single microring resonator, we achieved a sensitivity value of S = 220 nm/RIU and a maximum figure of merit value (FOM = S/FWHM, where FWHM is the full-width at half maximum of the Fano resonance) of 4400 RIU-1. It is possible to multiplex several sensors by adding more microring resonators of different radii to the sensor layout. Two possible multiplexing schemes will be discussed in this work. The proposed RI sensor concept is simple, easy-to-fabricate, multiplexed and free of environmental effects, which holds great promise for medical and environmental applications.
Fig. 1. Schematic of the compound resonator consisting of a microring resonator and a Fabry-Pérot resonator formed using two Sagnac loop mirrors. Definition of design parameters: t is the waveguide thickness, w is the waveguide width, r0 is the radius of the loop mirror, g is the gap and Lc is the length of the directional coupler, respectively, r1 is the radius of the microring resonator, and g1 is the gap between the straight waveguide and the microring, Ls is the length of the straight waveguide between Sagnac loop mirrors.
2. Device design
2.1 Material system and the waveguide geometry
The material system of the proposed sensor is 150-nm-thick Si on a thermally-oxidized silicon wafer. The oxide thickness is 8 μm with a refractive index value of 1.449 at 1.3 µm central wavelength. The refractive index of the Si layer is 3.5 at 1.3 µm. A polymer layer (fluorinated ethylene propylene (FEP)) with a refractive index value of 1.33 and a thickness value of tpoly = 0.5 µm was used as the top cladding as it is an optically transparent and chemically resistant material that is routinely used in wiring, 3D printing, and microscopy applications. The wavelength range is chosen to be 1.2-1.3 µm since Si is transparent at wavelengths larger than 1.1µm and the absorption of the polymer layer is lower in this range. A channel waveguide geometry was chosen as it is being more tolerant to fabrication variations. Single mode channel waveguides with waveguide width of w = 250 nm were designed. For the transverse electric (TE) polarization, the effective refractive index of the waveguide was calculated to be 1.6 by using beam propagation method simulations. The mode profile of the waveguide is given in Fig. 2(a).
Fig. 2. (a) The waveguide geometry and the mode profile. Note that thickness of the polymer, Si and SiO2 layers are not to scale. (b) Transmission spectra of the compound resonator for different resonant wavelengths, λ0, of the microring resonator. Note that when the resonant frequency does not coincide with a maximum of the FP oscillations, the transmission exhibits asymmetric Fano-like line shape.
2.2 Theoretical analysis
The compound resonator given in Fig. 1 can be analyzed using the transfer matrix method by combining the transfer functions of each optical element. A similar analysis has been made in Ref. [25] for a microring resonator coupled with a FP microcavity, which is formed by the end facet reflections. The final form of the transfer matrix was given in [25] as:
- I. To have a (quasi) continuum state, it is necessary to design the FP resonator with low finesse, F, which is given as $F = \pi \sqrt R /(1 - R)$, where R = r2 is the reflectivity of the mirrors and r is the amplitude reflection coefficient. For the Sagnac loop mirror, r is given in Eq. (2), which depends on the directional coupler parameters K, κ and Lc. Directional couplers are wavelength dependent. To extend the working range of this sensor, one can use a wavelength-insensitive coupler [28].
- II. Microring resonator is providing the discrete state. A higher quality factor (Q) factor results in a steeper Fano slope. The Q factor of the microring resonator is inversely proportional to the losses. For higher Q factors, the bending losses should be reduced by choosing a sufficiently large radius in the design. The critical coupling of the light to the microring cavity also has an influence on the Q factor, which is mainly determined by the gap between the microring and the straight waveguide for a given waveguide geometry. The gap should be optimized through FDTD simulations.
2.3 Self-referencing operation
The presented sensor design offers the advantage of inherent, internal self-referencing to eliminate the adverse effects of temperature and bulk index variations without the need of an additional reference channel. The transmission spectrum of the sensor is comprised of FP oscillations and Fano-like resonances. The FP oscillations are used as an internal reference as they stay unchanged when the RI of the microring cladding is changed. The self-referencing operation is demonstrated in a two-mirror based compound resonator structure shown in Fig. 1. It consists of a microring resonator (radius, r1), two Sagnac loop mirrors comprised of symmetric directional couplers (length Lc and gap g) and circular waveguide sections (radius, r0), and a connecting straight waveguide (Ls). The effect of the values of Ls and the phase shift, δ, (induced by increasing the length of Ls on the left side of the microring resonator) on the transmission response was simulated using varFDTD method (Lumerical Inc.). The results given in Fig. 3(a) and Fig. 3(c) show that for different values of Ls and δ, the location, shape and amplitude of Fano resonances change. Unless the transmission peaks of the microring resonator coincide with the maximum of the FP oscillations, Fano resonances can always be observed in this sensor configuration. Ls = 9 µm is chosen for the proposed sensor design as it results in Fano peaks with larger amplitude. To have a fabrication tolerant design, we chose g = 0.4 μm. For this gap value, the effect of different Lc values on the transmission response of the compound cavity was investigated. The simulation results given in Fig. 3(b) show that the value of Lc has a significant effect on the overall characteristics of the FP oscillations; however, it is still possible to observe Fano resonances at different parts of the spectrum for different Lc values. Therefore, to keep the device size small, we chose Lc = 7 μm. For Lc = 7 μm and g = 0.4 μm, the reflectivity of the loop mirror is simulated and the results are given in Fig. 3(d). Except the central wavelength of 1.25 µm where there is almost zero reflection, the FP oscillations will be observed in the rest of the spectrum. We set the ring resonator radius as r1 = 6 µm to avoid bending losses and thereby achieve higher Q. The gap between the ring resonator and the straight waveguide, g1, was optimized through FDTD simulations, and the optimum value was obtained as g1 = 0.4µm. The value of r0 was selected as 7 µm to have a sufficiently small FSRFP range while ensuring a small footprint.
Fig. 3. The effect of (a) Ls, (b) Lc and (c) phase shift, δ, values on the transmission response of the compound microcavity. (d) Transmission and reflection versus wavelength values of the Sagnac loop mirror used in the compound resonator design for Lc = 7 µm.
2.4 Multiplexed sensing
Different multiplexing schemes are possible for the proposed sensor and two of them are shown in Fig. 4. The design given in Fig. 4(a) has two microrings with radius values of r1 and r2 placed in between two Sagnac loop mirrors, where in Fig. 4(b) these microrings are placed in between three Sagnac loop mirrors.
Fig. 4. Schematic of the multiplexed sensor formed by two microring resonators with radius of r1 and r2, and (a) two Sagnac loop mirrors and (b) three Sagnac loop mirrors.
In general, having more cavities that are coupled to each other could result in a more complex transmission response; e.g. multiple Fano resonances. Multimirror FP resonators readily give rise to multipeaked spectral orders. Therefore, the transmission response of the three-mirror FP cavity shows double peaks in contrast to two-mirror FP cavity case. The radius of the microring resonators were chosen slightly different; i.e. r1 = 5 µm and r2 = 6 µm, to be able to differentiate the contribution of each microring resonator. The FP resonances stay constant, which makes the self-referencing possible for this configuration as well. In proposed multiplexing schemes, only one light source and a detection unit will be sufficient to detect different samples in parallel in contrast to most of other multiplexing schemes. This feature will make the sensor more cost-effective. The advantage of the design given in Fig. 4(a) is the reduced number of mirrors and thereby a more compact multiplexed sensor unit compared to the design given in Fig. 4(b). On the other hand, the design given in Fig. 4(b) has more design flexibility; i.e. several FP cavities with different cavity lengths can be designed easily. Multiplexing potential of the sensor is demonstrated by using the simulation results of the design given in Fig. 4(a).
3. Simulation results
3.1 Self-referencing operation
The transmission response of the compound structure for the wavelength range of 1.2-1.3 µm is given in Fig. 5(a). The free spectral range (FSR) of the FP and microring resonator is calculated to be FSRRING = 11.2 nm and FSRFP = 2.8 nm, respectively. The finesse (F) of the FP oscillations is 3.9. The sample under test will act as the cladding layer of the microring resonator. Its RI was changed by steps of Δn = 2×10−3 in the simulations and the wavelength shifts of the Fano peaks were calculated. As expected, the FP resonances that are sufficiently away from the Fano peaks stay constant as the cladding RI of the microring resonator increases as shown in Fig. 5(b). We observed that the amplitude of the Fano peak reaches a minimum intensity (still detectable) at Δn = 0.004 and it increases again with larger index change. We achieved a sensitivity value of S = 220 nm/RIU, which is significantly better than existing self-referencing optical sensors (104 nm/RIU [15], 163 nm/RIU [16] and 0.26 nm/RIU [20]). We also used FOM to estimate the performance of the sensor more comprehensively. The FWHM values of the Fano-like resonances in Fig. 5(b) were measured to be 0.13 nm, 0.09 nm and 0.05 nm for the first (Δn = 0), second (Δn = 0.001) and the third (Δn = 0.002) peaks, respectively. The corresponding FOM values are 1692 RIU-1, 2444 RIU-1 and 4400 RIU-1, respectively. The Q factors are calculated to be 9944, 14367 and 25865, respectively.
Fig. 5. Transmission spectra of the two-mirror FP resonator coupled with a microring resonator (a) for the whole range and when (b) the RI of the microring cladding layer is changed by steps of Δn = 2×10−3 and (c) the temperature of the sensor changed by steps of ΔT = 1 °C. Note that in (b) only the sensing peaks are shifting while in (c) both reference and sensing peaks are shifting at the same rate of 0.065 nm/°C.
For this sensor configuration, the spectral difference between the reference peak and the sensing peak is in the order of several nanometers. Although electronic detection will not be applicable to this case [12], a tunable laser with a photodiode [20] can be easily used to measure large spectral differences.
The effect of temperature on the sensor response was simulated by changing the temperature of the sensor with steps of ΔT = 1 °C (Fig. 5(c)). The sensing peak and the reference peak both shifted linearly at the same rate, 0.065 nm/°C, which means that the distance between the reference peak and the sensing peak will be constant and thereby the changes in the cladding RI can be measured independent of the temperature. The temperature variations are included in the simulations by changing the refractive indices of the different materials using their thermo-optic coefficients of -2.053 × 10−4/℃ [29], -1.12 × 10−4/℃ [30], 2 × 10−4/℃ [31], and 1.178 × 10−5/℃ [32] for FEP, water, Si, and SiO2, respectively.
The thickness of the top cladding layer has to be sufficiently large to isolate optical mode from environmental effects. The proposed sensor is simulated for a thicker polymer layer tpoly = 0.8 µm to investigate the effect of polymer layer thickness on the device performance. The results are given in Fig. 6. The effective refractive index is calculated to be 1.612 for tpoly = 0.8 µm, which resulted in a 0.4 nm red shift in the microring resonator spectrum, whereas reference peak stayed stable. The sensitivity of the sensor also did not change; i.e. S = 220 nm/RIU.
Fig. 6. The effect of polymer thickness on device performance. (a) The transmission spectra for the polymer thickness of tpoly = 0.5 µm and tpoly = 0.8 µm. (b) Transmission spectra for the thicker (i.e. tpoly = 0.8 µm) polymer layer when the RI of the microring cladding layer is changed by steps of Δn = 10−3.
3.2 Multiplexed sensing
Figure 7(a) shows the transmission response of the sensor when the RI of the covering layer of the second microring was changed by index steps of Δn = 2×10−3. The transmission response of the first microring has double Fano-like resonances and at certain parts resonance splitting was observed. The resonance peaks associated to each microring resonators are spatially separated, which is essential for parallel measurements. As expected, only the peaks associated with the second microring shifted linearly while the FP peaks and the resonance peaks of the first microring resonator stayed constant. The finesse of the FP oscillations is F = 2.9. Figure 7(b) shows the transmission response of the sensor when the RI of the covering layers of both microring resonators changed by index steps of Δn = 2×10−3. The resonance peaks of each microring resonator shifted linearly at the same rate. The sensitivity was calculated to be S = 220 nm/RIU for both microring resonators.
Fig. 7. Transmission spectra of the multiplexed sensor device when the RI of the covering layer of (a) the first microring (r1) and (b) both microrings is changed with Δn = 2×10−3 steps.
The calculated FWHM values of the double Fano-like resonances correspond to the first microring (r1) in Fig. 7(b) are 0.05 nm, 0.06 nm, 0.1 nm and 0.25 nm for the first (Δn = 0), second (Δn = 0.002), third (Δn = 0.004) and fourth (Δn = 0.006) peaks, respectively. The second dip of the resonances were used for the FWHM calculations. The corresponding FOM values are 4400 RIU-1, 3666 RIU-1, 2200 RIU-1 and 880 RIU-1, respectively. The corresponding Q-factors are calculated to be 24760, 20633, 12380 and 4952, respectively. The FWHM values of the resonances associated to the second microring (r2) in Fig. 7(b) are 0.11 nm, 0.1nm, 0.1 nm and 0.09 nm for the first (Δn = 0), second (Δn = 0.002), third (Δn = 0.004), and fourth (Δn = 0.006) peaks, respectively. The corresponding FOM values are 2000 RIU-1, 2200 RIU-1, 2200 RIU-1 and 2444 RIU-1 respectively. The Q-factors are calculated to be 11210, 12330, 12330 and 13700, respectively.
3.4 Fabrication tolerance analysis
The proposed sensor can be fabricated using e-beam writing, which has subnanometer accuracy. First, the sensor components (i.e. Sagnac loops, straight waveguides and microring resonator) will be written on the wafer using e-beam direct writing, then using reactive ion etching (RIE) these patterns will be transferred to Si layer and finally top cladding layer will be spin coated. Using e-beam writing, the opening over the microring part (for placing liquid samples) will also be defined with subnanometer accuracy.
The fabrication tolerance of the proposed sensor is investigated through FDTD simulations. The thickness accuracy of commercial Si wafers is in the nanometer range. Therefore, in the simulations, we used ±1 nm fabrication tolerances for the given waveguide width and height with respect to the nominal dimensions (i.e., w = 250 nm, tSi = 150 nm). The overall spectra shift in both cases due to effective refractive index change as shown in Fig. 8. Fano resonances are still visible in both cases; however, the amplitude and shape of the Fano resonances change more dramatically when the waveguide width changes.
Fig. 8. Fabrication tolerance analysis of the two-mirror FP cavity coupled with a microring resonator when (a) the waveguide width and (b) the thickness of the Si layer is varied by ±1 nm.
The waveguide surface roughness will also have an effect on the sensor performance by increasing the overall loss. It will reduce the fringe visibility of the FP oscillations whereas the resonance peaks of the microring resonator become broader. Since Fano resonances are the result of interference between continuous and discrete states, we will be able to observe Fano resonances until microring resonances become too broad to be considered as discrete states. However, this is a common problem for most of the optical waveguides and it can be solved by applying resist reflowing method to reduce surface roughness significantly [33].
4. Conclusion
In summary, a novel self-referencing RI sensor based on a compound resonator concept is designed and simulated. A sensitivity value of 220 nm/RIU and a maximum FOM value of 4400 RIU-1 were achieved with a single microring resonator evanescently coupled to the FP resonator. The multiplexing potential of the proposed sensor concept has been investigated in two different schemes by placing two microring resonators with different radii in two-mirror and three-mirror FP cavity resonators. By changing the RI of the overlay layer of the microring resonators, we differentiated the contribution of each cover RI change separately, proving that the proposed sensor can be used in a multiplexed format to measure multiple samples simultaneously. Moreover, only one light source and a detection unit will be sufficient to perform parallel measurements, which will make this sensor cost-effective. In conclusion, the proposed RI sensor points the way to inexpensive, easily fabricated and inherently self-calibrating devices for medical and environmental sensing.
Funding
China Scholarship Council (202007720007).
Acknowledgements
The authors wish to thank Dr. Lantian Chang for their support and fruitful discussions.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [34].
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