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We report a cascaded ring resonator (CRR) based, silicon photonic temperature sensor for simultaneous sensitivity and range enhancement. To achieve the dual enhancement, the proposed CRR temperature sensor employs two micro ring resonators with different temperature sensitivities and different free spectral ranges (FSRs). The differences in the temperature sensitivities and FSRs are obtained by tailoring the in-plane geometric parameters of the two ring resonators. The CRR temperature sensor was fabricated by using a single-mask complementary metal-oxide-semiconductor (CMOS)-compatible process. The experimental results demonstrated a temperature sensitivity of 293.9 pm/°C, which was 6.3 times higher than that of an individual ring resonator. The sensor was also shown to enhance the temperature sensing range by 5.3 times.
© 2016 Optical Society of America
1. Introduction
Recently, silicon photonics based temperature sensors have received much attention. These sensors are robust against electromagnetic interference and drift due to environmental disturbances such as mechanical shock and humidity [1–3], which make them superior to conventional electrical temperature sensors in many applications. Silicon-on-insulator (SOI) based micro ring resonators [1,4], waveguide Bragg gratings [2], and Michelson interferometers [5,6] have been demonstrated for temperature sensing. Compared with optical fiber based temperature sensors, these sensors can achieve much higher sensitivity due to the high thermo-optic coefficient of silicon [7–9]. Furthermore, the integration of silicon photonic sensors with the complementary metal-oxide-semiconductor (CMOS) process enables cost-effective on-chip temperature sensing [10], which is not readily achievable with optical fiber Bragg gratings [11,12] or fiber tip based temperature sensors [13,14].
Among many silicon photonics based structures, SOI micro ring resonators offer some unique features that render them an attractive choice for high performance temperature sensing. The high quality (Q) factor spectral response of silicon ring resonators manifests a strong temperature-dependence [15], which enables high resolution temperature sensing. Furthermore, the high refractive-index contrast of the SOI waveguide provides excellent optical confinement and reduces the waveguide bending loss [16], thus facilitates the development of ultra-compact photonic sensors [17–19].
Most ring resonator based temperature sensors operate by monitoring the resonance wavelength shift with a tunable laser or spectrometer [1,4,20]. This shift results from the optical path length change of the ring waveguide, which is primarily due to the thermally-induced effective refractive index change. The temperature sensitivity of SOI ring resonators is typically limited to be ~80 pm/°C [1,4]. Note that the temperature detection limit (i.e., resolution) is determined by the sensitivity of the sensor and the resolution of the spectral measurement system. Due to the limited sensitivity of a single ring resonator, in order to achieve high resolution temperature detection, an expensive, narrow linewidth tunable laser or fine resolution optical spectrum analyzer (OSA) is often required. On the other hand, the sensing range is determined by the free spectral range (FSR) of the ring resonator, which corresponds to the temperature change that can induce the resonance wavelength shift to a full FSR. The sensing range can be increased by increasing the FSR, which is usually achieved by reducing the ring size. For example, a 120 °C of sensing range was obtained by a 9.2 µm-radius ring resonator [1], and a 280°C of sensing range by a 4 µm-radius ring resonator [4].
There have been many efforts devoted towards enhancing the performance of ring resonator based sensors by employing various ring resonator architectures. These include cascaded ring resonators (CRR) [21,22] for realizing the Vernier effect [23], vertically stacked ring resonators for obtaining resonance splitting [24], and Bragg grating ring resonators for achieving resonance splitting and Fano resonance [25]. While the resonance splitting and Fano resonance have been used to improve the sensor resolution, the CRR-based Vernier effect has been widely used to enhance the sensitivity of the ring resonator based sensors. It has also been used to tailor the spectral characteristics of ring resonators such as suppressing undesired resonance modes and increasing finesse and FSR [26–28]. In a conventional CRR sensor configuration, two ring resonators (a reference resonator and a sensor resonator) are designed to have slightly different FSRs (FSR1 and FSR2, respectively). The resonance wavelength of the sensor resonator shifts with respect to a sensory input, while the reference resonator is designed to be isolated from the sensory input, and thus its resonance wavelength remains unchanged. The major resonance wavelength of the CRR is located at the common resonance wavelength of the two ring resonators. Neglecting the dispersion, the FSR of the CRR is [29]
Note that when the resonance wavelength of the sensor resonator shifts one FSR, the resonance wavelength shift of CRR is amplified to one FSRCRR. Therefore, the sensitivity of the CRR is amplified by a factor of FSRCRR/FSR2. It should be noted that although the conventional CRR based sensors can help enhance the sensitivity by increasing the overall FSRCRR, the sensing range will not be enhanced as it is determined by the FSR of the sensor resonator. On the other hand, to isolate the reference resonator from the sensory input, a multi-mask fabrication process is required: one mask for patterning the waveguides of the CRR and another mask for selectively removing the top cladding of the sensor resonator [29–32].The conventional CRR based sensors have been demonstrated for biological or chemical sensing [29–32]. However, enhancing temperature sensitivity with CRRs has not yet been demonstrated. The main challenge is the isolation of the reference resonator from a temperature change. Alternatively, the temperature sensitivity of the reference ring resonator can be suppressed by depositing a cladding layer with negative thermo-optic coefficient such as polymer or TiO2 [33,34]. However, polymers are not CMOS compatible, and the selective deposition of a negative thermo-optic cladding layer on the reference resonator requires a more complicated multi-mask fabrication process.
In this paper, we propose a novel CRR device that can help simultaneously enhance both sensitivity and sensing range, and for proof-of-concept, we demonstrate a SOI photonic temperature sensor utilizing this non-conventional CRR approach for both temperature sensitivity and sensing range enhancement. Instead of using one of the ring resonators as a reference and thermally isolating the reference, we utilize two ring resonators with different temperature sensitivities and different FSRs, both as sensor resonators. Because the proposed approach does not require isolation of one of the ring resonators from a temperature input, the sensor fabrication can be achieved with a single-mask CMOS-compatible process. More importantly, since the enhanced FSRCRR is obtained from the Vernier effect of two sensor resonators, the device can be tailored to enhance both the temperature sensitivity and sensing range, or to ultimately enhance one of the performance parameters (sensitivity or sensing range).
2. Principle of operation
Figure 1 shows the schematic of the proposed CRR temperature sensor operation. Ring 1 is designed to have a smaller temperature sensitivity (i.e., S1<S2) and a larger FSR compared to Ring 2 (i.e., FSR1>FSR2). This is achieved by using different ring waveguide widths and ring radii [Fig. 1(a) and 1(b)]. Furthermore, temperature sensing is achieved by monitoring the position of the envelope peak of the output transmission spectrum [Fig. 1(c)] (sensitivity of SCRR). This will help compensate the sensor resolution degradation induced by monitoring the discrete shift of the major resonance peak [21]. To better determine the envelope of the output transmission spectrum, the difference (ΔFSR) in FSRs of the two ring resonators should be smaller than the full-width half-maximum (FWHM) of the resonance peak [29].
Fig. 1 Schematic of the CRR temperature sensor operation. (a) Cascaded configuration of Rings 1 and 2. Transmission spectra (b) at the drop ports of the two ring resonators, and (c) at the output of the CRR. (d) Power output at the drop port of a single ring resonator as a function of wavelength and temperature.
As schematically shown in Fig. 1(d), the power output at the drop port of each individual ring resonator is a periodic function of both wavelength (λ) and temperature (T). When the temperature changes by a temperature period (TP), the resonance wavelength of a single ring resonator will shift by one FSR. Thus, the temperature sensitivity of each individual ring resonator can be written as
Note that the temperature period determines the temperature sensing range. For a CRR sensor, the temperature period TPCRR is obtained as . When TP1 and TP2 are close, the temperature sensing range of the CRR sensor will be much larger than that of each individual ring resonator. Furthermore, the sensitivity (SCRR) of the CRR sensor can be expressed asWhen the two ring resonators have different sensitivity, the SCRR will be enhanced. Based on Eqs. (2) and (3), we can define the overall figure of merit (FOM) of the CRR sensor as the amplification of FSR compared with that of a single ring resonator:Equation (4) indicates that the FOM represents the product of the sensitivity enhancement and the sensing range enhancement. Therefore, by using the proposed CRR sensor design, the sensitivity and sensing range can be enhanced simultaneously.In general, the FOM can be enhanced by increasing the FSRCRR, rendering the capability of enhancing both the sensitivity and the sensing range. However, depending on the applications, it is possible to use the FOM for ultimately enhancing only one performance parameter. In other words, the performance of the CRR sensor can be tailored to either solely enhance the sensitivity or sensing range, or both. According to Eq. (3), for given FSR1 and FSR2, the key to tailor the sensor performance is S2/FSR2 – S1/FSR1 (i.e., the sensitivity difference (ΔS) between the two single ring resonators). The larger the ΔS, the higher the sensitivity enhancement. However, increasing the ΔS will compromise the sensing range enhancement. On the other hand, the enhancement of sensing range can be achieved by decreasing the ΔS at the expense of reducing the sensitivity enhancement. At a given S2, the maximum SCRR will be achieved when the S1 is zero, which represents the case of a conventional CRR sensor; while the maximum sensing range will be achieved when the S1 is the same as the S2 (there will be no sensitivity enhancement in this case). Therefore, compared with a conventional CRR sensor, our CRR sensor allows more flexibility to tailor the sensitivity and sensing range.
3. Sensor design
For an SOI device, the temperature sensitivity and FSR of each individual ring resonator can be controlled by changing the waveguide width and ring radius. The temperature sensitivity is related to the thermo-optic effect and thermal expansion of the ring waveguide [4]:
where neff is the effective index of the waveguide and is the coefficient of thermal expansion of silicon. The group index of the waveguide ng is [15]Note that (2.5 × 10−6 /°C [7]) is ~100 times smaller than the thermo-optic coefficients of silicon and silicon dioxide (1.86 × 10−4/°C and 1.0 × 10−5/°C, respectively [4]). Therefore, the temperature sensitivity is dominated by the thermo-optic effect (i.e., ∂neff/∂T), which is closely related to the mode confinement of the waveguide [33,35]. The mode confinement can be controlled by changing the waveguide geometric parameters. For an SOI device with a fixed waveguide thickness, the mode confinement increases with the waveguide width. Figure 2 shows the finite-difference time-domain (FDTD) simulations performed for a single ring resonator with a 210 nm-thick waveguide at 1550 nm at the room temperature, where the refractive indices of silicon and silicon dioxide were 3.48 and 1.45, respectively. Both ∂neff/∂T and ng increase with the waveguide width for the fundamental quasi-TM mode [Fig. 2(a)]. However, for the fundamental quasi-TE mode, as the waveguide width increases, ∂neff/∂T and ng first increase, then ∂neff/∂T saturates and ng decreases slightly. As a result, for both modes, the temperature sensitivity is shown to increase with the waveguide width but with slightly different trends [Fig. 2(b)]. The FSR is determined by the ring radius and waveguide width. For a chosen waveguide width, ng is fixed, and thus the FSR can be controlled by changing the ring radius [15]where R is the ring radius. Figure 2(c) shows the FSR as a function of a ring radius at a resonance wavelength of 1550 ± 0.05 nm. The temperature period TP (i.e., the sensing range) of a ring resonator is related to its FSR and temperature sensitivity, and therefore, for a chosen waveguide width it is determined by the ring radius [Fig. 2(d)].Fig. 2 (a) ∂neff/∂T, ng, and (b) temperature sensitivity of a ring resonator as a function of waveguide width. (c) FSR and (d) TP as a function of ring radius with 350 nm and 450 nm wide waveguides at the quasi-TM mode. FDTD simulation and analytical calculation were performed at 1550 nm. The waveguide thickness is 210 nm.
Based on the above simulation results, a CRR temperature sensor with desired sensitivity/sensing range enhancement can be developed. For proof-of-concept, we designed a sensor operating at the fundamental quasi-TM mode for less susceptibility to waveguide sidewall roughness induced power attenuation. Considering the single mode operation and optical confinement of the waveguide, the waveguide widths of Rings 1 and 2 were chosen to be 350 nm and 450 nm, respectively. Then, based on the simulations [Fig. 2(b)], the S1 and S2 were obtained to be 42.3 pm/°C and 48.0 pm/°C, respectively. The FSRCRR was chosen to be ~17 nm, so that it can be smaller than the spectral width of the broadband light source to be used in the experiment. Furthermore, the FSR1 and FSR2 were set to be 0.515 nm and 0.500 nm, respectively, rendering the sensing ranges of 12.17°C and 10.42°C [Fig. 2(d)]. It was taken into the consideration that ΔFSR should be less than the FWHM of a single resonator. For an SOI ring resonator with a typical Q factor of ~10,000, the FHWMs were estimated to be ~0.155 nm at 1550 nm. Based on the FSRs, the corresponding radii of Rings 1 and 2 were determined to be 271.94 µm and 232.23 µm, respectively [Fig. 2(c)]. The bus to ring waveguide coupling gaps were designed to obtain critical coupling by using FDTD simulations (Gaps of 310 nm and 250 nm were obtained for Rings 1 and 2, respectively). From Eq. (3), the sensitivity and sensing range of the designed CRR temperature sensor were estimated to be 238.0 pm/°C and 72.13°C, respectively. A sensitivity enhancement of 5.0 times and sensing range enhancement of 6.9 times compared to Ring 2 (i.e., FOM of 34.5) were expected.
Note that in the above design values, the dispersion was not taken into account. To investigate the effect of dispersion on the sensitivity and sensing range, we obtained neff with dispersion for Rings 1 and 2 using FDTD simulations [Fig. 3(a)]. Here, only the waveguide dispersion was considered, since it dominates the material dispersion in a high refractive-index contrast SOI waveguide [36]. Using the obtained neff and setting the reference at the room temperature (i.e., ΔT = 0), the envelope peak of interest was located at 1550 nm and the FSRCRR was determined to be 16.87 nm [Fig. 3(b)]. The temperature-dependent envelope peak shift of the CRR temperature sensor was calculated [Fig. 3(c)]. The sensitivity and sensing range were obtained to be 229.6 pm/°C and 73.48°C, respectively, which compare well with those values obtained by neglecting the dispersion. Furthermore, to investigate the effect of the bus-to-ring coupling conditions on the sensor, we obtained the transmission spectra at different coupling conditions [Fig. 3(b)]. The results show a trade-off between the envelop peak sharpness and the transmission power. The critically-coupled CRR sensor renders a sharper envelope peak than the over-coupled CRR sensor and a higher transmission power than the under-coupled CRR sensor. The sharp envelope peak can help reduce the envelope fitting error, and thus improve the sensor resolution. For example, the fitting errors were ~3.2 pm for the over-coupled condition and ~1.2 pm for the critically-coupled and under-coupled conditions. However, the envelope peak locations and FSRCRR of both the over-coupled and under-coupled CRR sensors are the same as the critically-coupled CRR sensor. Therefore, the coupling condition of the CRR sensor does not affect the sensitivity and sensing range.
Fig. 3 (a) FDTD simulation results of neff for Rings 1 and 2 as a function of wavelength. The waveguide thickness is 210 nm. (b) Transmission spectra of the over-coupled, critically-coupled, and under-coupled CRR sensors at the room temperature (ΔT = 0 °C). (c) Calculated temperature-induced peak shifts of the designed CRR temperature sensor and Rings 1 and 2.
4. Farication and experimental setup
The CRR temperature sensor was fabricated by using an SOI wafer with a 210 nm-thick silicon layer and a 3 µm-thick buried oxide layer. The SOI wafer was spin-coated with poly(methyl methacrylate) (PMMA) followed by e-beam lithography for patterning the ring and bus waveguides. A 20 nm-thick chromium (Cr) layer was then deposited on top of the patterned PMMA layer followed by the Cr lift-off process. The ring and bus waveguides were formed by the inductively coupled plasma reactive ion etching process. After releasing the Cr etch mask, a 1 µm-thick oxide cladding layer was deposited by the plasma-enhanced chemical vapor deposition. Figure 4 shows the fabricated sensor. The sensor was tested in the quasi-TM mode. A broadband light source (M1702, AT&T) and a 60 pm resolution OSA (86142B, Agilent) were used to obtain the transmission spectrum of the sensor. The temperature control was achieved with a micro-hotplate and a k-type thermocouple (CO1, Omega).
Fig. 4 (a) Optical microscope image of the fabricated CRR temperature sensor. SEM images of the ring and bus waveguides in the coupling region for (b) Ring 1 and (c) Ring 2.
5. Results and discussion
The measured transmission spectra of the two ring resonators at the pass port are shown in Fig. 5(a). The Q factors of Rings 1 and 2 were 9,000 and 10,000, respectively. The FSR1 and FSR2 were ~0.515 nm and ~0.500 nm, respectively. The difference in FSRs (ΔFSR = ~0.015 nm) was 10 times smaller than the measured FWHM (~0.145 nm). The resonance wavelength shifts of each individual ring resonator as a function of temperature were measured, which exhibited a good linearity [Fig. 5(b)]. The temperature sensitivities of Rings 1 and 2 were determined to be 38.9 pm/°C and 46.6 pm/°C, respectively, which were slightly lower than the designed values (42.3 pm/°C and 48.0 pm/°C, respectively). The discrepancies are believed to result from the differences in the device geometric parameters and material properties (i.e., refractive indices and thermo-optic coefficients of silicon and silicon dioxide) between the experiment and simulations.
Fig. 5 (a) Normalized transmission spectra at the pass port of Rings 1 and 2 at 23.74°C. (b) Resonance wavelength shift of Rings 1 and 2 and the envelope peak shift of the CRR temperature sensor as a function of temperature. (c) and (d) Normalized transmission spectra of the CRR temperature sensor and the corresponding envelopes by the Lorentzian fit at 23.74°C and 48.46°C.
Furthermore, the performance of the CRR temperature sensor was characterized. The envelope peak position was determined by the Lorentzian fit of the output transmission spectrum. At the room temperature (23.74°C), the envelope peak was located at ~1546 nm and the FSRCRR was 16.63 nm [Fig. 5(c)]. The shift of the envelope peak with respect to temperature was clearly observed [Fig. 5(c) and 5(d)] and a good linearity was obtained [Fig. 5(b)]. The sensitivity and sensing range were 293.9 pm/°C and 56.85°C, which exhibit an enhancement of 6.3 times and 5.3 times compared with those of Ring 2. The corresponding FOM was 33.4. The resolution of the CRR temperature sensor was determined from the sensitivity and envelope peak fitting error (i.e., sensor resolution = envelope peak fitting error / sensitivity) [29]. Based on the measured transmission spectrum, the envelope peak fitting error was determined to be 53 pm, and hence, the resolution of the CRR temperature sensor was obtained as 0.18°C. The resolution can be improved by further enhancing the sensitivity and/or reducing the fitting error. The error can be reduced by using a two-step fitting (i.e., constituent peaks fitting and envelope fitting) and a higher resolution spectrum measurement system. For example, an 18 pm fitting error was demonstrated in [29] by using the two-step fitting and a tunable laser with a 1 pm resolution.
Although with the proof-of-concept sensor, we only demonstrated a sensing range of 56.85°C, it should be noted that for the obtained FOM of 33.4, the sensing range of the sensor can be ultimately enhanced to be ~358°C when the S1 is designed to be equal to the S2, and there will be no sensitivity enhancement (i.e., the sensitivity will be 46.6 pm/°C, same as that of each single ring resonator). On the other hand, for the same FOM, a larger sensing range can be obtained without compromising the sensitivity by reducing the ring radii. For example, if the radii of Rings 1 and 2 are reduced to 10% of the current values (i.e., 27.2 μm and 23.2 μm), the FSRs and thus the sensing ranges of Rings 1 and 2 will increase by ten times. Since both the sensing range enhancement and sensitivity enhancement will remain unchanged, a sensing range of 568.5°C with a sensitivity of 293.9 pm/°C will be achievable with the CRR sensor. In this case, a light source with a larger spectral width is required for the full-range sensing since the FSRCRR will also increase by ten times. Furthermore, with the designed waveguide widths, if the quasi-TE mode operation is used, the achievable ΔS will be ~27% larger than that of the quasi-TM mode operation, which can help further enhance the sensitivity. However, for the quasi-TE mode operation, precise fabrication of the waveguides is required to decrease the sidewall roughness so that the power attenuation can be reduced. The sensor performance adjustment can be achieved by tailoring the in-plane geometric parameters of Rings 1 and 2 (i.e., waveguide widths and ring radii). The out-of-plane geometry and core/cladding layer materials are the same for Rings 1 and 2, which enables to fabricate the sensor with a single-mask CMOS-compatible process.
6. Concluding remark
In conclusion, we report a CRR-based, silicon photonic temperature sensor with the capability of enhancing both sensitivity and sensing range. The CRR temperature sensor was fabricated by using a single-mask CMOS-compatbile process. In experiment, the sensor was demonstrated to have an enhancement of 6.3 times in the sensitivity and 5.3 times in the sensing range compared to the single ring resonator sensor. Furthermore, we theoretically showed that either the sensitivity or the sensing range can be ultimately enhanced by tailoring the ΔS, and both the sensitivity and the sensing range can be enhanced by increasing the FOM. As pointed by previous studies [21,29], owing to the sensitivity enhancement of the proposed temperature sensor, one can potentially use an on-chip, low resolution micro optical spectrometry such as an arrayed waveguide grating [37] for sensor interrogation without significant compromise in resolution. This can help reduce the size and cost of the photonic temperature monitoring system. On the other hand, it is possible to tailor the sensor to obtain an extended temperature sensing range, so that it can be utilized to monitor large temperature changes.
Acknowledgment
This work was supported by National Science Foundation (NSF) (CMMI1200420) and Office of Naval Research (ONR). Authors thank Dr. Yongyao Chen for his advice on FDTD simulations.
References and links
1. H. Xu, M. Hafezi, J. Fan, J. M. Taylor, G. F. Strouse, and Z. Ahmed, “Ultra-sensitive chip-based photonic temperature sensor using ring resonator structures,” Opt. Express 22(3), 3098–3104 (2014). [CrossRef] [PubMed]
2. N. N. Klimov, S. Mittal, M. Berger, and Z. Ahmed, “On-chip silicon waveguide Bragg grating photonic temperature sensor,” Opt. Lett. 40(17), 3934–3936 (2015). [CrossRef] [PubMed]
3. G. Strouse, “Standard platinum resistance thermometer calibrations from the Ar TP to the Ag FP,” NIST Special Publication 250, 81 (2008).
4. G.-D. Kim, H.-S. Lee, C.-H. Park, S.-S. Lee, B. T. Lim, H. K. Bae, and W.-G. Lee, “Silicon photonic temperature sensor employing a ring resonator manufactured using a standard CMOS process,” Opt. Express 18(21), 22215–22221 (2010). [CrossRef] [PubMed]
5. J. F. Tao, H. Cai, Y. D. Gu, J. Wu, and A. Q. Liu, “Demonstration of a Photonic-Based Linear Temperature Sensor,” IEEE Photonics Technol. Lett. 27(7), 767–769 (2015). [CrossRef]
6. S. L. Tsao and P. C. Peng, “An SOI Michelson interferometer sensor with waveguide Bragg reflective gratings for temperature monitoring,” Microw. Opt. Technol. Lett. 30(5), 321–322 (2001). [CrossRef]
7. G. Cocorullo, F. Della Corte, and I. Rendina, “Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550 K at the wavelength of 1523 nm,” Appl. Phys. Lett. 74(22), 3338–3340 (1999). [CrossRef]
8. G. Coppola, L. Sirleto, I. Rendina, and M. Iodice, “Advance in thermo-optical switches: principles, materials, design, and device structure,” Opt. Eng. 50, 071112 (2011).
9. C. Ciminelli, F. Dell’Olio, C. Campanella, V. Passaro, and M. Armenise, Integrated optical ring resonators: modelling and technologies (NOVA Science Publishers, 2009).
10. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]
11. A. Kersey and T. Berkoff, “Fiber-optic Bragg-grating differential-temperature sensor,” IEEE Photonics Technol. Lett. 4(10), 1183–1185 (1992). [CrossRef]
12. Y.-J. Rao, D. J. Webb, D. Jackson, L. Zhang, and I. Bennion, “In-fiber Bragg-grating temperature sensor system for medical applications,” J. Lightwave Technol. 15(5), 779–785 (1997). [CrossRef]
13. H. Bae, D. Yun, H. Liu, D. A. Olson, and M. Yu, “Hybrid miniature Fabry–Perot sensor with dual optical cavities for simultaneous pressure and temperature measurements,” J. Lightwave Technol. 32(8), 1585–1593 (2014). [CrossRef]
14. Z. Zhang, Y. Chen, H. Liu, H. Bae, D. A. Olson, A. K. Gupta, and M. Yu, “On-fiber plasmonic interferometer for multi-parameter sensing,” Opt. Express 23(8), 10732–10740 (2015). [CrossRef] [PubMed]
15. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012). [CrossRef]
16. Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004). [CrossRef] [PubMed]
17. X. Wang, X. Guan, Q. Huang, J. Zheng, Y. Shi, and D. Dai, “Suspended ultra-small disk resonator on silicon for optical sensing,” Opt. Lett. 38(24), 5405–5408 (2013). [CrossRef] [PubMed]
18. M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Toward ultimate miniaturization of high Q silicon traveling-wave microresonators,” Opt. Express 18(19), 19541–19557 (2010). [CrossRef] [PubMed]
19. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008). [CrossRef] [PubMed]
20. M.-S. Kwon and W. H. Steier, “Microring-resonator-based sensor measuring both the concentration and temperature of a solution,” Opt. Express 16(13), 9372–9377 (2008). [CrossRef] [PubMed]
21. D. Dai, “Highly sensitive digital optical sensor based on cascaded high-Q ring-resonators,” Opt. Express 17(26), 23817–23822 (2009). [CrossRef] [PubMed]
22. V. Zamora, P. Lützow, M. Weiland, and D. Pergande, “Investigation of cascaded SiN microring resonators at 1.3 µm and 1.5 µm,” Opt. Express 21(23), 27550–27557 (2013). [CrossRef] [PubMed]
23. E. S. Ferry, A Handbook of Physics Measurements: By Ervin S. Ferry. In Collaboration with OW Silvey, GW Sherman, Jr., and DC Duncan (John Wiley & Sons, 1926).
24. C. Campanella, C. Campanella, F. De Leonardis, and V. Passaro, “A high efficiency label-free photonic biosensor based on vertically stacked ring resonators,” Eur. Phys. J. Spec. Top. 223(10), 2009–2021 (2014). [CrossRef]
25. F. De Leonardis, C. E. Campanella, B. Troia, A. G. Perri, and V. M. Passaro, “Performance of SOI Bragg grating ring resonator for nonlinear sensing applications,” Sensors (Basel) 14(9), 16017–16034 (2014). [CrossRef] [PubMed]
26. P. Urquhart, “Compound optical-fiber-based resonators,” J. Opt. Soc. Am. A 5(6), 803–812 (1988). [CrossRef]
27. K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9(6), 728–736 (1991). [CrossRef]
28. L. Y. Tobing, D. C. Lim, P. Dumon, R. Baets, and M.-K. Chin, “Finesse enhancement in silicon-on-insulator two-ring resonator system,” Appl. Phys. Lett. 92(10), 101122 (2008). [CrossRef]
29. T. Claes, W. Bogaerts, and P. Bienstman, “Experimental characterization of a silicon photonic biosensor consisting of two cascaded ring resonators based on the Vernier-effect and introduction of a curve fitting method for an improved detection limit,” Opt. Express 18(22), 22747–22761 (2010). [CrossRef] [PubMed]
30. L. Jin, M. Li, and J.-J. He, “Highly-sensitive silicon-on-insulator sensor based on two cascaded micro-ring resonators with vernier effect,” Opt. Commun. 284(1), 156–159 (2011). [CrossRef]
31. J. Hu and D. Dai, “Cascaded-ring optical sensor with enhanced sensitivity by using suspended Si-nanowires,” IEEE Photonics Technol. Lett. 23(13), 842–844 (2011). [CrossRef]
32. L. Jin, M. Li, and J.-J. He, “Optical waveguide double-ring sensor using intensity interrogation with a low-cost broadband source,” Opt. Lett. 36(7), 1128–1130 (2011). [CrossRef] [PubMed]
33. W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photonics Technol. Lett. 20(11), 885–887 (2008). [CrossRef]
34. B. Guha, J. Cardenas, and M. Lipson, “Athermal silicon microring resonators with titanium oxide cladding,” Opt. Express 21(22), 26557–26563 (2013). [CrossRef] [PubMed]
35. M. Uenuma and T. Motooka, “Temperature-independent silicon waveguide optical filter,” Opt. Lett. 34(5), 599–601 (2009). [CrossRef] [PubMed]
36. E. Dulkeith, F. Xia, L. Schares, W. M. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006). [CrossRef] [PubMed]
37. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15(5), 2299–2306 (2007). [CrossRef] [PubMed]
