Open Access
Add to BibSonomy
Abstract
Sensors based on Fano resonance (FR) have become a promising platform for various biological and chemical applications. However, most investigations on FR are limited to the generation of individual resonance. In this paper, based on the coupling between surface plasmon polariton (SPP) and two photonic waveguide modes, a dual-FR system is designed and analyzed. To explain the coupling mechanism, an extended temporal coupled-mode model is established to provide the physical insight. The spectral response obtained from the model matches well with the numerical one. Due to the decoupled nature of the FRs, a self-calibrated or dual-parameter sensing scheme for refractive index and temperature is proposed. The refractive index sensitivity up to 765 nm/RIU and temperature sensitivity up to 0.087 nm/°C are obtained by wavelength interrogation with figure-of-merit (FOM) up to 33260.9 RIU−1 and 3.78 °C−1 respectively. The proposed sensor provides great potential in fields of the multi-parameter sensing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon polariton (SPP) is known as surface waves generated by the oscillation between photon and electron at the interface of two materials with negative and positive real parts of dielectric constants, respectively [1]. When the parallel wavevector of the incident light matches the propagation constant of SPP wave, the energy of the incident light is transferred to the surface wave. This leads to a sharp attenuation of the reflected light, which is known as surface plasmon resonance (SPR) [2]. The SPR condition is highly sensitive to the environmental variations and can be utilized to detect and analyze various chemical and biological molecules by observing the refractive index changes. Due to the advantages such as non-destructive, sensitive, convenient, label-free and real-time capability, SPR sensors have a broad prospect in practical applications [3–6]. However, compared with their electronic counterpart which can work normally under the temperature change of tens of degrees Celsius, the integrated photonic device suffers from temperature crosstalk caused by the thermal-optical coefficient (TOCs) of the device, especially in the condition of high refractive index sensitivity regime [7]. The variation of temperature changes the refractive index of materials and consequently results in additional resonance shifts. In order to overcome this problem, an appropriate temperature control mechanism is necessary to compensate such drawback, which make the whole system more complicate and increases the fabrication cost.
In order to improve the sensing performance and simplify the system, simultaneous measurement of refractive index and temperature is required. Recently, the coupling between the two electromagnetic modes supported by nanostructures has become a hot research topic [8,9]. Fano resonance (FR) in multilayered system, generated by the coupling between the dark mode and the bright mode, has shown great potential for sensor performance improvement [10–17]. The SPP mode that is, supported by metal-dielectric interface, usually corresponds to a broad resonance (bright mode). On the contrary, the planar waveguide mode (PWG) formed in dielectric planar waveguide structure, results in sharp resonance (dark mode). These two modes interact with each other through overlap of their evanescent fields. If two different modes are successfully coupled, the FR characterized by an asymmetrical sharp resonance shape will occur. S. Hayashi et al. firstly investigated a structure consisting of SF11-prism-Au-ZnS-SiO2 surrounded by water. The coupling between SPP and PWG mode resulted in FR [10]. D. Nesterenko et al. employed the coupling oscillator system to make an analogy to the multi-mode coupled electromagnetic system, and further analyzed the influence of loss on FR spectral line in multi-layer structure, which demonstrated the great advantages of FR [11]. G. Zheng et al. reported the experimental and numerical studies on the FR in a multilayer structure consisting of an Au layer, a SiO2 layer, and a ZrO2 layer surrounded by water [14]. The effects of the spacer thickness on the width of the Fano line and the Q-factor were studied in detail as well [15]. Our group have designed the multilayered structure operating at near-infrared wavelength regime and investigated the coupling between long range SPP and PWG [16,17]. However, all the reported structures can only support an individual FR, which is difficult to meet the requirements of simultaneous dual-parameter measurement.
It is worthy to note that, in the multilayer structure, the FR originates from the coupling between SPP and PWG modes. However, if another structure which also satisfies the total internal reflection exists and its resonance locates within the regime of the SPR, an additional PWG may be excited to form a new FR. In this case, multiple FRs can be generated in the reflective spectrum. Z. Sekkat et al. have proposed a metal-insulator-metal multilayer structure to obtain multiple resonances, and explored the coupling between these resonances, including the coupling between two SPP at the metal-insulator interface and FRs formed by the metal film and the high index dielectric layer [18]. However, there are few reports on the investigation of multiple FRs based on the coupling mechanism of SPP and multiple PWG modes [19,20]. In these works, multiple FRs are attributed to the coupling between the SPP mode and the multiple higher-order PWG modes. However, the multiple FRs are generated in the same waveguide layer, which means it is difficult to tune the resonance independently and consequently limited the design freedom to some degree. In this paper, a multilayered structure with dual FRs is designed based on SPP-PWG-PWG coupling. The two waveguide modes couple with SPP separately leading to two sharply asymmetric FRs. Additionally, a three-resonance temporal coupled-mode theory is built to explain the physical mechanism, which matches the numerical analysis very well. Based on this device, a self-calibrated or dual-parameter sensing scheme is further proposed for both temperature and refractive index variations. The results show that refractive index sensitivity up to 765 nm/RIU and temperature sensitivity up to 0.087 nm/°C can be obtained by wavelength interrogation, with figure-of-merit (FOM) as high as 33260.9 RIU−1 and 3.78 °C−1, respectively. The proposed sensor has great potential in the areas of highly precision bio-sensing and chemical sensing.
2. Device design and theoretical model
2.1 Device design
The structure of the proposed dual-FR device is schematically shown in Fig. 1, which is a typical Kretschmann configuration consisting of a prism, metal layer, and five dielectric layers. SF11 glass acts as the coupling prism. The metal-dielectric interface supports SPP modes which provides a broad resonance (bright mode) in the reflective spectrum. The metal used in this configuration is Ag. Meanwhile, there are five dielectric layers supporting two PWG modes. The SiO2-Si3N4-SiO2 multilayer forms the first waveguide structure and the SiO2-TiO2-aqueous solution forms the second one. The proposed structure employs Si3N4 with TOC of 2.45×10−5 K−1 [21,22], surrounded by SiO2 with TOC of 1×10−5 K−1 to support PWG1 mode. For PWG2 mode, TiO2 layer with negative TOC of −1×10−4 K−1 aqueous solution with positive TOC of ∼8×10−5 K−1 are employed [23].
The temperature-dependent of dielectric constant of Ag is given by the Drude model as follows [24]:
2.2 Theoretical model
To investigate the coupling behavior for such SPP-PWG-PWG multilayer, we develop the theoretical model based on the temporal coupled-mode theory [29]. Since the attenuated total reflectance condition is satisfied, the incident energy light is directly coupled with the SPP mode while the PWG and SPP mode are coupled with each other through evanescent field. The schematic diagram is shown in Fig. 2, where Sin and Sout represent the incoming and outcoming waves to the prism, km = ωm/(2Qom) + ωm/(2Qim) (m represents SPP, PWG1 and PWG2 mode) are the loss including decay rate due to the energy coupled into the structure and the intrinsic loss of SPP, PWG1 and PWG2 mode, respectively. In particular, k01 = (ωSPP/QoSPP)1/2 is the decay rate of coupling between SPP mode and incident light. µnm = ωm/(2Qcm) (m ≠ n) is the direct coupling coefficient between the different resonant modes. The three resonance modes can be described as:
To verify the theoretical model, we compare the reflective spectra obtained by the transfer matrix method (TMM) and the theoretical model. At room temperature, with the thickness of the SiO2 layer of t1 = t2 = 700 nm, d1 = 106 nm and d2 = 93 nm, the reflectivity curves as a function of wavelength obtained by these two methods are shown in Fig. 3(a). With ωSPP = 469 THz, ωPWG1 = 504 THz, ωPWG2 = 442 THz, QoSPP = 65.4, QiSPP = 47.4, QoPWG1 = 1075.3, QiPWG1 = 954.2, QoPWG2 = 19607.8, QiPWG2 = 9880.4, µ12 = 6.2 × 1011 and µ12 = 3.5 × 1011, the reflective spectrum matches well with the numerical one, indicating the reliability of the proposed model. The broad resonance dip appears at 638.92 nm indicating the efficient excitation of SPP mode at the SiO2/Ag interface, and two sharp resonances denote two PWG modes are successfully excited. FRs appears when the sharp resonance is closed to the broad SPP resonance. It is worth mentioning that in this model, the coupling between the PWG1 and PWG2 modes is ignored. In fact, it may be still a weak interaction between the two PWG modes, resulting in the deviations between the spectral response of TMM and the theoretical model. The distributions of electric field |E| at different resonance dips further explain the properties of FRs, as shown in Figs. 3(b)–3(d). In particular, Fig. 3(c) corresponds to the SPR dip, where the strong electric field is generated only at the SiO2/Ag interface, and exponentially attenuated away from the interface, which is a typical signature of the SPP mode. Figure 3(b) corresponds to the spectrum dip caused by PWG1, the electric field is mainly distributed around Si3N4 and metal, which verifies the hybridization and coupling of SPP and PWG1 modes. The electric field at the position of PWG2 expresses the same phenomenon. However, since TiO2 is farther away from the SiO2/Ag interface, the electric field at PWG2 is weaker comparing to PWG1 mode, resulting in weaker coupling and narrower resonance, as shown in Fig. 3(d).
Fig. 3. (a) The reflectivity curves as a function of wavelength obtained by the TMM (black line) and temporal coupled mode theory (blue line). (b)–(d) The distributions of electric field at the resonance dips of PWG1, SPP, and PWG2 as noted in Fig. 3(a).
3. Spectral response
To obtain the proper FR with asymmetric line shape, we studied the spectra response under different coupling conditions. The coupling strength between two modes is related to their effective refractive indices and mode overlap, which could be changed by adjusting the thickness of Si3N4 and TiO2 layer. The dispersion relations of SPP, PWG1 and PWG2 mode d1 = 106 nm and d2 = 93 nm with infinite boundary conditions are plotted in Fig. 4. Among them, kxinc = k0nprismsinθinc represents the horizontal component of the incident wave vector, where k0 is the incident wave vector in free space, nprism represents the refractive indices of SF11 and θinc denotes the incident angle with 61.947°. The intersection points between kxinc and PWG1, PWG2 and SPP corresponds to the resonance peak of each mode, which means the excitation of this mode.
Fig. 4. Wave vector of SPP, PWG1 and PWG2 mode as a function of wavelength with d1 = 106 nm and d2 = 93 nm, where resonance frequency and propagation constant of corresponding mode are indicated.
The reflective spectra with different Si3N4 and TiO2 thickness are shown in Fig. 5. Figure 5(a) shows the reflectivity with different Si3N4 thickness under t1 = t2 = 700 nm and d2 = 93 nm. Because of the growing effective refractive indices of PWG1 mode with the increment of d1, the resonance wavelength moves to the longer wavelength to meet the phase matching condition [12]. When the effective refractive index of PWG1 mode is getting close to the resonance of the SPP mode, the typical asymmetric FR line shape appears. However, further increasing the Si3N4 thickness, the effective refractive indices of SPP and PWG1 mode are getting to be equal, resulting in plasmon-induced transparency (PIT) effect with a transparent window locating in the resonance dip of the broad absorptive SPR. The extinction ratio and slope with different d1 are demonstrated in Fig. 5(e), where extinction ratio is defined as 10 × log(Rpeak/Rdip) and the slope is defined as (Rpeak - Rdip)/ FWHM, where Rpeak and Rdip are the maximal and minimal reflection of the resonance, and FWHM is the full width at half maximum of the resonance, which is defined as the wavelength difference of Rpeak and Rdip. It can be found that thinner Si3N4 layer leads to higher extinction ratio and slope. However, opposite phenomenon can be found in Figs. 5(b) and 5(f). Figure 5(b) shows the reflective spectra as a function of incident wavelength with different TiO2 thicknesses under t1 = t2 = 700 nm and d1 = 106 nm. The position of FR peak moves to a long wavelength due to the higher effective index of PWG2. Larger incident wavelength is required to match the resonant condition and the slope increases as the d2 increases. Figures 5(c) and 5(d) show the calculated reflective spectra by Eq. (8) corresponding to Figs. 5(a) and 5(b). The simulation results are consistent with the calculated ones, which not only further proves the correctness of the theoretical model, but also provides a physical insight to the coupling behavior. Noted that in such configuration, the two FRs can be tuned independently, such decoupled behavior is very suitable for sensing applications. From the viewpoint of fabrication, the thickness tolerances for d1 and d2 to form FRs are ∼10 nm.
Fig. 5. Reflectivity curves of the numerical calculations with (a) different value of Si3N4, where the thickness of TiO2 d2 = 93 nm, and (b) different value of TiO2, where the thickness of Si3N4 d1 = 106 nm. The thickness of SiO2 t1 = t2 = 700 nm. (c) The theoretical calculations corresponding to (a). (d) The theoretical calculations corresponding to (b). (e) The extinction ratio and slope of FR with different value of Si3N4, and (f) with different value of TiO2.
As a coupling layer, the thickness of SiO2 plays an important role in the coupling strength. The reflective spectra with t1 = 600, 800 and 1000 nm are plotted in Fig. 6(a) with t2 fixed to 700 nm. The extinction ratio barely changes with thicker t1, but the slope increases obviously with thicker coupling layer, as plotted in Fig. 6(e). The thinner thickness strengthens the coupling due to the stronger evanescent field overlap, leading to broader resonance. However, since the structure is made of multiple materials stacked on top of each other, thicker t1 will affect the coupling between SPP and PWG2 mode as well. We will show that the appropriate thickness of SiO2 layer is key for sensing applications. The same phenomenon occurs with the variation of t2, as shown in the Figs. 6(b) and 6(f). Figures 6(c) and 6(d) show the calculated reflective spectra by Eq. (8) corresponding to Figs. 6(a) and 6(b). Considering the fabrication, we believe the challenge lies in the deposition of thin layers instead of the thick ones and thus the fabrication risk of the coupling layer can be mitigated.
Fig. 6. Reflectivity curves of the numerical calculations with (a) t1 while t2 = 700 nm, and (b) t2 while t1 = 700 nm. The thickness of TiO2 and Si3N4 are fixed at 93 nm and 106 nm, respectively. (c) The theoretical calculations corresponding to (a). (d) The theoretical calculations corresponding to (b). (e) The extinction ratio and slope of FR with different value of t1, and (f) with different value of t2.
In the real fabrication process, the waveguide layers may show different losses caused by different preparation methods and conditions. In our calculation, all possible losses are incorporated effectively in the nonzero imaginary part of refractive index of Si3N4 and TiO2. The resonance features of FR1 and FR2 obtained for different imaginary part of refractive index of Si3N4, κ1 and TiO2, κ2 are plotted in Fig. 7. When κ is less than 10−5, the loss has no significant effect on the resonance curve.
Fig. 7. Reflectivity curves of the numerical calculations with (a) t1 while t2 = 700 nm, and (b) t2 while t1 = 700 nm. The thickness of TiO2 and Si3N4 are fixed at 93 nm and 106 nm, respectively. (c) The theoretical calculations corresponding to (a). (d) The theoretical calculations corresponding to (b). (e) The extinction ratio and slope of FR with different value of t1, and (f) with different value of t2.
4. Self-calibrated sensing performance
The decoupled dual-FR nature of the proposed device is suitable for self-calibrated sensors. Since one of the cladding sides of PWG2 is aqueous solution, FR2 is sensitive to the environmental refractive index variation. In contrast, PWG1 is sandwiched between two dielectrics as a result almost immuning to the environmental index change. In contrary, both FR1 and FR2 are temperature-sensitive.
To investigate the sensing performance, wavelength modulation (characterized by wavelength peak shift of the curve Δλres) is considered. The refractive index sensitivity is given as Kn = Δλres/Δn while the temperature sensitivity is given as KT = Δλres/ΔT, Δn and ΔT is the variation of the refractive index of sensing medium and temperature, respectively. The reflective spectrum with Δn = 2.0 × 10−3 is plotted in Fig. 8(a) with the thicknesses of each layer t1 = t2 = 700 nm, d1 = 106 nm and d2 = 93 nm. There is an obvious shift of the resonance dip of FR2 with the increasing refractive index of sensing medium, whereas the resonance dip of FR1 shifts little. The wavelength shifts of the resonant dips of FR1 and FR2 mode are 0 nm and 1.42 nm, respectively, leading to refractive index sensitivities of 0 nm/RIU and 710 nm/RIU respectively. For temperature sensing, the reflectivity spectrum with temperature T = 20 °C and 30 °C is plotted in Fig. 8(b). Both FR1 and FR2 shift with temperature with sensitivities of 0.02 nm/°C and 0.082 nm/°C, respectively. Since FR1 is almost insensitive to refractive index changes, which can be employed as a reference to eliminate the influence of temperature on the sensor. Therefore, the proposed sensor is of the capability of self-calibration.
Fig. 8. The reflectivity curves (a) various of refractive index Δn = 2.0×10−3, and (b) temperature T = 20 °C and 30 °C.
In order to further optimize the performance of the sensor, Figs. 9(a) and 9(b) show the refractive index sensitivity for both FR1 and FR2 with different t1 and t2, when d1 and d2 is fixed at 106 nm and 93 nm, respectively. Since the PWG1 does not contact with the sensing medium, FR1 shifts little with the refractive index change. For FR2, when the thickness of t1 is fixed, the sensitivity decreases with the increasing of t2 mainly due to the weaker coupling between SPP and PWG2 mode, the interaction between optical field and sensing medium becomes weaker. However, there is an opposite tendency for the temperature variation, as shown in Figs. 9(c) and 9(d). When the thickness of t1 is fixed, the sensitivity increases with t2. It is worth noting that though TiO2 with negative TOC is adopted to compensate the temperature, due to the high TOC of aqueous solution, the temperature sensitivity of FR2 is higher than that of FR1. The optimal Kn of FR1 and FR2 are 0 nm/RIU and 760 nm/RIU and the optimal KT of FR1 and FR2 are 0.022 nm/°C and 0.082 nm/°C, respectively.
Fig. 9. Variation of the refractive index sensitivity with wavelength of (a) FR1 and (b) FR2, and that of the temperature sensitivity with wavelength of (c) FR1 and (d) FR2 as a function of the value of t2 with various value of t1.
With two FRs, the wavelength shifts ΔλFR1 and ΔλFR2 can be expressed as [31,32]:
According to the above results, matrix coefficients can be obtained as:
The performance of the SPR sensor is related to the linewidth of the resonance. Compared to conventional SPR sensors, FR-based sensors provide narrower reflectance curves with higher slopes. It is necessary to employ the FOM for evaluation, which is expressed as:
The larger FOM represents the sharper resonance and higher sensitivity. Figures 10(a) and 10(b) show the refractive index FOMs of FR1 and FR2 mode with different SiO2 layer thicknesses, with d1 = 106 nm, d2 = 93 nm. When the refractive index is measured by FR1 and FR2, the FOM of FR1 is much smaller than FR2 since the shifts of FR1 does not depend on the refractive index changes, while the FOM of FR2 increases with increasing of t1 and t2 because of the weaker coupling strength between SPP mode and PWG2. The temperature FOMs of FR1 and FR2 are demonstrated in Figs. 10(c) and 10(d). The temperature FOM of FR1 increases with increasing of t1 and decreases with thicker t2.Fig. 10. Variation of the FOM of refractive index of (a) FR1 and (b) FR2, and that of temperature of (c) FR1 and (d) FR2 as a function of the value of t2 with various value of t1
With t1 = 900 nm and t2 = 600 nm, sensitivity and FOM are plotted as a function of d1 and d2, as shown in Fig. 11. FOMn and FOMT show almost the same dependence on d1, decreasing to zero with increasing d1. When FR2 is used for temperature and refractive index measurement, both sensitivity and FOM of FR2 increase with d2. With d1 = 102 nm, the FOMn and FOMT of FR1 are 150 RIU−1 and 1.16 °C−1 where the Kn and KT of FR1 are 2.5 nm/RIU and 0.023 nm/°C, respectively. And the FOMn and FOMT of FR2 are 33260.9 RIU−1 and 3.78 °C−1 with d1 = 98 nm, where the Kn and KT of FR2 are 765 nm/RIU and 0.087 nm/°C. respectively.
Fig. 11. Variation of the FOM and sensitivity of refractive index of (a) FR1 and (b) FR2, and that of temperature of (c) FR1 and (d) FR2 as a function of the value of d1 and d2.
5. Conclusion
In this paper, a dual-FRs structure with independent tuning properties are proposed. The FRs are generated by the coupling between SPP and two PWG modes. A theoretical model is established to give physical and systematic insight of the coupling behavior. The theoretical results match well with the one obtained by rigorous TMM method with various structural parameters. Based on the configuration, a dual-parameter sensor is designed for the detection of refractive index and temperature variations. It is shown that one of the FR is nearly insensitive to the index change, which can be used as a natural reference for self-calibrated sensing. Overall, refractive index sensitivity up to 765 nm/RIU and temperature sensitivity up to 0.087 nm/°C are obtained with wavelength modulation. FOM of refractive index up to 33260.9 RIU−1 and that of temperature up to 3.78 °C−1 are achieved. The proposed structure provides a promising platform for multiple FRs generation and high-performance sensing.
Funding
National Key Research and Development Program of China (2016YFC0201101); Wuhan Science and Technology Bureau (2018010401011297); the Open Project Program of Wuhan National Laboratory for Optoelectronics (2019WNLOKF005); the Natural Science Foundation of Hubei Province (2019CFB598); the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (1910491B06, G1320311998, ZL201917).
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
References
1. Y. H. Huang, H. P. Ho, S. K. Kong, and A. V. Kabashin, “Phase-Sensitive Surface Plasmon Resonance Biosensors: Methodology, Instrumentation and Applications,” Ann. Phys. 524(11), 637–662 (2012). [CrossRef]
2. E. Kretschmann and H. Raether, “Notizen: Radiative Decay of Non Radiative Surface Plasmons Excited by Light,” Z. Naturforsch. A 23(12), 2135–2136 (1968). [CrossRef]
3. H. Ahn, H. Song, J. R. Choi, and K. Kim, “A Localized Surface Plasmon Resonance Sensor Using Double-Metal-Complex Nanostructures and a Review of Recent Approaches,” Sensors 18(2), 98 (2017). [CrossRef]
4. S. Zeng, K. V. Sreekanth, J. Shang, T. Yu, C. K. Chen, F. Yin, D. Baillargeat, P. Coquet, H. P. Ho, A. V. Kabashin, and K. T. Yong, “Graphene–Gold Metasurface Architectures for Ultrasensitive Plasmonic Biosensing,” Adv. Mater. 27(40), 6163–6169 (2015). [CrossRef]
5. G. Wang, C. Wang, R. Yang, W. Liu, and S. Sun, “A Sensitive and Stable Surface Plasmon Resonance Sensor Based on Monolayer Protected Silver Film,” Sensors 17(12), 2777 (2017). [CrossRef]
6. S. Zeng, D. Baillargeat H, P. Hod, and K. T. Yong, “Nanomaterials Enhanced Surface Plasmon Resonance for Biological and Chemical Sensing Applications,” Chem. Soc. Rev. 43(10), 3426–3452 (2014). [CrossRef]
7. L. He, Y. Guo, Z. Han, K. Wada, J. Michel, A. M. Agarwal, L. C. Kimerling, G. Li, and L. Zhang, “Broadband Athermal Waveguides and Resonators for Datacom and Telecom Applications,” Photonics Res. 6(11), 987–990 (2018). [CrossRef]
8. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano Resonance in Plasmonic Nanostructures and Metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef]
9. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano Resonances in Nanoscale Structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]
10. S. Hayashi, D. V. Nesterenko, and Z. Sekkat, “Fano Resonance and Plasmon-Induced Transparency in Waveguide-Coupled Surface Plasmon Resonance Sensors,” Appl. Phys. Express 8(2), 022201 (2015). [CrossRef]
11. S. Hayashi, D. V. Nesterenko, and Z. Sekkat, “Waveguide-Coupled Surface Plasmon Resonance Sensor Structures: Fano Lineshape Engineering for Ultrahigh-Resolution Sensing,” J. Phys. D: Appl. Phys. 48(32), 325303 (2015). [CrossRef]
12. D. V. Nesterenko, S. Hayashi, and Z. Sekkat, “Extremely Narrow Resonances, Giant Sensitivity and Field Enhancement in Low-Loss Waveguide Sensors,” J. Opt. 18(6), 065004 (2016). [CrossRef]
13. L. Wu, J. Guo, H. Xu, X. Dai, and Y. Xiang, “Ultrasensitive Biosensors Based on Long-Range Surface Plasmon Polariton and Dielectric Waveguide Modes,” Photonics Res. 4(6), 262–266 (2016). [CrossRef]
14. G. Zheng, J. Cong, L. Xu, and J. Wang, “High-Resolution Surface Plasmon Resonance Sensor with Fano Resonance in Waveguide-Coupled Multilayer Structures,” Appl. Phys. Express 10(4), 042202 (2017). [CrossRef]
15. S. Hayashi, Y. Fujiwara, B. Kang, M. Fujii, D. V. Nesterenko, and Z. Sekkat, “Line Shape Engineering of Sharp Fano Resonance in Al-Based Metal-Dielectric Multilayer Structure,” J. Appl. Phys. 122(16), 163103 (2017). [CrossRef]
16. T. Huang, S. Zeng, X. Zhao, Z. Cheng, and P. P. Shum, “Fano Resonance Enhanced Surface Plasmon Resonance Sensors Operating in Near-Infrared,” Photonics 5(3), 23 (2018). [CrossRef]
17. L. Li, T. Huang, X. Zhao, X. Wu, and Z. Cheng, “Highly Sensitive SPR Sensor Based on Hybrid Coupling Between Plasmon and Photonic Mode,” IEEE Photonics Technol. Lett. 30(15), 1364–1367 (2018). [CrossRef]
18. Z. Sekkat, S. Hayashi, D. V. Nesterenko, A. Rahmouni, S. Refki, H. Ishitobi, Y. Inouye, and S. Kawata, “Plasmonic Coupled Modes in Metal-Dielectric Multilayer Structures: Fano Resonance and Giant Field Enhancement,” Opt. Express 24(18), 20080–20088 (2016). [CrossRef]
19. L. Yang, J. Wang, L. Yang, Z. Hu, X. Wu, and G. Zheng, “Characteristics of Multiple Fano Resonances in Waveguide-coupled Surface Plasmon Resonance Sensors based on Waveguide Theory,” Sci. Rep. 8(1), 2560 (2018). [CrossRef]
20. H. Yang, Z. Li, K. Liu, H. Mao, C. Song, and J. Wang, “Systematic Evolution of Resonant Coupling Behavior Between Surface Plasmon Polaritons and Multi-waveguide Modes in Metal-Dielectric Multi-layers,” Plasmonic 35, (2020).
21. A. Arbabi and L. L. Goddard, “Measurements of the Refractive Indices and Thermo-Optic Coefficients of Si3N4 and SiOx Using Microring Resonances,” Opt. Lett. 38(19), 3878–3888 (2013). [CrossRef]
22. A. W. Elshaari, I. E. Zadeh, K. D. Jons, and V. Zwiller, “Thermo-Optic Characterization of Silicon Nitride Resonators for Cryogenic Photonic Circuits,” IEEE Photonics J. 8(3), 1–9 (2016). [CrossRef]
23. B. Guha, J. Cardenas, and M. Lipson, “Athermal Silicon Microring Resonators with Titanium Oxide Cladding,” Opt. Express 21(22), 26557–26563 (2013). [CrossRef]
24. Y. Ma, M. Eldlio, H. Maeda, J. Zhou, and M. Cada, “Plasmonic Properties of Superconductor–Insulator–Superconductor Waveguide,” Appl. Phys. Express 9(7), 072201 (2016). [CrossRef]
25. X. C. Long and S. R. J. Brueck, “Composition Dependence of the Photoinduced Refractive-Index Change in Lead Silicate Glasses,” Opt. Lett. 24(16), 1136–1138 (1999). [CrossRef]
26. T. Toyoda and M. Yabe, “The Temperature Dependence of The Refractive Indices of SrTiO3 and TiO2,” J. Phys. D: Appl. Phys. 16(12), L251–L255 (1983). [CrossRef]
27. J. Bauer, “Optical Properties, Band Gap, and Surface Roughness of Si3N4,” Phys. Stat. Sol. (a) 39(2), 411–418 (1977). [CrossRef]
28. G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-Dependent Sellmeier Coefficients and Chromatic Dispersions for Some Optical Fiber Glasses,” J. Lightwave Technol. 12(8), 1338–1342 (1994). [CrossRef]
29. C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling Effects in Single-Mode and Multimode Resonator-Coupled System,” Opt. Express 27(13), 17718–17728 (2019). [CrossRef]
30. X. He, P. Gao, and W. Shi, “A Further Comparison of Graphene and Thin Metal Layers for Plasmonics,” Nanoscale 8(19), 10388–10397 (2016). [CrossRef]
31. Z. Cao, X. Ji, R. Wang, Z. Zhang, T. Shui, F. Xu, and B. Yu, “Compact Fiber Sensor With High Spatial Resolution for Simultaneous Strain and Temperature Measurement,” IEEE Sensors J. 13(5), 1447–1451 (2013). [CrossRef]
32. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber Grating Sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997). [CrossRef]
