Abstract

High-sensitivity complex refractive index sensing is proposed and experimentally demonstrated, favoring with sharp Fano resonance at 1550 nm wavelength based on subwavelength grating waveguide (SWG) micro-ring resonator. The micro-ring is composed by trapezoidal silicon pillars with subwavelength period to enhance the light-analyte overlap and get high quality factor as well. One straight SWG waveguide is side coupled with the micro-ring, which is specially designed to produce partial Fabry-Perot (FP) effect. Due to the interaction of resonant state of micro-ring and partial FP effect in straight waveguide, a sharp asymmetrical Fano resonance is formed at 1550 nm wavelength. Benefit from the large light-analyte overlap of the SWG waveguide structure and the sharp asymmetrical Fano resonance in spectrum, high theoretical sensitivities of 366 nm/RIU and 9700/RIU can be realized for the real part (n) and the imaginary part (κ) of refractive index respectively. We also experimentally demonstrate the sensing for glucose solution concentrations, and high experimental sensitivity of 363nm/RIU is obtained for n, and for κ the experimental results are also in well agreement with the simulation results.

© 2017 Optical Society of America

1. Introduction

On-chip integrated optical resonant cavities for sensing applications have drawn great interests in recent years [1–3]. Benefit from their high Q factors and small mode volumes [4], which contribute to generating a considerable evanescent field and significantly enhancing the interaction between the light and material [5], high sensitivity and low detection limit sensing can be achieved. As we know, the conventional sensing mechanism of optical resonant cavities is based on the detection of the real part of the refractive index [6]. In this case, the cavity resonance wavelength would shift along with the changing of the analyte’s refractive index real part [7]. If a multi-element mixture detection is wanted, then a cavity array has to be used. Each of the cavity in the array need to be immobilized with a specific functional group to detect the corresponding element in the mixture, which is very complex and inefficient for bio/chemical sensing. To achieve multi-element mixture detection without the surface immobilization of functional groups, complex refractive index sensing has been proposed [6]. However, the sensitivity is not very high in the previous work [6].

In this paper, we proposed a new method to achieve ultra-high sensitivity for complex refractive index sensing based on the sharp asymmetric Fano resonance line shape in a subwavelength grating waveguide micro-ring resonator (SWGMR) structure [8]. The resonator includes a micro-ring and a straight waveguide side coupled with it, both are composed by SWG structures. A large amount of mode field of the SWG structure is located in the low index air gap [9, 10], which could greatly enhance its overlap with the filling analyte for bio/chemical sensing [11–13]. The straight SWG is specially designed to form partial FP effect. Due to the interference of micro-ring resonant mode and the straight waveguide partial FP mode, a sharp asymmetric Fano resonance appears [14, 15], which is different from the conventional symmetric Lorentzian resonance line shape [16]. The extremely steep slope of the Fano resonance would have an obvious advantage for high sensitivity and low detection limit in sensing application field [17–19]. Combining these two special advantages of SWGMR structure, we designed and fabricated a high-sensitivity complex refractive index sensor. The real part and imaginary part of refractive index are separately determined by the wavelength shift and the slope variations of Fano resonance. The theoretical sensitivities of the complex refractive index’s real part and imaginary part are ~366nm/RIU and ~9700/RIU, respectively. The experiments of detecting glucose solution concentrations have been done to demonstrate the ultrahigh sensitivities of the proposed structure.

2. Structure and principle

The subwavelength grating waveguide (SWG) is composed by high and low refractive index materials arranged alternatively in space with subwavelength period, as shown in Fig. 1. The space period should be smaller than half of the effective wavelength in waveguide to suppress the diffraction effect [9]. Due to the freedom of tuning the filling ratio f and the period Λ, its optical properties, such as effective refractive index, loss and dispersion, can be tailored smartly as will.

 

Fig. 1 The sketch of the SWG structure, nsub is the index of the substrate, n1 and n2 refer to the high and low indexes, Λ is the space period, and f is the filling ratio of the high index medium.

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Subwavelength grating waveguide-based micro-ring resonator (SWGMR) is a promising platform for enhance light-material interactions, due to the resonance of ring resonator and the enhanced field overlap with low index analyte. Here in our work, we well design the SWGMR to cooperate the ring resonance and a partial Fabry-Perot effect together, which can generate a Fano resonance near 1550nm wavelength in the transmission spectrum. In order to reduce the bending loss of micro-ring and obtain a high quality factor, we design the SWGMR’s ring component with trapezoidal silicon pillars [20].

Our SWGMR structure is designed based on silicon-on-insulator (SOI) wafer with 220 nm thick top silicon layer. We assume that the structure is covered by deionized water with refractive index of 1.333. The 3D schematic of SWGMR with trapezoidal silicon pillars is shown in Fig. 2. The SWGMR’s ring component is built with trapezoidal silicon pillars to increase the quality factor (Q), while the SWG bus waveguide is still built with rectangular silicon pillars.

 

Fig. 2 The 3D schematic of SWGMR with trapezoidal silicon pillars.

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The structural parameters of the SWGMR is labeled in Fig. 3. As shown in Fig. 3, the bus waveguide and the ring have the same width, denoted as W. We choose W = 500 nm so that the SWG waveguides can only support fundamental TE0 mode. For the straight SWG bus waveguide, Λ=360nm and f=0.7 are optimized to generate Fabry-Perot effect at 1550 nm wavelength. For the trapezoidal silicon pillars forming the ring, every pillar has outer width LT = 220 nm and inner width LB = 280 nm. LT and LB have been optimized according to two aspects. First, mode effective index matching should be satisfied between the micro-ring (based on trapezoidal silicon pillars) and the bus waveguide (based on rectangular silicon pillars). Second, the bending loss of micro-ring should be reduced to obtain a high quality factor. The radius of the SWGMR is R = 5.042 μm, and the number of the trapezoidal silicon pillars is 88. The edge-to-edge gap between the SWG bus waveguide and the SWG ring waveguide is optimized to be g = 400nm to obtain an appropriate coupling strength. The intrinsic quality factor (Q value) of the subwavelength grating waveguide micro-ring is calculated to be ~12900 by numerical simulation.

 

Fig. 3 (a) Top view of the SWGMR, which radius is R; (b) Magnified view of the coupling region, marked by doted block in (a). The gap between the SWGMR and the bus waveguide is g. The trapezoidal and rectangular SWGs have same width of w. The filling ratio and period of rectangular SWG are f and Λ; (c) The structure parameters of trapezoidal silicon pillars, which top and bottom widths are LB and LT respectively.

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Now, we will explain how to get a sharp asymmetrical Fano resonance at 1550 nm wavelength with the proposed SWGMR. As mentioned before, light can propagate with no reflection or diffraction in the SWG waveguide only under the diffraction free condition2neffΛ<<λ, where neff is the modal effective refractive index of the waveguide, Λ is the period of the grating, and λ is the vacuum wavelength. However, if we slightly enlarge the period Λ of SWG in the bus waveguide, partial Fabry-Perot reflection could be introduced near 1550 nm wavelength. In this case the SWG structure acts as a partially reflecting element at the two ports of the bus waveguide. When this kind bus waveguide couples with a cavity, shown in the Fig. 4, the FP resonant mode will interfere with the cavity mode, and therefore leads to a sharp asymmetric Fano resonance in output spectrum [15].

 

Fig. 4 The mechanism of Fano resonance formation in the system of a cavity couple with a partially reflecting bus waveguide.

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In order to verify the partially reflecting effect in the SWG bus waveguide, we simulated its transmission spectrum with 3D Finite-Difference-Time-Domain (FDTD) method [21]. For comparison, we also simulated another SWG bus waveguide with a different grating period but the same duty circle (Λ=250nm,η=0.7) .The simulation results are shown in Fig. 5. From Fig. 5(a), it is obvious that the SWG waveguide with Λ=360nmhas a Fabry-Perot effect at wavelength range of 1500~1600nm, but that with Λ=250nmhas not. Figure 5(b) shows the further details. The propagation field distributions in these two SWGs for 1.55μm wavelength are also shown in Figs. 5(c) and 5(d).

 

Fig. 5 The transmission spectra are shown in (a) large wavelength range from 1200~2000nm and (b) enlarge view in small wavelength range from 1500~1600nm. Black line refers to a SWG stripe waveguide with Λ = 250nm, f = 0.7, and red line refers to a SWG stripe waveguide with Λ = 360nm, f = 0.7; (c) The light field distribution of the SWG stripe waveguide with Λ = 250nm, f = 0.7; (d) the light field distribution of the SWG stripe waveguide with Λ = 360nm, f = 0.7.

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3. Simulation and analysis

The transmission spectrum of the SWGMR was simulated by 3D FDTD method. We assume the SWGMR is covered by deionized water with complex refractive index n = 1.333, which imaginary part is set to be 0 for simplify the theoretical analysis. In the calculated spectrum, a Fano resonance with very steep slope appears near 1550nm wavelength, as shown in Fig. 6. For further analysis, we define several key parameters firstly. The parameters λpeak and λdip are the peak and dip wavelengths for the Fano resonance, respectively. Imax and Imin are the normalized transmission at wavelengths ofλpeak and λdip respectively. A parameter V is introduced to evaluate the fringe visibility [22] between the peak and dip intensity, defined as:

V=ImaxIminImax+Imin.
The wavelength difference between the peak and dip is
D(λ)=|λdipλpeak|.
In our work, the slope of the Fano resonance in the green area is characterized by the P value defined below:

 

Fig. 6 The transmission spectrum when our SWGMR is immersed in the deionized water environment.

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P=VD(λ).

To study the complex refractive index sensing properties of the Fano resonance in our SWGMR, we arrange our simulation steps as follows. Firstly, the real part of the refractive index is varied as five values of n = 1.333, 1.3355, 1.338, 1.3405 and 1.343, and their transmission spectrums are plotted in the Fig. 7(a). It is clear that the resonant wavelength shifts when the real part of the complex refractive index changes, and the overall spectrum shape is similar. There is a perfectly linear relation between the Fano wavelength shift and the refractive index change, as shown in Fig. 8(a). The sensitivity of the refractive index real part can be calculated as below:

Sn=ΔλΔn=366nm/RIU
Secondly, we keep the real part of the refractive index as 1.333 but change the imaginary part from κ = 0 toκ=1×103 RIU, with an increasing step of 2.5×104RIU. The simulated spectra are shown in Fig. 7(b), which the resonant wavelength does not shift but the slope of Fano resonance becomes smaller when the imaginary part of index increases. According to Eq. (3) mentioned before, the slope evaluation parameter P is calculated and plotted in Fig. 8(b). The P value exhibits an exponential declining trend as κ increases. Then we redefine a new parameter F:
F=10log(P)
The relationship between F and κ is plotted in the Fig. 8(c), which shows a perfect linear decreasing trend. From a linear fitting, we can calculate the sensitivity for κ as follow:

 

Fig. 7 (a) Transmission spectra when κ = 0 and n varies; (b) Transmission spectra when n = 1.333 and κ varies.

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Fig. 8 (a) Resonant wavelength shifts with the variation of n and the linear fit; (b) The relationship between P value and κ, and the exponential fit; (c) The relationship between F value and κ, as well as the linear fit.

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Sκ=ΔFΔκ=9700/RIU

By analyzing the data obtained from the Fig. 7(a), the effect of n on the F value can be calculated to be ~29.25/RIU, which is rather small and could be ignored compared with the sensitivity of κ (~9700/RIU). So in a certain range of sensing, the Fano resonance’s slope is mainly depending on the value of κ. And from the Fig. 7(b), we can obviously see that the Fano resonant wavelength remains nearly unchanged when only κ changes while n not. It explains that the complex refractive index sensing (n and κ) characterized by the resonance wavelength and slope of the Fano spectrum is reasonable.

Then the theoretical limit of detection (LOD) have been studied. Such as the above results, the sensitivity of n is 366 nm/RIU. Accounting for the wavelength resolution of the optical spectrometer is 0.02 nm, the LOD of the sensing for n can be evaluated as:

LODn=0.02nm366nm/RIU=5.4645×105RIU
For κ, the detection limit is depended on the errors caused by n. We assume that the variation of the F caused by κ should be one order of magnitude larger than the errors of caused by the n, so the LOD of the sensing for κ could be roughly evaluated as:

LODκ=(29.25/RIU)10LODn9700/RIU=1.6478×106RIU

4. Device fabrication and sensing experiment

4.1 Fabrication process

The devices were fabricated on the commercial silicon-on-insulator (SOI) wafer with 220 nm thick top silicon layer and 2 μm thick under cladding SiO2 layer. At first, the device structures were transferred to the ZEP520A resist by electron-beam lithography using a Vistec EBPG 5000 + system. Then inductively coupled plasma reactive ion etching (ICP-RIE) with SF6 and C4F8 chemistry was used to transfer the pattern to the upper silicon layer of SOI wafer. All the devices and test structures, including the grating couplers, were fabricated with a single etching process. Figure 9 shows the scanning electron microscope (SEM) images of the device. Figure 9(a) is the grating coupler, Fig. 9(b) is the taper structure to connect traditional stripe waveguide and the SWG waveguide with a very low loss. The ring section which is composed of trapezoidal silicon pillars is shown in Fig. 9(c), and the magnified view of the gap region between ring and bus waveguide is shown in the Fig. 9(d). The parameters of the fabricated device is the same as what we described in the section 2.

 

Fig. 9 SEM images of the fabricated SWGMR device. (a) Grating coupler; (b) Taper structure connecting traditional stripe waveguide and SWG; (c) SWG micro-ring resonator; (d) Magnified view of the gap region between the ring and bus waveguide.

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4.2 Sensing experiment

The sensing experiment setup is shown in Fig. 10. The light output from the ASE light source passes through a polarization controller (PC), which can tune the polarization to TE before coupling into the device. Two vertically positioned single-mode fibers are aligned with the grating couplers on chip to couple light in and out from the device. Then a 3dB splitter is used to send the output light into the optical spectrum analyzer (OSA) and the optical power meter as well. The precise alignment of the optical fiber and the grating coupler is achieved by using a waveguide alignment stage. The microscope, CCD and monitor system can help us to make alignment, and the spectrum of the device is measured by the OSA.

 

Fig. 10 The setup of the sensing experiment system.

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In order to get the sensing performance of our devices, we immerse our device in glucose solutions and test the spectrum. Deionized water and glucose solutions with different concentrations of 2 g/100ml, 4 g/100ml, 6 g/100ml, 8 g/100ml and 10 g/100ml have been prepared. The measured transmission spectra of the SWGMR device in deionized water and glucose solutions are shown in Fig. 11. From Fig. 11, clear Fano resonance peaks can be found near 1550 nm wavelength in all cases. For better comparison, the experiment results have been consolidated in a single panel, and the transmission spectra of Figs. 11(b)-11(f) have been moved downward by step of −25dBm.

 

Fig. 11 Experimental transmission spectra of the SWGMR device immersed in (a) deionized water and (b)-(f) different concentrations of glucose solutions. For better comparison, the transmission spectra of (b)-(f) have been moved downward by step of −25dBm.

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To get more details, we have analyzed the experimental data. Firstly, the peak wavelength of Fano resonance shifts linearly with glucose concentration changes, as shown in Fig. 12(a). From the refractive index data for different concentrations of glucose solutions in [23], the sensitivity of n is calculated to be Sn = 363 nm/RIU. Secondly, the P values (defined in the Eq. (3)) of the Fano resonance are shown in Fig. 12(b). The P value really shows an exponential decreasing with the glucose concentration increasing. Then the F values are calculated by Eq. (4) and shown in Fig. 12(c), which decreases approximately linearly with the increase of the glucose concentration. Although we cannot get the κ values of glucose solutions with different concentrations from the literatures to calculate the experimental sensitivity for κ, the experimental results are coincide well with the theoretical analysis before.

 

Fig. 12 Experimental sensing data analysis. (a) Resonant wavelength shifts with the variation of glucose solution’s concentration and the linear fit; (b) The relationship between the P value and the glucose solution’s concentration and the exponential fit; (c) The relationship between the F value and the glucose solution’s concentration and the linear fit.

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5. Conclusion

In conclusion, we have proposed a subwavelength grating waveguide micro-ring resonator based on SOI wafer, which can produce a sharp asymmetrical Fano resonance near 1550 nm wavelength. Benefit from the large field localization in low index region of the SWG waveguide structure and the sharp asymmetrical Fano resonance of the proposed SWGMR, a high-sensitivity is achieved for complex refractive index sensing. The theoretical sensitivities of the real part n and imaginary part κ of refractive index are ~366nm/RIU and ~9700/RIU, respectively. High experimental sensitivity of 363nm/RIU for n has been demonstrated for sensing glucose solution concentration. The Fano slope evaluation parameter P values have exponential decreasing relation with the increasing of κ, which are also in agreement with the simulation results. We believe our proposed Fano resonance in SWGMR has great potential in future high sensitivity bio/chemical sensing.

Funding

National Natural Science Foundation of China (NSFC) (11374115, 61261130586); National Key Research and Development Program of China (2016YFB0402503); National High Technology Research and Development Program of China (2015AA017101); Opened Fund of the State Key Laboratory on Integrated Optoelectronics (IOSKL2015KF38).

References and links

1. A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008). [CrossRef]   [PubMed]  

2. T. Ling, S.-L. Chen, and L. J. Guo, “Fabrication and characterization of high Q polymer micro-ring resonator and its application as a sensitive ultrasonic detector,” Opt. Express 19(2), 861–869 (2011). [CrossRef]   [PubMed]  

3. 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]  

4. A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006). [CrossRef]  

5. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef]   [PubMed]  

6. X. Zhang, G. Zhou, P. Shi, H. Du, T. Lin, J. Teng, and F. S. Chau, “On-chip integrated optofluidic complex refractive index sensing using silicon photonic crystal nanobeam cavities,” Opt. Lett. 41(6), 1197–1200 (2016). [CrossRef]   [PubMed]  

7. T. Li, D. Gao, D. Zhang, and E. Cassan, “High-Q and high-sensitivity one-dimensional photonic crystal slot nanobeam cavity sensors,” IEEE Photonics Technol. Lett. 28(6), 689–692 (2016). [CrossRef]  

8. V. Donzella, A. Sherwali, J. Flueckiger, S. M. Grist, S. T. Fard, and L. Chrostowski, “Design and fabrication of SOI micro-ring resonators based on sub-wavelength grating waveguides,” Opt. Express 23(4), 4791–4803 (2015). [CrossRef]   [PubMed]  

9. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010). [CrossRef]   [PubMed]  

10. V. Donzella, A. Sherwali, J. Flueckiger, S. Talebi Fard, S. M. Grist, and L. Chrostowski, “Sub-wavelength grating components for integrated optics applications on SOI chips,” Opt. Express 22(17), 21037–21050 (2014). [CrossRef]   [PubMed]  

11. J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014). [CrossRef]   [PubMed]  

12. H. Yan, L. Huang, X. Xu, S. Chakravarty, N. Tang, H. Tian, and R. T. Chen, “Unique surface sensing property and enhanced sensitivity in microring resonator biosensors based on subwavelength grating waveguides,” Opt. Express 24(26), 29724–29733 (2016). [CrossRef]   [PubMed]  

13. J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, “Sub-wavelength grating for enhanced ring resonator biosensor,” Opt. Express 24(14), 15672–15686 (2016). [CrossRef]   [PubMed]  

14. U. Fano, “Effects of configuration interaction on the intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]  

15. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002). [CrossRef]  

16. P. Xu, K. Yao, J. Zheng, X. Guan, and Y. Shi, “Slotted photonic crystal nanobeam cavity with parabolic modulated width stack for refractive index sensing,” Opt. Express 21(22), 26908–26913 (2013). [CrossRef]   [PubMed]  

17. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003). [CrossRef]  

18. H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010). [CrossRef]   [PubMed]  

19. L. Huang, H. Yan, X. Xu, S. Chakravarty, N. Tang, H. Tian, and R. T. Chen, “Improving the detection limit for on-chip photonic sensors based on subwavelength grating racetrack resonators,” Opt. Express 25(9), 10527–10535 (2017). [CrossRef]   [PubMed]  

20. Z. Wang, X. Xu, D. Fan, Y. Wang, and R. T. Chen, “High quality factor subwavelength grating waveguide micro-ring resonator based on trapezoidal silicon pillars,” Opt. Lett. 41(14), 3375–3378 (2016). [CrossRef]   [PubMed]  

21. F. D. T. D. Solutions, Lumerical Solutions, Inc, http://www.lumerical.com.

22. A. C. Ruege and R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17(6), 4295–4305 (2009). [CrossRef]   [PubMed]  

23. Y. L. Yeh, “Real-time measurement of glucose concentration and average refractive index using a laser interferometer,” Opt. Lasers Eng. 46(9), 666–670 (2008). [CrossRef]  

References

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  1. A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
    [Crossref] [PubMed]
  2. T. Ling, S.-L. Chen, and L. J. Guo, “Fabrication and characterization of high Q polymer micro-ring resonator and its application as a sensitive ultrasonic detector,” Opt. Express 19(2), 861–869 (2011).
    [Crossref] [PubMed]
  3. 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]
  4. A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
    [Crossref]
  5. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
    [Crossref] [PubMed]
  6. X. Zhang, G. Zhou, P. Shi, H. Du, T. Lin, J. Teng, and F. S. Chau, “On-chip integrated optofluidic complex refractive index sensing using silicon photonic crystal nanobeam cavities,” Opt. Lett. 41(6), 1197–1200 (2016).
    [Crossref] [PubMed]
  7. T. Li, D. Gao, D. Zhang, and E. Cassan, “High-Q and high-sensitivity one-dimensional photonic crystal slot nanobeam cavity sensors,” IEEE Photonics Technol. Lett. 28(6), 689–692 (2016).
    [Crossref]
  8. V. Donzella, A. Sherwali, J. Flueckiger, S. M. Grist, S. T. Fard, and L. Chrostowski, “Design and fabrication of SOI micro-ring resonators based on sub-wavelength grating waveguides,” Opt. Express 23(4), 4791–4803 (2015).
    [Crossref] [PubMed]
  9. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
    [Crossref] [PubMed]
  10. V. Donzella, A. Sherwali, J. Flueckiger, S. Talebi Fard, S. M. Grist, and L. Chrostowski, “Sub-wavelength grating components for integrated optics applications on SOI chips,” Opt. Express 22(17), 21037–21050 (2014).
    [Crossref] [PubMed]
  11. J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
    [Crossref] [PubMed]
  12. H. Yan, L. Huang, X. Xu, S. Chakravarty, N. Tang, H. Tian, and R. T. Chen, “Unique surface sensing property and enhanced sensitivity in microring resonator biosensors based on subwavelength grating waveguides,” Opt. Express 24(26), 29724–29733 (2016).
    [Crossref] [PubMed]
  13. J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, “Sub-wavelength grating for enhanced ring resonator biosensor,” Opt. Express 24(14), 15672–15686 (2016).
    [Crossref] [PubMed]
  14. U. Fano, “Effects of configuration interaction on the intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
    [Crossref]
  15. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
    [Crossref]
  16. P. Xu, K. Yao, J. Zheng, X. Guan, and Y. Shi, “Slotted photonic crystal nanobeam cavity with parabolic modulated width stack for refractive index sensing,” Opt. Express 21(22), 26908–26913 (2013).
    [Crossref] [PubMed]
  17. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
    [Crossref]
  18. H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010).
    [Crossref] [PubMed]
  19. L. Huang, H. Yan, X. Xu, S. Chakravarty, N. Tang, H. Tian, and R. T. Chen, “Improving the detection limit for on-chip photonic sensors based on subwavelength grating racetrack resonators,” Opt. Express 25(9), 10527–10535 (2017).
    [Crossref] [PubMed]
  20. Z. Wang, X. Xu, D. Fan, Y. Wang, and R. T. Chen, “High quality factor subwavelength grating waveguide micro-ring resonator based on trapezoidal silicon pillars,” Opt. Lett. 41(14), 3375–3378 (2016).
    [Crossref] [PubMed]
  21. F. D. T. D. Solutions, Lumerical Solutions, Inc, http://www.lumerical.com .
  22. A. C. Ruege and R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17(6), 4295–4305 (2009).
    [Crossref] [PubMed]
  23. Y. L. Yeh, “Real-time measurement of glucose concentration and average refractive index using a laser interferometer,” Opt. Lasers Eng. 46(9), 666–670 (2008).
    [Crossref]

2017 (1)

2016 (5)

2015 (1)

2014 (2)

2013 (1)

2011 (2)

T. Ling, S.-L. Chen, and L. J. Guo, “Fabrication and characterization of high Q polymer micro-ring resonator and its application as a sensitive ultrasonic detector,” Opt. Express 19(2), 861–869 (2011).
[Crossref] [PubMed]

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]

2010 (2)

2009 (1)

2008 (2)

Y. L. Yeh, “Real-time measurement of glucose concentration and average refractive index using a laser interferometer,” Opt. Lasers Eng. 46(9), 666–670 (2008).
[Crossref]

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

2006 (1)

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

2003 (2)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

2002 (1)

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

1961 (1)

U. Fano, “Effects of configuration interaction on the intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Aers, G. C.

Alonso-Ramos, C.

Bock, P. J.

Cassan, E.

T. Li, D. Gao, D. Zhang, and E. Cassan, “High-Q and high-sensitivity one-dimensional photonic crystal slot nanobeam cavity sensors,” IEEE Photonics Technol. Lett. 28(6), 689–692 (2016).
[Crossref]

Chakravarty, S.

Chao, C.-Y.

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

Chau, F. S.

Cheben, P.

Chen, R. T.

Chen, S.-L.

Chen, W.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Cheung, K. C.

Chrostowski, L.

Chu, S. T.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Citrin, D. S.

Clarke, J.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Delâge, A.

Densmore, A.

Donzella, V.

Du, H.

Fan, D.

Fan, S.

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

Fano, U.

U. Fano, “Effects of configuration interaction on the intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Fard, S. T.

Flood, E. M.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Flueckiger, J.

Gao, D.

T. Li, D. Gao, D. Zhang, and E. Cassan, “High-Q and high-sensitivity one-dimensional photonic crystal slot nanobeam cavity sensors,” IEEE Photonics Technol. Lett. 28(6), 689–692 (2016).
[Crossref]

Gill, D.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Goad, D.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Gonzalo Wangüemert-Pérez, J.

Grist, S. M.

Guan, X.

Guo, L. J.

T. Ling, S.-L. Chen, and L. J. Guo, “Fabrication and characterization of high Q polymer micro-ring resonator and its application as a sensitive ultrasonic detector,” Opt. Express 19(2), 861–869 (2011).
[Crossref] [PubMed]

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

Halir, R.

Hall, T. J.

He, J. J.

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]

Hryniewicz, J. V.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Huang, L.

Ilchenko, V.

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

Ja, S. J.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Janz, S.

Jin, L.

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]

King, O.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Knobbe, E.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Lapointe, J.

Li, M.

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]

Li, T.

T. Li, D. Gao, D. Zhang, and E. Cassan, “High-Q and high-sensitivity one-dimensional photonic crystal slot nanobeam cavity sensors,” IEEE Photonics Technol. Lett. 28(6), 689–692 (2016).
[Crossref]

Lin, T.

Ling, T.

Little, B. E.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Matsko, A.

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

Molina-Fernández, I.

Ortega-Moñux, A.

Pérez-Galacho, D.

Ramachandran, A.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Ratner, D. M.

Reano, R. M.

Ruege, A. C.

Schmid, J. H.

Schmidt, S.

Sherwali, A.

Shi, P.

Shi, Y.

Talebi Fard, S.

Tang, N.

Teng, J.

Tian, H.

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

Wald, L.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Wang, S.

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

Wang, Y.

Wang, Z.

Xu, D.-X.

Xu, P.

Xu, X.

Yan, H.

Yao, K.

Yeh, Y. L.

Y. L. Yeh, “Real-time measurement of glucose concentration and average refractive index using a laser interferometer,” Opt. Lasers Eng. 46(9), 666–670 (2008).
[Crossref]

Yi, H.

Zhang, D.

T. Li, D. Gao, D. Zhang, and E. Cassan, “High-Q and high-sensitivity one-dimensional photonic crystal slot nanobeam cavity sensors,” IEEE Photonics Technol. Lett. 28(6), 689–692 (2016).
[Crossref]

Zhang, X.

Zheng, J.

Zhou, G.

Zhou, Z.

Appl. Phys. Lett. (2)

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

Biosens. Bioelectron. (1)

A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008).
[Crossref] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Matsko and V. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (1)

T. Li, D. Gao, D. Zhang, and E. Cassan, “High-Q and high-sensitivity one-dimensional photonic crystal slot nanobeam cavity sensors,” IEEE Photonics Technol. Lett. 28(6), 689–692 (2016).
[Crossref]

Nature (1)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

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]

Opt. Express (10)

A. C. Ruege and R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17(6), 4295–4305 (2009).
[Crossref] [PubMed]

T. Ling, S.-L. Chen, and L. J. Guo, “Fabrication and characterization of high Q polymer micro-ring resonator and its application as a sensitive ultrasonic detector,” Opt. Express 19(2), 861–869 (2011).
[Crossref] [PubMed]

V. Donzella, A. Sherwali, J. Flueckiger, S. M. Grist, S. T. Fard, and L. Chrostowski, “Design and fabrication of SOI micro-ring resonators based on sub-wavelength grating waveguides,” Opt. Express 23(4), 4791–4803 (2015).
[Crossref] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
[Crossref] [PubMed]

V. Donzella, A. Sherwali, J. Flueckiger, S. Talebi Fard, S. M. Grist, and L. Chrostowski, “Sub-wavelength grating components for integrated optics applications on SOI chips,” Opt. Express 22(17), 21037–21050 (2014).
[Crossref] [PubMed]

H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010).
[Crossref] [PubMed]

L. Huang, H. Yan, X. Xu, S. Chakravarty, N. Tang, H. Tian, and R. T. Chen, “Improving the detection limit for on-chip photonic sensors based on subwavelength grating racetrack resonators,” Opt. Express 25(9), 10527–10535 (2017).
[Crossref] [PubMed]

P. Xu, K. Yao, J. Zheng, X. Guan, and Y. Shi, “Slotted photonic crystal nanobeam cavity with parabolic modulated width stack for refractive index sensing,” Opt. Express 21(22), 26908–26913 (2013).
[Crossref] [PubMed]

H. Yan, L. Huang, X. Xu, S. Chakravarty, N. Tang, H. Tian, and R. T. Chen, “Unique surface sensing property and enhanced sensitivity in microring resonator biosensors based on subwavelength grating waveguides,” Opt. Express 24(26), 29724–29733 (2016).
[Crossref] [PubMed]

J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, “Sub-wavelength grating for enhanced ring resonator biosensor,” Opt. Express 24(14), 15672–15686 (2016).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

Y. L. Yeh, “Real-time measurement of glucose concentration and average refractive index using a laser interferometer,” Opt. Lasers Eng. 46(9), 666–670 (2008).
[Crossref]

Opt. Lett. (3)

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on the intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Other (1)

F. D. T. D. Solutions, Lumerical Solutions, Inc, http://www.lumerical.com .

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Figures (12)

Fig. 1
Fig. 1 The sketch of the SWG structure, nsub is the index of the substrate, n1 and n2 refer to the high and low indexes, Λ is the space period, and f is the filling ratio of the high index medium.
Fig. 2
Fig. 2 The 3D schematic of SWGMR with trapezoidal silicon pillars.
Fig. 3
Fig. 3 (a) Top view of the SWGMR, which radius is R; (b) Magnified view of the coupling region, marked by doted block in (a). The gap between the SWGMR and the bus waveguide is g. The trapezoidal and rectangular SWGs have same width of w. The filling ratio and period of rectangular SWG are f and Λ; (c) The structure parameters of trapezoidal silicon pillars, which top and bottom widths are LB and LT respectively.
Fig. 4
Fig. 4 The mechanism of Fano resonance formation in the system of a cavity couple with a partially reflecting bus waveguide.
Fig. 5
Fig. 5 The transmission spectra are shown in (a) large wavelength range from 1200~2000nm and (b) enlarge view in small wavelength range from 1500~1600nm. Black line refers to a SWG stripe waveguide with Λ = 250nm, f = 0.7, and red line refers to a SWG stripe waveguide with Λ = 360nm, f = 0.7; (c) The light field distribution of the SWG stripe waveguide with Λ = 250nm, f = 0.7; (d) the light field distribution of the SWG stripe waveguide with Λ = 360nm, f = 0.7.
Fig. 6
Fig. 6 The transmission spectrum when our SWGMR is immersed in the deionized water environment.
Fig. 7
Fig. 7 (a) Transmission spectra when κ = 0 and n varies; (b) Transmission spectra when n = 1.333 and κ varies.
Fig. 8
Fig. 8 (a) Resonant wavelength shifts with the variation of n and the linear fit; (b) The relationship between P value and κ, and the exponential fit; (c) The relationship between F value and κ, as well as the linear fit.
Fig. 9
Fig. 9 SEM images of the fabricated SWGMR device. (a) Grating coupler; (b) Taper structure connecting traditional stripe waveguide and SWG; (c) SWG micro-ring resonator; (d) Magnified view of the gap region between the ring and bus waveguide.
Fig. 10
Fig. 10 The setup of the sensing experiment system.
Fig. 11
Fig. 11 Experimental transmission spectra of the SWGMR device immersed in (a) deionized water and (b)-(f) different concentrations of glucose solutions. For better comparison, the transmission spectra of (b)-(f) have been moved downward by step of −25dBm.
Fig. 12
Fig. 12 Experimental sensing data analysis. (a) Resonant wavelength shifts with the variation of glucose solution’s concentration and the linear fit; (b) The relationship between the P value and the glucose solution’s concentration and the exponential fit; (c) The relationship between the F value and the glucose solution’s concentration and the linear fit.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

V = I max I min I max + I min .
D ( λ ) = | λ d i p λ p e a k | .
P = V D ( λ ) .
S n = Δ λ Δ n = 366 nm / R I U
F = 10 log ( P )
S κ = Δ F Δ κ = 9700 / R I U
L O D n = 0.02 n m 366 n m / R I U = 5.4645 × 10 5 R I U
L O D κ = ( 29.25 / R I U ) 10 L O D n 9700 / R I U = 1.6478 × 10 6 R I U

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