# Refractive Index Sensor Based on a Metal–Insulator–Metal Waveguide Coupled with a Symmetric Structure

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{z}field with a perfectly matched layer absorbing boundary condition and was calculated by the finite element method. We varied the coupling distance between the stub and notched ring resonator, and the external diameter of the notched ring resonator and length of the stub to study its sensing characteristics and refractive index sensitivity.

## 2. Model and Analytical Method

_{0}mode) [31]. g represents both sides of the coupling distance between the stub and notched ring resonator. The inner diameter and external diameter of the notched ring resonator are r and R, respectively, while l represents the length of the stub.

^{−15}s, ${\epsilon}_{s}$ = −9530.5, and $\sigma $ = 1.1486 × 10

^{7}S/m are the infinite frequency permittivity, relaxation time, static permittivity, and conductivity of Ag, respectively. Although the dielectric parameters of silver were validated within 400–1200 nm, it is feasible to evaluate the Fano resonance of the MIM structure in this simulation experiment. COMSOL Multiphysics software based on the finite element method can be applied to solve the partial differential equation, and the transmission spectra of the coupling structure under different incident light frequencies can be obtained. The transmittance is defined as T = (S

_{21})

^{2}, where S

_{21}is the transmission coefficient from input to output (P

_{1}to P

_{2}) [28].

## 3. Results and Discussion

_{z}of the plasmonic waveguide-coupled system at ${\lambda}_{\mathrm{dip}}$ = 910 nm and ${\lambda}_{\mathrm{peak}}$ = 965 nm. In Figure 3a, a weak coupling at the right side of the MIM waveguide is shown and has no SPPs coupled to it. There is a clear in-phase relationship between the lower part of the notched ring resonator and stub, and the relationship between the higher part and lower part of the notched ring resonator is anti-phase in Figure 3b.

_{left}factor increases from 6 to 14 nm at intervals of 2 nm while keeping the g

_{right}= 10 nm as well to the right side. The transmittance spectra are as shown in Figure 5c,d. Furthermore, the effects on the Fano resonance of the asymmetric structure are similar to the symmetric structure.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Barnes, W.L.; Dereux, A.; Ebbesen, T.W. Surface plasmon subwavelength optics. Nature
**2003**, 424, 824–830. [Google Scholar] [CrossRef] [PubMed] - Zayats, A.V.; Smolyaninov, I.I.; Maradudin, A.A. Nano-optics of surface plasmon polaritons. Phys. Rep.
**2005**, 408, 131–314. [Google Scholar] [CrossRef] - Prasad, P.N. Nanophotonics; John Wiley & Sons: Hoboken, NJ, USA, 2004. [Google Scholar]
- Berini, P. Integrated Optics Based on Long-Range Surface Plasmon Polaritons. In Surface Plasmon Nanophotonics; Brongersma, M.L., Kik, P.G., Eds.; Springer: Berlin, Germany, 2007; pp. 217–233. [Google Scholar]
- Lu, H.; Liu, X.; Mao, D.; Wang, G. Plasmonic nanosensor based on fano resonance in waveguide-coupled resonators. Opt. Lett.
**2012**, 37, 3780–3782. [Google Scholar] [CrossRef] [PubMed] - Zhao, C.; Li, Y. Multiple fano resonances based on different waveguide modes in a symmetry breaking plasmonic system. IEEE Photonics J.
**1943**, 6, 1–8. [Google Scholar] - Wu, T.; Liu, Y.; Yu, Z.; Ye, H.; Shu, C.; Peng, Y.; Wang, J.; He, H. Tuning the fano resonances in a single defect nanocavity coupled with a plasmonic waveguide for sensing applications. Opt. Int. J. Light Electron Opt.
**2015**, 29, 1550218. [Google Scholar] - Gramotnev, D.K.; Bozhevolnyi, S.I. Plasmonics beyond the diffraction limit. Nat. Photonics
**2010**, 4, 83–91. [Google Scholar] [CrossRef] - Yin, Y.; Qiu, T.; Li, J.; Chu, P.K. Plasmonic nano-lasers. Nano Energy
**2012**, 1, 25–41. [Google Scholar] [CrossRef] - Zhou, N.; Ye, C.; Polavarapu, L.; Xu, Q.H. Controlled preparation of Au/Ag/SnO
_{2}core-shell nanoparticles using a photochemical method and applications in LSPR based sensing. Nanoscale**2015**, 7, 9025–9032. [Google Scholar] [CrossRef] [PubMed] - Ozbay, E. Plasmonics: Merging photonics and electronics at nanoscale dimensions. Science
**2006**, 311, 189. [Google Scholar] [CrossRef] [PubMed] - Xiao, S.; Liu, L.; Qiu, M. Resonator channel drop filters in a plasmon-polaritons metal. Opt. Express
**2006**, 14, 2932–2937. [Google Scholar] [CrossRef] [PubMed] - Lin, X.S.; Huang, X.G. Tooth-shaped plasmonic waveguide filters with nanometeric sizes. Opt. Lett.
**2008**, 33, 2874. [Google Scholar] [CrossRef] [PubMed] - Xiao, B.; Kong, S.; Gu, M. Parallel coupled filter based on spoof surface plasmon polaritons. In Proceedings of the International Conference on Optical Communications and Networks, Hangzhou, China, 24–27 September 2017; pp. 1–3. [Google Scholar]
- Fan, C.; Shi, F.; Wu, H.; Chen, Y. Tunable all-optical plasmonic diode based on fano resonance in nonlinear waveguide coupled with cavities. Opt. Lett.
**2015**, 40, 2449–2452. [Google Scholar] [CrossRef] [PubMed] - Hu, X.; Xin, C.; Li, Z.; Gong, Q. Ultrahigh-contrast all-optical diodes based on tunable surface plasmon polaritons. New J. Phys.
**2010**, 12, 023029. [Google Scholar] [CrossRef] - Krummacher, B.C.; Nowy, S.; Frischeisen, J.; Klein, M.; Brütting, W. Efficiency analysis of organic light-emitting diodes based on optical simulation. Org. Electron.
**2009**, 10, 478–485. [Google Scholar] [CrossRef] - Mao, D.; Lu, H.; Wang, L.; Liu, X.; Gong, Y. Ultrafast all-optical switching in nanoplasmonic waveguide with kerr nonlinear resonator. Opt. Express
**2011**, 19, 2910. [Google Scholar] - Wang, G.; Lu, H.; Liu, X.; Gong, Y. Numerical investigation of an all-optical switch in a graded nonlinear plasmonic grating. Nanotechnology
**2012**, 23, 444009. [Google Scholar] [CrossRef] [PubMed] - Li, Y.E.; Zhang, X.P. Nonlinear optical switch utilizing longrange surface plasmon polaritons. J. Electromagn. Waves Appl.
**2009**, 23, 2363–2371. [Google Scholar] - Zhang, Z.D.; Wang, H.Y.; Zhang, Z.Y. Fano resonance in a gear-shaped nanocavity of the metal–insulator–metal waveguide. Plasmonics
**2013**, 8, 797–801. [Google Scholar] [CrossRef] - Piao, X.; Yu, S.; Koo, S.; Lee, K.; Park, N. Fano-type spectral asymmetry and its control for plasmonic metal-insulator-metal stub structures. Opt. Express
**2011**, 19, 10907–10912. [Google Scholar] [CrossRef] [PubMed] - Yu, S.; Piao, X.; Hong, J.; Park, N. Progress toward high-Q perfect absorption: A Fano antilaser. Phys. Rev. A
**2015**, 92. [Google Scholar] [CrossRef] - Yan, X.; Wang, T.; Han, X.; Xiao, S.; Zhu, Y.; Wang, Y. High sensitivity nanoplasmonic sensor based on plasmon-induced transparency in a graphene nanoribbon waveguide coupled with detuned graphene square-nanoring resonators. Plasmonics
**2017**, 12, 1449–1455. [Google Scholar] [CrossRef] - Piao, X.; Yu, S.; Park, N. Control of Fano asymmetry in plasmon induced transparency and its application to plasmonic waveguide modulator. Opt. Express
**2012**, 20, 18994. [Google Scholar] [CrossRef] [PubMed] - Kulshreshtha, R.; Zafar, R. The sensing characteristics of plasmonic waveguide with rectangular stub and taper. In Proceedings of the International Conference on Recent Advances and Innovations in Engineering, Jaipur, India, 23–25 December 2017; pp. 1–4. [Google Scholar]
- Tang, Y.; Zhang, Z.; Wang, R.; Hai, Z.; Xue, C.; Zhang, W.; Zhang, W.; Yan, S. Refractive index sensor based on fano resonances in metal-insulator-metal waveguides coupled with resonators. Sensors
**2017**, 17, 784. [Google Scholar] [CrossRef] [PubMed] - Yun, J.G.; Kim, J.; Lee, K.; Lee, Y.; Lee, B. Numerical study on refractive index sensor based on hybrid-plasmonic mode. In Proceedings of the International Conference on Optical Fiber Sensors, Jeju, Korea, 24–28 April 2017. [Google Scholar]
- Zhao, X.; Zhang, Z.; Yan, S. Tunable fano resonance in asymmetric mim waveguide structure. Sensors
**2017**, 17, 1494. [Google Scholar] [CrossRef] [PubMed] - Zhang, Z.; Luo, L.; Xue, C.; Zhang, W.; Yan, S. Fano resonance based on metal-insulator-metal waveguide-coupled double rectangular cavities for plasmonic nanosensors. Sensors
**2016**, 16, 642. [Google Scholar] [CrossRef] [PubMed] - Kekatpure, R.D.; Hryciw, A.C.; Barnard, E.S.; Brongersma, M.L. Solving dielectric and plasmonic waveguide dispersion relations on a pocket calculator. Opt. Express
**2009**, 17, 24112–24129. [Google Scholar] [CrossRef] [PubMed] - Gai, H.; Wang, J.; Tian, Q. Modified debye model parameters of metals applicable for broadband calculations. Appl. Opt.
**2007**, 46, 2229–2233. [Google Scholar] [CrossRef] [PubMed] - Fano, U. Effects of configuration interaction on intensities and phase shifts. Phys. Rev.
**1961**, 124, 1866–1878. [Google Scholar] [CrossRef] - Mayer, K.M.; Hafner, J.H. Localized surface plasmon resonance sensors. Chem. Rev.
**2011**, 111, 3828–3857. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Two-dimensional schematic of the metal–insulator–metal (MIM) waveguide coupled with the notched ring resonator and stub.

**Figure 2.**Transmission spectrum of the MIM waveguide with the notched ring resonator and without the notched ring resonator.

**Figure 3.**Contour profiles of the normalized H

_{z}field of different structures at (

**a**) ${\lambda}_{\mathrm{dip}}$ = 910 nm and (

**b**) ${\lambda}_{\mathrm{peak}}$ = 965 nm.

**Figure 4.**(

**a**) Transmission spectra of the MIM waveguide coupled with the notched ring resonator and stub for different n. (

**b**) Fitting line of the Fano resonance peak shift ($\mathrm{\Delta}\lambda $) with the change in the refractive index ($\mathrm{\Delta}n$).

**Figure 5.**(

**a**) Transmission spectra for different coupling distances g between the notched ring resonator and MIM waveguide. (

**b**) Fitting line of the Fano resonance peak shift ($\mathrm{\Delta}\lambda $) with the change in the refractive index ($\mathrm{\Delta}n$). (

**c**) Transmission spectra for different coupling distances g

_{left}between the notched ring resonator and MIM waveguide. (

**d**) Transmission spectra for different coupling distances g

_{right}between the notched resonator and MIM waveguide.

**Figure 6.**(

**a**) Transmission spectra for different external diameters of the notched ring resonator R. (

**b**) Fitting line of the Fano resonance peak shift ($\mathrm{\Delta}\lambda $) with the change in refractive index ($\mathrm{\Delta}n$).

**Figure 7.**(

**a**) Transmission spectra for different stub lengths l. (

**b**) Fitting line of the Fano resonance peak shift ($\mathrm{\Delta}\lambda $) with the change in refractive index ($\mathrm{\Delta}n$).

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yan, S.; Zhang, M.; Zhao, X.; Zhang, Y.; Wang, J.; Jin, W. Refractive Index Sensor Based on a Metal–Insulator–Metal Waveguide Coupled with a Symmetric Structure. *Sensors* **2017**, *17*, 2879.
https://doi.org/10.3390/s17122879

**AMA Style**

Yan S, Zhang M, Zhao X, Zhang Y, Wang J, Jin W. Refractive Index Sensor Based on a Metal–Insulator–Metal Waveguide Coupled with a Symmetric Structure. *Sensors*. 2017; 17(12):2879.
https://doi.org/10.3390/s17122879

**Chicago/Turabian Style**

Yan, Shubin, Meng Zhang, Xuefeng Zhao, Yanjun Zhang, Jicheng Wang, and Wen Jin. 2017. "Refractive Index Sensor Based on a Metal–Insulator–Metal Waveguide Coupled with a Symmetric Structure" *Sensors* 17, no. 12: 2879.
https://doi.org/10.3390/s17122879