本論文中，將使用波導光柵的結構來設計高品質因數折射率感測器，這種結構是由波導模態共振效應與表面光柵結合。其中，波導模態效振效應會使入射光入射至光柵之中時產生出繞射光，則繞射光會在波導層之中激發出TE/TM 的波導模態，且被光柵結構所激發的模態會在傳播一段距離之後洩漏出去，當兩道洩漏的繞射光相位匹配時，就會有共振產生。
利用Rsoft Diffrac MOD模擬軟體進行模擬及分析一維波導光柵結構，並在結構上覆蓋一層高折射率薄膜。在覆蓋薄膜之後，會讓靈敏度減少從260.1至251.9(nm/RIU)下降了3.15%但因為光柵層的等效折射率增加，則能量更加地集中在結構之中，然而半峰全寬（Full width at half maximum，FWHM）就會變得更窄，TM模態的FWHM從原本1.8 × 10-3nm變窄至3 × 10-4nm，使變窄的FWHM讓品質因數(Figure of Merit，FOM)從144500(1/RIU)增加到839666(1/RIU)提升了481%。
在透過電場圖得知當改變結構參數，會因等效折射率提升和束縛模態與輻射模態之間的正交關係，使電場能量從一開始分散在結構之中變成侷限在等效波導層之中進行傳遞。

In this paper, we combine the waveguide mode resonance effect with a surface grating structure called a waveguide grating to design a high figure of merit refractive index sensor. When the incident light is incident on the grating, the diffracted wave will be generated, and the diffracted wave will excite the TE/TM waveguide mode in the waveguide layer, and the mode excited by the grating structure will leak out after propagating for a certain distance. When the phases of the two leaked diffracted waves are matched, resonance will occur.
Using Rsoft Diffrac MOD simulation software to simulate and analyze the one-dimensional waveguide grating structure, and cover the structure with a high refractive index film. After covering the film, the sensitivity reduction decreases by 3.15% from 260.1 to 251.9 (nm/RIU), but because the equivalent refractive index of the grating layer increases, the energy is more concentrated in the structure, while the full width at half maximum ( Full width at half maximum, FWHM) will become narrower, and the FWHM of the TM mode is narrowed from 1.8 × 10-3nm to 3 × 10-4nm, making the narrowed FWHM lower the quality factor (Figure of Merit, FOM). ) increased from 144500 (1/RIU) to 839666 (1/RIU) by 481%.
It can be seen from the electric field diagram that when the structural parameters are changed, due to the increase in the effective refractive index and the orthogonal relationship between the bound mode and the radiation mode, the electric field energy will be dispersed in the structure from the beginning to confined in the effective waveguide transfer between layers.

[1] Z. S. Liu, S. Tibuleac, D. Shin, pp. pp. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Optics Letters, 23(19), pp. 1556-1558, (1998).
[2] R. Magnusson, D. Wawro, S. Zimmerman, and Y. Ding, “Resonant Photonic Biosensors with Polarization-Based Multiparametric Discrimination in Each Channel,” Sensors, 11(2), pp. 1476-1488, (2011).
[3] . Paulsen, S. Jahns, M. Gerken,“ Intensity-based readout of resonantwaveguide grating biosensors: systems and nanostructures,” Photonics Nanostructures, 26, pp.69-79,(2017).
[4] S. Jahns, F. von Oertzen, T. Karrock, Y. Nazirizadeh, M. Gerken, “Photonic Crystal Slabs for Biosensing,” Progress in Electromagnetics Research Symposium Proceedings, pp.1217–1220, (2014).
[5] M. Piliarik, J. Homola, Z. Manı´kova, and J. Cˇ tyroky, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sensors and Actuators B, 90(1-3), pp. 236-242, (2003).
[6] J. Zhu, L. Qin, S. Song, J. Zhong, and S. Lin, “Design of a Surface Plasmon Resonance Sensor Based on Grating Connection,” Photonic Sensors, 5(2), pp. 159-165, (2015).
[7] I. D. Villar, A. B. Socorro, M. Hernaez, J. M. Corres, C. R. Zamarreño, pp. Sanchez, F. J. Arregui, and I. R. Matias, “Sensors Based on Thin-Film Coated Cladding Removed Multimode Optical Fiber and Single-Mode Multimode Single-Mode Fiber: A Comparative Study,”.Journal of Sensors, pp. 1-7, (2015).
[8] W. T. Hsu, W. H. Hsieh, S. F. Cheng, C. pp. Jen, C. C. Wu, C. H. Li, C. Y. Lee, W. Y. Li, L. K. Chau, C. Y. Chiang, and S. R. Lyu, “Integration of fiber optic-particle plasmon resonance biosensor with microfluidic chip ,“. Analytica Chimica Acta, 697(1-2), pp. 75-82, (2011).
[9] R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,”. Proc. Phys. Soc. London, 18(1), pp. 269–275, (1902).
[10] A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,”. Appl. Opt. 4(10), pp.1275–1297, (1965).
[11] M. Sarrazin and J. pp. Vigneron, “Bounded modes to the rescue of optical transmission,”. Europhys. News, 38(3), pp.27–31, (2007).
[12] R. R. Boye, R. W. Ziolkowski, R. K. Kostuk, “Resonant waveguide-grating switching device with nonlinear optical material,”. Appl. Opt, 38(24), pp.5181–5185, (1999).
[13] J. H. Lin, Y. C. Huang, N. D. Lai, H. C. Kan, and C. C. Hsu, “Optical modulation of guided mode resonance in the waveguide grating structure incorporated with azo-doped-poly(methylmethacrylate) cladding layer,”. Opt. Express, 20(1), pp. 377–384, (2012).
[14] J. H. Lin, J. H. Huang, H. C. Kan, and C. C. Hsu, “Optical tuning of guided mode resonance in an azo-copolymer waveguide grating structure inscribed with a surface relief grating,”. Adv. Device Mater., 1(3), pp. 74–79, (2015).
[15] Y. Nazirizadeh, F. Oertzen, T. Karrock, J. Greve, and M. Gerken, “Enhanced sensitivity of photonic crystal slab transducers by oblique-angle layer deposition,”. Opt. Express, 21(16), pp. 18661–18670, (2013).
[16] S. Zhang, Y. Wang, S. Wang, and W. Zheng, “Wavelength-tunable perfect absorber based on guided-mode resonances,”. Appl. Opt., 55(12), pp. 3176–3181, (2016).
[17] D. Rosenblatt, A. Sharon. and A. A. Friesem, “Resonant grating waveguide structures,”. IEEE Journal of Quant. Electronics, 33(11), pp. 2038–2059, (1997).
[18] N. Darwish, L. Dieguez, M. Moreno, F. Munoz, R. Mas, J. Mas, J. Samitier, B. Nilsson, G. Petersson, “Second order effects of aspect ratio variations in high sensitivity grating couplers,”. Microelectron Eng, 84(5-8), pp. 1775-1778, (2007).
[19] J.G. Wangueeme rt Perez, pp. Cheben, A. Ortega Monux, C. Alonso Ramos, D. Perez Galacho, R. Halir, I. Molina Fernandez, D.X. Xu, Schmid J.H., “Evanescent field waveguide sensing with subwavelength grating structures in silicon on insulator,”. Opt Lett, 39(15), pp. 4442-4445, (2014).
[20] R. Horvath, H.C. Pedersen, N. D. Skivesen, Selmeczi, N.B. Larsen, “Optical waveguide sensor for on line moni toring of bacteria,”. Opt Lett, 28(14), pp. 1233-1235, (2003).
[21] B.K. Kim, K.H. Kim, J. Hong, W.J. Kim, H. Ko, C. Huh, G.Y. Sung, W.I. Jang, S.H. Park, S.J. Park, “Sensitivity material thickness for an optical resonant reflective biosensor based response to coating material thickness for an optical resonant reflective biosensor based on a guided mode resonance filter,”. BioChip J, 8(1), pp. 35–41 (2014).
[22] H.Y. Li, W.C. Hsu, K.C. Liu, Y.L. Chen, L.K. Chau, S. Hsieh, W.H. Hsieh, “A low cost, label free biosensor based on a novel double sided grating waveguide coupler with sub surface cavities,”. Sensor Actuat B Chem, 206, pp. 371-380, (2015).
[23] S. Isaacs, A. Hajoj, M. Abutoama, A. Kozlovsky, E. Golan, I. Abdulhalim. “Resonant Grating without a Planar Waveguide Layer as a Refractive Index Sensor,”. Sensors, 19(13), pp. 3003, (2019).
[24] Y. Zhou, X. Li, S. Li, Z. Guo, pp. Zeng, J. He, D. Wang, R. Zhang, M. Lu, S. Zhang, “Symmetric guided-mode resonance sensors in aqueous media with ultrahigh figure of merit,”. Opt. Express, 27(24), pp. 34788–34802, (2019).
[25] S. Sahu, J. Ali, G. Singh. “Refractive index biosensor using sidewall gratings in dualslot waveguide,”. Opt Commun,402(1), pp.408–412, (2017).
[26] Y. N. Bao, X. H. Liu, J. H. Hu, J. Zou, H. Y. Han, and C. Wang, “Enhanced optical sensing performance in stacked resonant compound gratings,”. Opt. Express, 29(18), pp.29458-29465, (2021).
[27] S. Mesli, H. Yala, M. Hamidi, A. BelKhir, F.I. Baida. “High performance for refractive index sensors via symmetry-protected guided mode resonance,”. Opt Express, 29(14), pp.21199-21211, (2021).
[28] Y. Y. Li1, Y. Liu, Z. Q. Liu, Q. Tang, L. L. Shi, Q. Q. Chen, G. Z. Du, B. Wu, G. Q. Liu, L. Li., “Grating-assisted ultra-narrow multispectral plasmonic resonances for sensing application,”. Appl. Phys. Expp.,12(7), (2019).
[29] X. X. Wang, J. K. Zhu, X. L. Wen, X. X. Wu, Y. Wu, Y. W. Su, H. Tong, Y. pp. Qi, H. Yang. “Wide range refractive index sensor based on a coupled structure of Au nanocubes and Au film,”. Opt. Mater. Expp., 9(7), pp. 3079, (2019).
[30] Z. Liu, G. Liu, X. Liu, and G. Fu, “Plasmonic sensors with an ultra-high figure of merit,”. Nanotechnology, 31(11), pp.115208, (2020).
[31] Y. F. Chou Chau, C. T. Chou Chao, H. J. Huang, M. R. R. Kooh, NTRN Kumara, C. M. Lim, H. pp. Chiang, “Perfect dual-band absorber based on plasmonic moniceffect with the cross-hair/nanorod combination,”. Nanomaterials, 10(3), pp. 493, (2020).
[32] G. Z. Li, Y. Shen, G. H. Xiao, and C. J. Jin. “Double-layered metal grating for high-performance refractive index sensing,”. Opt. Express, 23(7), pp.8995-9003, (2015).
[33] S. Sahu, J. Ali, and G. Singh, “Refractive index biosensor using sidewall gratings in dual-slot waveguide,”. Optics Communications, 402, pp.408‒412, (2017).
[34] Y. Zhou, B. Wang, Z. Guo, X. Wu, “Guided Mode Resonance Sensors with Optimized Figure of Merit,”. Nanomaterials, 9(6), pp. 837, (2019).
[35] G. Lan, S. Zhang, H. Zhang, Y. Zhu, L. Qing, D. Li, J. Nong, W. Wang, L. Chen, W. Wei, “High-performance refractive index sensor based on guided-mode resonance in all-dielectric nano-silt array,”. Phys. Lett. A, 383(13), pp.1478–1482, (2019).
[36] L. Y. Qian, K. N. Wang, W. Zhu, C. Q. Han, C. C. Yan. “Enhanced sensing ability in a single-layer guided-mode resonant optical biosensor with deep grating,”. Optics Communications, 452, pp. 273-280, (2019).
[37] T. Smirnova, V. Fitio, O. Sakhno, pp. Yezhov, A. Bendziak, V. Hryn, S. Bellucci. “Resonant and Sensing Performance of Volume Waveguide Structures Based on Polymer Nanomaterials,”. Nanomaterials, 10(11), pp.2114, (2020).
[38] C. Zhang, Y. Zhou, L. Mi, J. Ma, X. Wu, Y. Fei. “High Performance of a Metal Layer-Assisted Guided-Mode Resonance Biosensor Modulated by Double-Grating,”. Biosensors ,11(7), pp. 221, (2021).
[39] M. Piliarik, J. Homola, Z. Manı´kova, and J. C tyroky, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sensors and Actuators B, 90(1-3), pp. 236-242, (2003).
[40] J. Zhu, L. Qin, S. Song, J. Zhong, and S. Lin, “Design of a Surface Plasmon Resonance Sensor Based on Grating Connection,” Photonic Sensors, 5(2), pp. 159-165, (2015).
[41] T. Kobayashi, Y. Kanamori, K. Hane. “Surface laser emission from solid polymer dye in a guided mode resonant grating filter structure,”. Appl. Phys. Lett. 87(15), pp.151106, (2005).
[42] L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,”. J. Mod. Opt. 40(4), pp.553–573, (1993).
[43] R. R. Boye and R. K. Kostuk, “Investigation of the effect of finite grating size on the performance of guided-mode resonance filters,”. Appl. Opt. 39(21), pp. 3649–3653, (2000).
[44] K. Knop, “Rigorous diffraction theory for transmission phase grating with deep rectangular grooves,”. J. Opt. Soc. Am., 68(9), pp. 1206-1210, (1978).
[45] M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,”. J. Opt. Soc. Am., 73(4), pp. 451-455, (1983).
[46] S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,”. Appl. Opt.,32(14), pp. 2606-2613, (1993).
[47] S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,”. J. Opt. Soc. Am., 7(8), pp. 1470-1474, (1990).
[48] T. Sang, L. Wang, S. Ji, Y. Ji, H. Chen, and Z. Wang, “Systematic study of the mirror effect in a poly-Si subwavelength periodic membrane,”. J. Opt. Soc. Am., 26(3), pp. 559–565, (2009).
[49] J.R. Piper, S.H. Fan. “Total Absorption in a Graphene Monolayer in the Optical Regime by Critical Coupling with a Photonic Crystal Guided Resonance,”. ACS Photonics, 1(4), pp.347–353, (2014).
[50] L.Y. Qian, K.N. Wang, Dmitry A. Bykov, Y.F. Xu, L. Zhu, and C.C. Yan, “Improving the sensitivity of guided-mode resonance sensors under oblique incidence condition,”. Opt. Express, 27(21), pp. 30563-30575, (2019)
[51] E. Andrey. Miroshnichenko, Sergej Flach, and Yuri S. Kivshar, “Fano resonances in nanoscale structures,”. Rev, Mod. Phys., 82(3), pp. 2257-2298, (2010).
[52] Scott M. Norton, Turan Erdogan, and G. Michael Morris, “Coupled-mode theory of resonant-grating filters,”. J. Opt. Soc. Am. A ,14(3), pp. 629-639, (1997).
[53] B. Yuan, F. Zhang, and T. Ning, “Relationship between linewidth and electric field intensity of guide-mode resonance filter,”. Optik-Int. J. Light Electron Opt. 123(5), pp. 439–441 (2012).
[54] W.X. Liu, Y.H. Li, H.T. Jiang, Z.Q. Lai, and H. Chen, “Controlling the spectral width in compound waveguide grating structures, ”. Opt. Lett., 38(2), pp. 163-165 (2013).
[55] R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, pp. M. Johansen. “Analytical and numerical study on grating depth effects in grating coupled waveguide sensors,”. Appl. Phys. B 81(1), pp. 65–73, (2005).
[56] G. Zheng, X. Zou, L. Xu, J. Wang, “Single layer narrow bandwidth angle-insensitive guided-mode resonance badstop filters.”. Optik, 130, pp. 19–23, (2017).