In this work, we demonstrate a multi-mode refractive index sensors based on split ring resonators (SRRs). The SRR structures show multiple reflectance peaks under normal incidence, which can be interpreted by the model of standing-wave plasmonic resonances,
(1)
where L represents the total length of SRR, λm the wavelength of the resonance mode m (λ0 depends to the geometric structure), and n the refractive index of the surrounding medium. The multiple reflectance peaks present two distinct sets of resonance modes: 1||, 3||, 5||, 7|| and 2┴, 4┴, 6┴, 8┴ corresponding to two orthogonal E-field excitations (E|| and E┴), respectively.
Next, by applying analytes with different different refractive indices on the planar SRRs, there appear red-shifts in the reflectance spectra. According to the SWPR model, we further obtain the sensitivity of our SRR-based sensors as below:
(2)
Here the additional correction factor Xa depends on the thickness of the dielectric layer and the decay length of the localized E-filed. Eq. (2) manifests the relationship among sensitivity (to change of local refractive index), resonant modes and the size of SRRs, which are verified by both our simulated and measured results. For example, our simulation suggests an impressive sensitivity of the SRR-based sensor of ranging from around 1850 nm/RIU to 400 nm/RIU for different modes (from 1st to 5th) when 200 nm-thick analyte was applied. In addition, we measure different analytes including PMMA, air and water by micro-FTIR spectroscopy and observe significant peak shifts consistent with our simulation.
Finally, we examined the detection length (i.e. thickness effect) for the SRR system. For lower modes, 1||, 2|| and 3|| modes, the shift of wavelengths saturates when the thickness increases from 200 to 500 nm, while no saturation effect is observed for higher modes ( 5||, 6||and 7||) even the thickness becomes 2 um. This valuable merit may be used for the analysis of activation-dependent cellular interactions that other label-free techniques like surface plasmon resonance (SPR) have not been used. For bio-sensing application, lower modes can be utilized to detect small molecules, adhesions or bio-events that happened on the cell membrane, in order to take advantage of the high sensitivity and also reduce noise from environment. Higher modes own micron scale detection region and can help us detect intracellular bio-events.
In conclusion, the SRR-based optical sensor possesses various advantages beyond conventional optical sensors (e.g., fluorescent and Raman scattering techniques) such as label free, high sensitivity, real-time diagnosis. In addition, it also demonstrates further benefits compared with the-state-of-the-art techniques (e.g., surface plasmon polariton and localized surface plasmon resonance) such as coupler free for simple and inexpensive optical setup, great detection lengths (up to micron scale) to enable intracellular detection, and scalable working frequencies in particular in IR regimes to prevent photo damage to cells and to reserve the characteristic fingerprints of molecules) by choosing different resonant modes and sizes. As a consequence, the SRR-based optical sensors promise a real-time, operation frequency flexible and multi-mode solution for biological and chemical detection, drug delivery and other applications.

References
1. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phy. Usp 10, 509-514, (1968).
2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
3. J. Yao, Z. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical Negative Refraction in Bulk Metamaterials of Nanowires,” Science 321, 930-930 (2008).
4. Y. J. Chiang, and T. J. Yen, “A highly symmetric two-handed metamaterial spontaneously matching the wave impedance,” Opt. Lett. 16, 12764-12770 (2008).
5. M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials : The fishnet structure and its variation,” Phys. Rev. B 75, 235114 (2007).
6. D. Schurig, J. J Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencys,” Science 314, 977-980 (2006)
7. I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102, 213901 (2009)
8. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
9. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005)
10. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303,1494 (2004).
11. H. T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Phtonics 3, 148-151 (2009)
12. H. T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597-600 (2006)
13. C. K. Tiang, J. Cunningham, C. Wood, I. C. Hunter, and A. G. Davies, “Electromagnetic simulation of terahertz frequency range filters for genetic sensing,” J. Appl. Phys. 100, 066105 (2006).
14. J. F. O’Hara, R. Singh, I.Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16, 1786 (2008).
15. Christian Debus and Peter Haring Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91, 184102 (2007).
16. Ibraheem A. Ibraheem Al-Naib, Christian Jansen, and Martin Koch, “Thin-film sensing with planar asymmetric metamaterial resonators,” Appl. Phys. Lett. 93, 083507 (2008).
17. Basudev Lahiri, Ali Z. Khokhar, Richard M. De La Rue, Scott G. McMeekin and Nigel P. Johnson, “Asymmetric split ring resonators for optical sensing of organic materials,” Opt. Express 17,1107 (2009).
18. A. Zayats, I. I. Smolyaninov and A. A. Maradudin, “Nano-optics of surface Plasmon polaritons,” Phys. Rep. 408, 131-314 (2005)
19. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39-46 (2007)
20. J. Homola, S. S. Yee, and G. T. Gauglitz, “Surface plasmon resonance sensors: review,” Sensors and Actuators B: Chemical 54, 3-15 (1999).
21. T. Driscoll, G. O. Andreev, and D. N. Basov, “Tuned permeability in terahertz split-ring resonators for devices and Sensors,” Appl. Phys. Lett. 91, 062511 (2007).
22. Chia-Yun Chen, Shich-Chuan Wu, and Ta-Jen Yen, “Experimental verification of standing-wave plasmonic resonances in split-ring resonators,” Appl. Phys. Lett. 93, 034110 (2008).
23. Francisco J. Rodríguez-Fortuño, Carlos García-Meca, Rubén Ortuño, Javier Martí, and Alejandro Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial, “ Phys. Rev. B 79, 075103 (2009).
24. Purdue University, College of Engineering, Brick Nanotechnology center, lecture.
25. J B Pendryy, A J Holdenz, D J Robbinsz and W J Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condensed. Matter 10, 4785 (1998).
26. T. Koschny and M. Kafesaki, “Effective Medium Theory of Left-Handed Materials,” Phys. Rev. Lett. 93, 10702 (2004).
27. D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184 (2000).
28. Shuang Zhang, Wenjun Fan, B. K. Minhas, Andrew Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
29. N. Katsarakis, T. Koschny, and M. Kafesaki, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943 (2004).
30. Carsten Rockstuhl and Falk Lederer, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827 (2006).
31. Jiangfeng Zhou, Thomas Koschny and Costas M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881 (2007).
32. A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tunable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
33. A. K. Sheridan,a_ A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Multiple plasmon resonances from gold nanostructures,” Appl. Phys. Lett. 90,143105 (2007).
34. R. H. Ritchie,“Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev. 106, 874 (1957).
35. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phys. Rev. B 10, 3038 (1974).
36. J. C. Ashley and L. C. Emerson, Surface Science 41, 615 (1974).
37. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Letters 22, 475 (1997).
38. T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancements,” Phys. Rev. B 75, 073402 (2007).
39. S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators,” Opt. Express 15, 10869 (2007).
40. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver Nanowires as Surface Plasmon Resonators,” Phys. Rev. Lett. 95, 257403 (2005).
41. E. K. Payne, K. L. Shuford, S. Park, G. C. Schatz, and C. A. Mirkin, “Multipole Plasmon Resonances in Gold Nanorods,” J. Phys. Chem. B 110, 2150 (2006).
42. T. Søndergaard and S. Bozhevolnyi, “Metal nano-strip optical resonators,” Opt. Express 15, 4198 (2007).
43. G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polarization nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867 (2008).
44. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. Mater. 11, 65 (2002).
45. Yimin Sun, Xiaoxiang Xia, Hui Feng, Haifang Yang, Changzhi Gu, and Li Wang, “Modulated terahertz responses of split ring resonators by nanometer thick liquid layers,” Appl. Phys. Lett. 92, 221101 (2008).
46. Hee-Jo Lee and Jong-Gwan Yook, “Biosensing using split-ring resonators at microwave regime,” Appl. Phys. Lett. 92, 254103 (2008).
47. Sher-Yi Chiam, Ranjan Singh, Jianqiang Gu, Jiaguang Han, Weili Zhang, and Andrew A. Bettiol, “Increased frequency shifts in high aspect ratio terahertz split ring resonators,” Appl. Phys. Lett. 94, 064102 (2009).
48. I. A. I. Al-Naib, C. Jansen, and M. Koch, “Improved Terahertz Sensors Based on Frequency Selective Surfaces For Thin-film Sensing,” IEEE Conference proceeding 978-1-4244-2120-6/08.
49. C.-c. Gong, “Innovative Surface Plasmon Resonance Biosensors Employing Dual Parabolic Mirrors,” in Institute of bio-photonics engineering (National Yang-Ming University, Taipei, Taiwan, 2008).
50. L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. N. Xia, "Localized surface plasmon resonance spectroscopy of single silver nanocubes," Nano Lett. 5, 2034-2038 (2005).