Dislocated Double-Layered Metal Gratings: Refractive Index Sensors with High Figure of Merit Yang Shen1; Tianran Liu1; Qiangzhong Zhu1; Jianfang Wang2; Chongjun Jin1* <c> Email: jinchjun@mail.sysu.edu.cn 1 State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering Sun Yat-sen University Guangzhou 510275, China 2 Department of Physics The Chinese University of Hong Kong Shatin, Hong Kong SAR, China Abstract We experimentally demonstrate an enhanced refractive index sensing using a dislocated double-layered metal grating (DDMG). The DDMG is capable of supporting a novel guided mode caused by the interaction between localized surface plasmon resonances (LSPRs) from the individual gold stripes and Wood's anomaly in the dielectric grating layer between two gold gratings. We show that this guided mode can only be induced and mediated by the coupling of lattice plasmon resonances sustained by upper and lower gold grating through introducing a lateral displacement between the two gold gratings. The DDMG provides an experimental figure of merit (FOM) value up to 36 under normal incidence, which is superior to those of most of nanoplasmonic sensors relying on Fano resonances. Additionally, the DDMGs can be fabricated by a very simple and cost-effective method via a combination of two-beam interference lithography and metal deposition. Accompanied with high FOM and simple detection scheme, this sensor will be found a wide range of applications in biomedical sensing. Keywords Localized surface plasmon resonance, Refractive index sensing, Figure of merit, Wood’s anomaly, Fano resonance 1 Introduction Isolated and continuous metallic nanostructures are well known to concentrate light into a nanoscale spatial region near the metal/dielectric interface by the excitation of surface plasmons (SPs) [1]. This ability results in a strong enhancement of local electric fields, which is extremely useful for sensing [2-7], enhanced optical nonlinearity [8,9], plasmonic laser [10], light harvesting [11]. Commercially available surface plasmon refractive index (RI) sensors are so far dominated by those based on propagating surface plasmon resonance (PSPR). They usually consist of a flat gold or silver film combined with prism- or grating-coupling elements [12]. Commercial PSPR-based sensing systems provide a benchmark of the RI sensitivity, the cumbersome and expensive nature of such optics for coupling and monitoring light, however, restricts their widespread use in the field of point-of-care (POC) testing and personal medicine as a biosensor. Compared to the PSPR-based sensing scheme, localized surface plasmon resonance (LSPR)-based sensors, carried by nanoplasmonic structures [13], have several undisputed advantages such as the cost-effective detection method, broad spectral tunability, no need of coupling configuration and compatibility for lab-on-a-chip integration. Despite these remarkable advantages, LSPR-based platforms present figure of merit (FOM) values which are at least an order of magnitude smaller than those of PSPR ones. Great efforts have been therefore made to enhance the sensitivity of LSPR-based sensors responding to the surrounding refractive index [14-16] or/and narrow the full width at half maximum (FWHM) of plasmon resonances [17-19]. Recently, a new concept of boosting FOM values of nanoplasmonic sensors by constructing a variety of plasmonic crystals has been developed. Plasmonic crystals sustain the LSPRs driven by the individual metallic units and some types of guided modes (such as surface plasmon plariton (SPP) and Wood’s anomaly (WA)) from their periodic arrays [20-25]. The interplay between the guided modes and localized modes acts as an effective way of creating hybrid guided modes with a narrow plasmon linewidth as well as a strong confinement of optical field [20-29]. Therefore, for index sensing, these hybrid plasmonic modes can offer not only the extreme detection capability inherited from the guided modes but also the advantages of the plasmonic nanostructures, such as enhancement of local electric fields and no need of complex measurement setups. For instance, a metamaterial system, consisting of an array of parallel gold nanorods, was constructed to boost the detection capability via coupling the LSPR of the individual nanorods with a waveguide mode mediated by the interaction among the nanorods [20]. However, it still requires a prism coupler for optical measurements. In our recent work [21], on the basis of the Fano resonance arising from the interference between the LSPRs and Wood’s anomaly, an array of gold submicrometer mushrooms was fabricated to achieve a high FOM value approaching the theoretically predicted upper limit of standard PSPR sensors under the Kretschmann configuration. However, the dipole nature of scattering from the individual nanoparticles requires nonzero incidence angle to achieve the coupling between incident light of p-polarization and diffracted waves propagating along the surface of the samples [28]. As a result, in such plasmonic crystals, this narrow and sharp spectral features arising from these hybrid modes are often observed under oblique illumination. Unfortunately, for an oblique incident detection system, it is probably inevitable that one must maintain constant incident angle between the surrounding medium and the sample when the surrounding media are changed. Even though introducing complex optics (such as prism) can solve this problem, it hinders the device miniaturization, eliminating the unique advantage of the LSPR-based sensors endowed by the plasmonic nanostructures. Therefore, this means that for LSPR-based sensors, the preferential measurement configuration would be a normally incident detection system. In this letter, we report a dislocated double-layered metal grating, where symmetry breaking can be easily achieved by lifting the upper gold grating, forming a lateral displacement with respect to the lower one. Double-layered metal gratings have been extensively studied in various aspects, including negative refraction [30], Fano resonance [31], vertical far-field coupling [32], tailoring of the intensity and phase delay in extraordinary optical transmission [33,34]. However, the design of double-layered metal gratings for sensing has rarely been explored. In our recent work, we demonstrated theoretically and experimentally that the dislocated double-layered gold grating can produce an exotic mode for launching SPP in a desired direction as a unidirectional coupler [35]. In this paper, we further revealed that the first-order unidirectional coupling mode in DDMG is a novel hybrid guided mode, which is created on the basis of the interplay between the LSPR of the individual gold stripes and Wood’s anomaly in the slanted dielectric grating layer sandwiched between these two gold gratings. This hybrid guided mode can actually confine a large fraction of optical field between the upper and lower gold grating, accompanied by a remarkably narrow plasmon linewidth. Furthermore, the symmetry breaking caused by a lateral displacement can give rise to this mode under normal illumination, which is not occurred for the non-dislocated double metallic grating. Based on the above consideration, we adopted and designed the structure of a dislocated double-layered grating (Fig. 1a) for sensing purpose. In this work, we further found that the intensity and position of this guided mode on the reflection/absorption spectra strongly depend on the amount of the dislocation between the upper and lower gold gratings and the effective refractive index of the dielectric grating layer, respectively. Finally, we experimentally demonstrated a high FOM up to 36 for this mode under normal incidence, which is one of the highest FOM values in LSPR-related sensors, including all types of metal nanoparticle-based sensors [13] and a variety of LSPR-based sensors relying on Fano resonance [36-39]. 2 Results and Discussion We developed a fabrication method which combines interference lithography with electron beam evaporation to form DDMGs. It is simple, cost-effective, and suitable for high-throughput production in low-cost POC testing applications. The fabrication procedure of the DDMG is schematically illustrated in Fig. 1a (more detailed fabrication parameters can be seen in Supporting Information). To create a lateral dislocation Δx between the two metallic gratings, we first prepared a slanted photoresist grating by rotating the sample at an angle α with respect to the plane that is perpendicular to the angle bisector formed by two laser beams (Fig. 1b) during exposure. A gold deposition was then employed where the angle between the normal direction of the sample and the direction of the evaporation is the same as the oblique angle α. The height and oblique angle of the slanted photoresist grating can be varied by adjusting the thickness of the photoresist film h and the rotation angle α, respectively. The thickness of the gold film is t. The periodicity of the grating is determined by the incident angle of the laser beams φ and the rotation angle α. The width w1 of each top gold stripe is slightly larger than the width w2 of the top of the slanted photoresist stripe (Fig. 1c). A poly(methyl methacrylate) (PMMA) layer at a thickness of ~50 nm was spin-coated on the quartz substrate in advance, which functions as an adhesive layer to ensure the firm attachment of the photoresist grating. Fig. 1d and e show the top-view and cross-sectional scanning electron microscopy (SEM) images of a DDMG. The black parts seen in the top view (Fig. 1d) represent the areas of the left sidewall that are uncovered by the gold film, as shown by the cross-sectional view (Fig. 1e). Based on this fabrication method, the periodicity of this DDMG is 770 nm, which is fully determined by the incident angle and rotation angle. The width of the top gold stripe and dislocation maintain 330±8 nm and 128 ±5 nm respectively at a circular region with the diameter of around 4 mm. The thickness of photoresist layer is in the range of 450–480 nm owing to the fluctuation in the humidity in the laboratory. We measured the zero-order reflection spectrum of a DDMG (a = 770 nm, w1= 330 nm, Δx=128 nm, h = 480 nm, and t = 120 nm) in air at normal incidence, as shown by the red curve in Fig. 2a. In this letter, all the zero-order reflection spectra were taken on a UV/visible/near-infrared spectrometer (Lambda 950, PerkinElmer) at normal incidence under p-polarization (the electric field was perpendicular to the gold stripes). For recording the reflection spectra at normal incidence, a beam splitter and three silver mirrors were placed in the optical path (Supporting Information Fig. S3). The corresponding simulation result was indicated by the black curve as well, which was performed using the finite-difference time-domain (FDTD) method (FDTD Solutions, Lumerical; the FDTD simulation details can be seen in Supporting Information). The simulated spectrum is in excellent agreement with the experiment one. Four resonant features, marked as D1, D2, D3, and D4, are clearly displayed (Fig. 2a and b), which are spectrally located at around 769 nm, 917 nm, 1115 nm and 1155 nm, respectively. Generally, for a one-dimensional grating, the incident light can be coupled to SPP and WA if the in-plane wavevectors of the incident light and these propagating modes meet the Bragg coupling condition [40]: k 0 sin iG x k mode (1) where i is the grating order for the reciprocal lattice vector Gx of the one-dimensional grating ( G x 2 / a , a is the lattice constant of the grating), θ is the incidence angle from air, k0 and kmode represent the wavevectors of the incident light and a specific mode (such as SPP or WA) of the grating structure, respectively. kSPP and kWA are described by [41,42]: k SP P k 0 m d m d (2) k WA k 0 d (3) where εm and εd are the dielectric constants of the metal and surrounding medium, respectively. According to the equations above, the spectral positions of D1, D2, D3 and D4 are found to be associated with those of WA(1)sup, WA(1)eff, WA(1)sub and SPP(-1)Au/PMMA modes (indicated by the dashed lines in Fig. 2a and b). WA(1)sup, WA(1)eff and WA(1)sub refer to Wood’s anomalies in the supstrate, in the effective medium layer between two gold grating layers, and in the quartz substrate respectively. SPP(-1)Au/PMMA represents the surface plasmon polariton at the gold-PMMA interface. It should be noted that the slanted photoresist grating layer sandwiched by the upper and lower gold grating layers is treated as an effective medium layer. When the electric field of the incident light is perpendicular to the stripes, the effective refractive index of this effective medium layer is given by [43]: neff f (1 f ) 2 n nsup 2 resist 1/2 (4) where f is the duty ratio of the photoresist, nresist and nsup are refractive indices of the photoresist and supstrate respectively. To further clarify the physical origin of these four resonant modes, we also performed the FDTD simulations to give the absorption spectra (Fig. 2b) and the electric field intensity distributions (Fig. 2c-2f) for the DDMG. The simulations show that a small absorption peak D1 is located at the wavelength of 769 nm (Fig. 2b). For this mode, the enhanced electric field is localized at the region above the upper gold grating (Fig. 2c), further indicating that D1 originates from the Wood’s anomaly in air caused by the upper gold grating. In addition, for the DDMG, the simulations also show another two strong absorption peaks D2 (917 nm) and D4 (1155 nm) (Fig. 2b). The electric field intensity distribution of D2 is confined to the region between the two gold grating as well as the one edge of each upper gold stripe (Fig. 2d). It shows a strong coupling of the incident light to the slanted photoresist grating, which is responsible for this absorption peak. To understand the physic of this resonant mode, we performed the simulations of the scattering cross-sections and the electric field intensity distribution of a single gold stripe on the top or bottom of the effective medium layer (See the Supporting information Fig. S1) as a comparison with the cases for gold grating structures. For the single gold stripe on the top and bottom of the effective medium layer, broad plasmon peaks (Fig. S1a and S1c) which are centered at the wavelength of 800 nm and 1400 nm are exhibited in the scattering spectra, respectively. The electric field intensity distributions (Fig. S1e and S1g) reveal that the broad resonances are dominated by the backscattering of the single gold stripe. In contrast, for the gold gratings, the narrow resonant dips at the wavelength of around 877 nm and 888 nm are presented in the reflection spectra of the upper and lower gratings respectively (Fig. S1b and S1d). These Fano-type asymmetric peak-and-dip spectral features are both nearly located at the wavelength of WA(1)eff (marked by the red dashed lines in Fig. S1b and S1d). These results confirm that there exist two coupled LSPR–WAeff modes (namely lattice plasmons) in the double-layered gold gratings. In addition, the simulated electric field intensity distribution of the lower gold grating (Fig. S1h) shows that a large fraction of incident light is coupled into the effective medium layer which consists of a slanted photoresist grating. This result is very similar to the case of DDMG, suggesting D2 is from the coupling of WA(1)eff and the LSPR of the lower gold grating. It is noted that D2 shows a slight red shift with respect to the wavelength of WA(1)eff, it indicates that the LSPR of the upper gold stripes also plays a key role in this guided mode at the WA(1)eff wavelength. Therefore, D2 can be considered as a special resonant guided mode in the dielectric grating layer assisted by the lattice plasmons of both upper and lower gold gratings, named as LSPR-WA(1)eff resonant mode. For D4, the electric field is bound to the bottom side and both edges of the top side of the lower gold stripes, indicating D4 is mainly ascribed to a SPP mode at the goldPMMA interface. We also measured the angle-resolved reflection spectra of the DDMG under p-polarized incident light and calculated the corresponding dispersion diagram of the SPP modes (See the Supporting Information Fig. S2). We found that the dip positions of D4 at varying incidence angles are in good agreement with the dispersion diagram of SPP(-1)Au/PMMA. D4 is therefore ascertained to be the SPP mode at the goldPMMA interface. Similarly, D4 is also pushed to a slightly longer wavelength. This is believed to be caused by the LSPR from the upper gold stripes. We therefore named D4 as an LSPR-SPP mode. For D3 (1115 nm), there is nearly no observable feature on the corresponding absorption spectra (Fig. 2b). From Fig. 2e, D3 exhibits an electric field pattern which is vertical to the interface of the gold grating and PMMA film, indicating the characteristic of a propagating plane wave being parallel to the interface with infinite extent. In addition, the electric field pattern shows a relatively low intensity but without significant decay away from the goldPMMA interface (Fig. 2e). Therefore, D3 is considered as the Wood’s anomaly in the substrate. Due to the weak enhancement of the near field, WA(1)sub does not lead to a strong absorption. Among these four resonances above, D2 (LSPR-WA(1)eff mode) is a promising mode for sensing applications, because this mode confines a large fraction of enhanced electric field at the surrounding environment, which is accessible by the analyte to be detected, and also possesses a fairly narrow linewidth due to the coupling between the LSPRs and WA(1)eff. To further explore the underlying physic of this LSPR-WA(1)eff mode, we fabricated a non-dislocated double-layered metal grating (NDDMG) (i.e. Δx = 0 nm) with similar geometrical parameters (Fig. 3b and d) as a reference. We measured the zero-order reflection spectrum of a NDDMG (a = 770 nm, w1 = 330 nm, Δx = 0 nm, h = 480 nm and t = 120 nm) in air at normal incidence under p-polarization as shown in Fig. 3f. Interestingly, in comparison with the reflection spectrum of the DDMG (Fig. 3e), D1, D3 and D4 modes all occur in both DDMG and NDDMG, but D2, the LSPR-WA(1)eff resonant mode located at the wavelength of ~900 nm, is absent in the NDDMG. A near-field optical picture is required to understand the difference of the far-field spectral features associated with this special mode between two grating structures. Fig. 3g-j show the simulated field distributions of Ez and Hy for the DDMG and NDDMG at the wavelength of 917 nm. Clearly, for the dislocated grating, an enhanced electric field exists in the dielectric layer together with the one edge of the top gold stripe (Fig. 3g). In contrast, the electric field is very weak in the non-dislocated one, indicating that there is no resonance (Fig. 3i). Due to a partial overlap between the top and bottom gold stripes, a quadrupole-like induced charge distribution appears at the surface of the bottom gold stripe in the DDMG (Fig. 3g), giving rise to two closed-loop currents with opposite directions between the top and bottom gold stripes (Fig. 3g). The closed-loop currents substantially strengthen the coupling between the lattice plasmons of the upper and lower gold gratings via a magnetic response (Fig. 3h), which is absent in the NDDMG (Fig. 3j). Therefore we believe that the symmetry breaking of the spatial geometry of the double-layered metal gratings is central for efficiently enhancing the coupling between the lattice plasmons of the upper and lower gold gratings and eventually launching such a novel guided mode. Moreover, we simulated the reflection and absorption spectra of the double-layered gold gratings with the dislocation varied from 0 to 128 nm, as shown in Fig. 3k and 3l. With the increase of the dislocation, resonant D2 shows up and is gradually strengthened, indicating such an LSPR-WA(1)eff mode can be induced and intensity-modulated by adjusting the dislocation between these two gold gratings. To demonstrate the potential of the DDMG for sensing applications, we measured the zero-order reflection spectra at normal incidence under p-polarization when the DDMG was immersed in glycerin-water mixture solutions with varying compositions (Fig. 4a). The concentrations of glycerin were chosen to be 0, 10, 20, 30, 40, 50, 60, 70 and 80 wt%, and the corresponding refractive indices were 1.333, 1.345, 1.357, 1.371, 1.384, 1.398, 1.413, 1.427 and 1.443 [44], respectively. To determine the standard deviation of the dip position at each refractive index, after each measurement, the sample was moved away, washed with water, blown with nitrogen gas, and then mounted on the spectroscopy system again for next measurement. This procedure was repeated, and three measurements were made at each refractive index. In water, the DDMG retained four dips, named as D1(1027 nm), D2(1081 nm), D3(1124 nm) and D4(1209 nm) on the reflection spectra (Fig. 4a), which are confirmed to be WA(1)sup, LSPR-WA(1)eff, WA(1)sub and LSPR-SPP(-1)Au/PMMA modes respectively. As the refractive index is increased, the dip positions of D1 and D4 redshift linearly. Interestingly, the shifts of D2 and D3 are linear at only RI ranges of 1.333~1.398 and 1.398~1.443 respectively, while at other RI ranges, the shifts of D2 and D3 are nonlinear (indicated in Fig. 4c). We therefore simulated the corresponding reflection spectra at normal incidence (Fig. 4b). The simulated results show the similar trend of the dependence of the dip positions of D2 and D3 on the refractive index (Fig. 4d), agreeing well with the measured ones (Fig. 4c). However, in principle, the dependence of the dip position of D2 on the surrounding refractive index should be linear according to the Equation 3, and D3 is index-insensitive as a substrate mode. To answer these contradictions, the evolution of the electric field intensity distributions at the dips of D2 and D3 under various surrounding refractive indices is plotted in Fig. 4e. At the RI range of 1.333~1.371, D2 is mostly confined to the effective medium layer between these two gold grating layers and the one edge of the top gold stripes, which is characterized by the LSPR-WA(1)eff mode. As the RI is larger than 1.371, the original optical energy turns remarkably into the substrate, which shows the characteristic of WA(1)sub mode. For D3, the opposite phenomenon in mode exchange is observed. This energy conversion or mode exchange clearly reveals that with the change of refractive index, there is an anti-crossing between the modes of D2 and D3 (indicated by the black dashed ellipse in Fig. 4d). This is the reason that D2 and D3 are partially linear. Actually, despite the interference with substrate mode, the reflection dip position of LSPR-WA(1)eff mode still keeps linear with respect to the refractive index in the ranges of 1.333~1.398 and 1.398~1.443 for D2 and D3 respectively in our measurement. Therefore, as a sensing mode, LSPR-WA(1)eff mode enables its feasibility in practical sensing applications, which are generally carried out in a small refractive index range. By linearly fitting the corresponding data, we obtain the index sensitivities of 481 and 413 nm RIU-1 (0.496 and 0.385 eV RIU-1) in the two linear regions (1.333~1.398 for D2 and 1.398~1.443 for D3 respectively) for the LSPR-WA(1)eff mode. According to these two limited ranges, only the first six data points of the higher-energy branch and the last four data points of the lower-energy branch were used for D2 and D3 respectively in the linear fittings. FOM is a widely accepted metric for characterizing the performance of a refractive index sensor. Generally, the standard FOM value of plasmonic sensors is defined as FOM = S (nm RIU-1)/FWHM (nm) or FOME = S (eV RIU-1)/FHWM (eV), where S (nm RIU-1) and S (eV RIU-1) refer to the sensitivities to the refractive index change in wavelength unit and energy unit, respectively, and FWHM (nm) and FHWM (eV) refer to the linewidths of the plasmonic resonance in wavelength unit and energy unit, respectively. The maximum values of FOM of the LSPR-WA(1)eff mode are determined to be, 36 (38) and 32 (31) for the RI ranges of 1.333~1.398 (D2) and 1.398~1.443 (D3) in wavelength (energy) unit respectively (The detailed sensing data are shown in the Table 1), which surpass the values for most of plasmonic sensors, including metal nanoparticle-based sensors and a number of the LSPR-related sensors using Fano resonance under normal incidence [38, 39, 45-49]. DDMG is somewhat similar to the gold mushroom array (GMRA) in two-dimensional structure we reported previously [21]. The FOM values of the GMRA can be up to 108, however it only happens under oblique incidence. As we mentioned before, the normally incident detection system is essential for a simple and portable device, this is the reason that we are still seeking the preferential system with a high FOM. In summary, we demonstrated a LSPR-related refractive index sensor with a high FOM under normal incidence based on a structure of dislocated double-layered metal grating, where a novel hybrid guided mode is supported and manipulated by the dislocation of the upper and lower gold gratings. Directly benefiting from the strong coupling of LSPRs and Wood’s anomaly, the incident optical field is strongly confined to the spatial region between these two gold grating layers and the one edge of the top gold stripes, enabling an enhanced index sensitivity and a narrow linewidth. Therefore, a FOM up to 36 is achieved for the LSPR-WA(1)eff mode at normal incidence, which is superior to most of LSPR-related sensors using Fano resonance. Moreover, we observed an anticrossing between two types of Wood’s anomalies from the substrate and effective medium layer, respectively, in refractive index modulation. The DDMG was fabricated by two-beam interference lithography together with electron beam evaporation of gold at an oblique angle. The robust and low-cost fabrication method, combined with high FOM and simple detection scheme will facilitate the widespread applications of the DDMG in practical sensing. Acknowledgments The authors acknowledge the financial support from the National Natural Science foundation of China (11374376, 11174374), the Key project of DEGP (No. 2012CXZD0001), SRFDP/RGC ERG (Ref.: M-CUHK410/12, Project Code: 2900701) and Innovative Talents Training Program for Doctoral Students of Sun Yat-sen University. Ethical Statement We have read the Ethical responsibilities of authors. We obey all the rules. The manuscript has not been submitted to more than one journal for simultaneous consideration. References 1. Maier SA (2007) Plasmonics: fundamentals and applications. Springer (New York). 2. Brolo AG (2012) Nat Photonics 6:709 3. Liu N, Tang ML, Hentschel M, Giessen H, Alivisatos AP (2011) Nat Mater 10:631636. 4. Yao JM, Le AP, Gray SK, Moore JS, Rogers JA, Nuzzo RG (2010) Adv Mater 22:1102 5. Lal S, Link S, Halas NJ (2007) Nat Photonics 1:641 6. Lee KL, Chih MJ, Shi X, Ueno K, Misawa H, Wei PK (2012) Adv Mater 24:OP253 7. Kumar M, Sandeep CSS, Kumar G, Mishra YK, Philip R, Reddy GB (2014) Plasmonics 9:129 8. Oulton RF, Sorger VJ, Zentgraf T, Ma RM, Gladden C, Dai L, Bartal G, Zhang X (2009) Nature 461:629 9. Tiwari V, Khokar MK, Tiwari M, Barala S, Kumar M (2014) J Nanomed Nanotechnol 5:246 10. Kim S, Jin JH, Kim YJ, Park IY, Kim Y, Kim SW (2008) Nature 453:757 11. Gan QQ, Bartoli FJ, Kafafi ZH (2013) Adv Mater 25:2385 12. Homola J, Yee SS, Gauglitz G (1999) Sens Actuators B 54:3 13. Mayer KM, Hafner JH (2011) Chem Rev 111:3828 14. Dmitriev A, Hagglund C, Chen S, Fredriksson H, Pakizeh T, Kall M, Sutherland DS (2008) Nano Lett 8:3893 15. Verellen N, Van Dorpe P, Huang CJ, Lodewijks K, Vandenbosch GAE, Lagae L, Moshchalkov VV (2011) Nano Lett 11:391 16. Brian B, Sepulveda B, Alaverdyan Y, Lechuga L M, Kall M (2009) Opt Express 17:2015 17. Jeppesen C, Xiao S, Mortensen NA, Kristensen A (2010) Opt Express 18:25075 18. Lee SH, Johnson TW, Lindquist NC, Im H, Norris DJ, Oh SH (2012) Adv Funct Mater 22:4439 19. Cattoni A, Ghenuche P, Haghiri-Gosnet AM, Decanini D, Chen J, Pelouard JL, Collin S (2011) Nano Lett 11:3557 20. Kabashin AV, Evans P, Pastkovsky S, Hendren W, Wurtz GA, Atkinson R, Pollard R, Podolskiy VA, Zayats AV (2009) Nat Mater 8:867 21. Shen Y, Zhou JH, Liu TR, Tao YT, Jiang RB, Liu MX, Xiao GH, Zhu JH, Zhou ZK, Wang XH, Jin CJ, Wang JF (2013) Nat Commun 4:2381 22. Otte MA, Estevez MC, Regatos D, Lechuga LM, Sepulveda B (2011) ACS nano 5:9179 23. Bendana XM, Lozano G, Pirruccio G, Rivas JG, de Abajo FJG (2013) Opt Express 21:5636 24. Stewart ME, Mack NH, Malyarchuk V, Soares JANT, Lee TW, Gray SK, Nuzzo RG, Rogers JA (2006) Proc Natl Acad Sci USA 103:17143 25. Yao JM, Le AP, Gray SK, Moore JS, Rogers JA, Nuzzo RG (2010) Adv Mater 22:1102 26. Li WD, Ding F, Hu J, Chou SY (2011) Opt Express 19:3925 27. Zhou W, Odom TW (2011) Nat Nanotechnol 6:423 28. Kravets VG, Schedin F, Grigorenko AN (2008) Phys Rev Lett 101:087403 29. Nikitin AG, Kabashin AV, Dallaporta H (2012) Opt Express 20:27941 30. Burokur SN, Sellier A, Kante B, de Lustrac A (2009) Appl Phys Lett 94:201111 31. Christ A, Martin OJF, Ekinci Y, Gippius NA, Tikhodeev SG (2008) Nano Lett 8:2171 32. Taubert R, Ameling R, Weiss T, Christ A, Giessen H (2011) Nano Lett 11:4421 33. Chan HB, Marcet Z, Woo K, Tanner DB, Carr DW, Bower JE, Cirelli RA, Ferry E, Klemens F, Miner J, Pai CS, Taylor JA (2006) Opt Lett 31:516 34. Marcet Z, Paster JW, Carr DW, Bower JE, Cirelli RA, Klemens F, Mansfield WM, Miner JF, Pai CS, Chan HB (2008) Opt Lett 33:1410 35. Liu TR, Shen Y, Shin W, Zhu QZ, Fan SH, Jin CJ (2014) Nano Lett 14:3848 36. Lassiter JB, Sobhani H, Fan JA, Kundu J, Capasso F, Nordlander P, Halas NJ (2010) Nano Lett 10:3184 37. Kubo W, Fujikawa S (2011) Nano Lett 11:8 38. Zhao J, Zhang CJ, Braun PV, Giessen H (2012) Adv Mater 24:OP247 39. Liu SD, Yang Z, Liu RP, Li XY (2011) J Phys Chem C 115:24469 40. Barnes WL, Murray WA, Dintinger J, Devaux E, Ebbesen TW (2004) Phys Rev Lett 92:107401. 41. Ghaemi HF, Thio T, Grupp DE, Ebbesen TW, Lezec HJ (1998) Phys Rev B 58:6779 42. Gao H, McMahon JM, Lee MH, Henzie J, Gray SK, Schatz GC, Odom TW (2009) Opt Express 17:2334 43. Schmid JH, Cheben P, Janz S, Lapointe J, Post E, Xu DX (2007) Opt Lett 32:1794 44. Hoyt LF (1934) Ind Eng Chem 26:329 45. Liu N, Mesch M, Weiss T, Hentschel M, Giessen H (2010) Nano Lett 10:2342 46. Schmidt MA, Lei DY, Wondraczek L, Nazabal V, Maier SA (2012) Nat Commun 3:1108 47. Pryce IM, Kelaita YA, Aydin K, Atwater HA (2011) ACS Nano 5:8167 48. Paivanranta B, Merbold H, Giannini R, Buchi L, Gorelick S, David C, Loffler JF, Feurer T, Ekinci Y (2011) ACS Nano 5:6374 49. Offermans P, Schaafsma MC, Rodriguez SRK, Zhang YC, Crego-Calama M, Brongersma SH, Rivas JG (2011) ACS Nano 5:5151 Fig. 1 DDMG fabrication: a) Schematic showing the fabrication procedure. IL stands for interference lithography. b) Interference lithography geometry for preparing the slanted photoresist grating. φ is the incident angle of two laser beams with respect to the normal (red dashed line). α is the rotation angle with respect to the plane that is perpendicular to the angle bisector formed by these two laser beams (black rectangle). c) Schematic of a single unit cell of the DDMG. a refers to the periodicity of the DDMG, w1 and w2 represent the widths of the top gold stripe and the photoresist stripe respectively, Δx is the dislocation between the upper and lower gold gratings, while h and t stand for the height of the slanted photoresist stripe and thickness of the gold film, respectively. d,e) Top-view and cross-sectional SEM images of a DDMG, the sizes of which are a = 770 nm, w1= 330 nm, Δx=128 nm, h = 480 nm, and t = 120 nm. The scalar bars in (d) and (e) are 400 nm. Fig. 2 Reflection, absorption spectra, and electric field intensity distributions of the DDMG in air: a) Reflection spectra of the DDMG (a = 770 nm, w1= 330 nm, Δx=128 nm, h = 480 nm, t = 120 nm). The red and black curves represent the measured and simulated results of the DDMG, respectively. b) Corresponding absorption spectra of the DDMG. The dashed lines in a) and b) indicate the modes of WA(1)sup, WA(1)eff, WA(1)sub and SPP(-1)Au/PMMA respectively, calculated by Equations (13). cf) Simulated electric field intensity distributions at the indicated resonance positions at the linear scale. Fig. 3 Generation and tuning of the LSPR-WA(1)eff mode on the reflection and absorption spectra by the dislocation of two gold gratings: a,b) Top-view SEM images of the DDMG with a dislocation of 128 nm (a = 770 nm, w1 = 330 nm, Δx = 128 nm, h = 480 nm and t = 120 nm) and NDDMG (a = 770 nm, w1 = 330 nm, Δx =0 nm, h = 480 nm and t = 120 nm) respectively. c,d) Cross-sectional SEM images of the same DDMG and NDDMG in a) and b) respectively. e,f) Reflection spectra of the DDMG and NDDMG in a) and b) in air at normal incidence under p-polarization. g,h) Electric field Ez and magnetic field Hy distributions at the wavelength of 917 nm in the DDMG. i,j) Electric field Ez and magnetic field Hy distributions at the wavelength of 917 nm in the NDDMG. Plus and minus signs indicate the polarity of charge on the surface of the gold stripe. The red and blue circles indicate the closed-loop currents between the top and bottom gold stripes. k,l) Simulated reflection and absorption spectra of the structures of the double-layered gold gratings with varying dislocations. As the dislocation is increased from 0 to 128 nm, the LSPR-WA(1)eff mode (indicated by the magenta band) is generated and gradually strengthened on the reflection and absorption spectra. The scalar bars in a), b), c) and d) are 200 nm. Fig. 4 Sensitivities of the DDMG in RI sensing: a,b) Measured and simulated reflection spectra of the DDMG (a = 770 nm, w1 = 330 nm, Δx = 128 nm, h = 480 nm and t = 120 nm) in glycerin-water mixture solutions at normal incidence under p-polarization, where the involved four resonant modes are marked with D1~D4. c,d) Relationships between the resonance wavelengths of D1(black), D2(red), D3(blue) and D4(magenta) and the refractive indices. The lines are linear fits. Specifically, all data points were used in the linear fitting for D1 and D4, only first six (three) ones and four (six) ones in the measurements (simulations) were used for D2 and D3, respectively. The measured and simulated refractive index sensitivities of D1, D2, D3 and D4 modes are determined to be 681, 481, 413, 385 nm RIU-1 and 723, 525, 503, 237 nm RIU-1, respectively. The standard deviations for all the measured data points (< 0.3 nm) are too small to be seen. e) Electric field intensity distributions of the resonant modes of the DDMG in RI modulation. Clearly, as the index is increased, a mode exchange between LSPR-WA(1)eff and WA(1)sub occurs. Specifically, at the index of 1.333, the electric field of D2 is mostly confined between these two gold grating layers and the one edge of the top gold stripe, nearly the same as that of D3 at the index of 1.398. Similarly, at the index of 1.333, the electric field of D3 is similar to that of D2 at the index of 1.398. Both are featured with the electric field pattern in the substrate that is perpendicular to the interface of the bottom gold grating and PMMA film, which is characteristic of Wood’s anomaly mode in the substrate. Table 1. Index sensitivities and FOMs of the resonant modes of the DDMG in Fig. 1 Mode Assignment RI range FWHM Sensitivity FOM nm eV nm eV FOMλ FOME -1 RIU RIU-1 D2 LSPR-WAeff(1) 1.333-1.398 13.2 0.013 481 0.496 36 38 D2 WAsub(1) 1.398-1.443 11.6 0.011 – – – – D3 WAsub(1) 1.333-1.398 12.1 0.012 – – – – D3 LSPR-WAeff(1) 1.398-1.443 13.0 0.012 413 0.385 32 31