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

1State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and EngineeringSun Yat-sen UniversityGuangzhou 510275, China2Department of PhysicsThe Chinese University of Hong KongShatin, 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]:

(1)

where i is the grating order for the reciprocal lattice vector Gx of the one-dimensional

grating ( 2 /x G 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]:

(2)

(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]:

(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 gold-PMMA 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 gold-PMMA

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 gold-PMMA 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.

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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 (1-3). c-f)

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. 1Mode Assignment RI range FWHM Sensitivity FOM

nm eV nm RIU-

1eV

RIU-1FOMλ FOME

D2 LSPR-WAeff(1) 1.333-1.398 13.2 0.013 481 0.496 36 38D2 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