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 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. 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
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