Plasmonic circular resonators for refractive index sensors and filters
Wei et al. Nanoscale Research Letters
Plasmonic circular resonators for refractive index sensors and filters
Wei Wei 0
Xia Zhang 0
Xiaomin Ren 0
0 State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications , P. O. Box 66, Beijing 100876 , China
A plasmonic refractive index sensor based on a circular resonator is proposed. With all three dimensions below 1 m, the sensor has a compact and simple structure granting it ease-of-fabrication and ease-of-use. It is capable of sensing trace amounts of liquid or gas samples. The sensing properties are investigated using finite elements method. The results demonstrate that the plasmonic sensor has a relatively high sensitivity of 1,010 nm/RIU, and the corresponding sensing resolution is 9.9 105 RIU. The sensor has a relatively high quality factor of 35, which is beneficial for identifying each transmission spectrum. More importantly, the sensitivity is not sensitive to changes of structure parameters, which means that the sensitivity of the sensor is immune to the fabrication deviation. In addition, with a transmittance of 5% at the resonant wavelength, this plasmonic structure can also be employed as a filter. In addition, by filling material like LiNbO3 or liquid crystal in the circular resonator, this filter can realize an adjustable wavelength-selective characteristic in a wide band.
Surface plasmons; Sensors; Filters
At present, more and more researchers pay their
attentions on the investigation of surface plasmons (SPs).
Thus, a lot of articles about SPs emerged, from which
numerous devices based on SPs are proposed. SPs are
optically induced oscillations of the free electrons at the
surface of a metal and can confine and propagate
electromagnetic energy far beyond the diffraction limit for
electromagnetic waves in dielectric media [1,2]. This
could lead to miniaturized photonic components with
dimensions scale much smaller than those currently
achieved [3,4], such as plasmonic waveguides [5-8] and
plasmonic nanolasers [9,10]. Due to the susceptibility of
SPs to surrounding dielectric, SPs and surface plasmon
resonance (SPR) exhibit excellent properties for sensing
applications [11-13]. In past decades, various plasmonic
sensors based on SPs and SPR have been proposed and
investigated [14-24], especially prism-coupled SPR
sensors [14-17] and fiber-coupled SPR sensors [20-24].
Generally, dimensions of prism-coupled SPR sensors are
huge for integration of sensors on chips and their
sensitivities are not high compared to fiber-coupled SPR
sensor. Although fibers make SPR sensors smaller and
more flexible, the dimensions are still too large for
sensing applications of lab on chip. Recently,
metalinsulator-metal (MIM) plasmonic waveguides offering
very high optical confinement and closer spacing to
adjacent waveguides or structures have been proposed for
diverse applications, such as MIM optical filers [25,26],
electromagnetically induced transparency [27,28], Bragg
gratings [29,30], and directional couplers [31,32].
Compared to other sensors, plasmonic sensors with MIM
structures have an inherent advantage to achieve high
In this paper, we focused on the compactness of the
sensor with an acceptable sensitivity and its integration
to other components. By employing the MIM structure,
we proposed a plasmonic refractive index sensor based
on a circular resonator. This sensor has a simple and
ultra-compact structure. It is comprised of a circular
resonator and a bus waveguide. All three dimensions of
the sensor are below 1 m. Combing such a compact
structure and sensing capability of SPs, this plasmonic
refractive index sensor can realize real-time and on-chip
sensing. Moreover, the structure parameters have neglected
impact on sensing sensitivity of the plasmonic sensor.
Figure 1 Schematic diagram of the plasmonic structure.
Besides the application of sensors, this structure can
be used as filters due to its low transmittance at the
resonant wavelength. Moreover, by filling material like
LiNbO3 or liquid crystal, the filter can realize an
adjustable wavelength-selective characteristic in a wide
The schematic of the plasmonic structure is
demonstrated in Figure 1, where the background material in gray
is silver, whose permittivity is described by the Drude
model r 2p=2 j , with = 3.7, p = 9.1 eV,
and = 0.018 eV . The parameters adopted here
fit the experimental data at the infrared frequencies
. The long strip waveguide filled with silica in the
silver pad is called bus waveguide. The circle above
the bus waveguide is a circular resonator behaving as
a Fabry-Perot (F-P) cavity. The empty circular
resonator in the silver pad is used to collect the analyte
(liquid or gas) to be sensed. When this structure is used
as a filter, the empty circular resonator can be filled by
liquid with proper refractive index, LiNbO3 or liquid
crystal, to realize customized or adjustable
wavelengthselective characteristic. The small gap between the
bus waveguide and the circular resonator is designed
to enhance coupling between them. The width of the
bus waveguide is 100 nm. In spite of transmission
loss in the waveguide, the length of the bus waveguide
has no influence on sensing and wavelength-selective
characteristics of this plasmonic structure, so its length is fixed
at 800 nm considering the compactness and integration.
The radius of the circular resonator is R, and the height and
width of the small gap are denoted by H and W, respectively.
Figure 2 Transmission spectra of the plasmonic refractive index sensor for varying refractive index of analyte. Insets are magnetic field Hz
corresponding to the index of 1.4 at the wavelengths of 1.476 and 1.576 m.
The gratings at the start and end of the bus waveguide are
used to couple super-continuum light into the sensor and
the transmission spectrum out of the bus waveguide. This
plasmonic structure could be fabricated by steps as follows:
first, deposit an Ag film with a thickness of 500 nm on a
silica substrate; then, fabricate the required pattern by
EBL and etching, and deposit a silica film with a
thickness of 500 nm; last, clear the redundant silica on the
Ag film and in the circular resonator, and fabricate the
gratings at the two ends of the bus waveguide by EBL
Results and discussion
In this section, we first investigated the sensing
properties of the plasmonic structure and then indicated its
wavelength-selective properties as a filter at the end of
this section. Sensing properties including distribution of
electromagnetic field, transmission spectrum, and
sensitivity are numerically analyzed using finite elements
method with scatter boundary conditions. In the
calculation, a plane wave was injected from the left side of the bus
waveguide by a port to excite fundamental TM modes of
SPs. The transmitted light was collected from the right side
of the bus waveguide which is defined as T = Pout/Pin, where
Pin = PoavzdS1 and Pout = PoavzdS2; Poavzd is the z
component of time-average power flow. The transmission
spectra of the plasmonic structure are obtained by
parametrically sweeping the input wavelength with step of
For various refractive indices of analyte in the circular
resonator, Figure 2 demonstrates the corresponding
transmission spectra of this plasmonic sensor with a structure
of R = 300 nm, H = 100 nm, and W = 100 nm. For the
transmission spectrum corresponding to the refractive
index 1.4, there is a dip in the transmission spectrum and
most other wavelengths of the injected wideband light are
transmitted through the bus waveguide. The wavelength
corresponding to the deepest dip is called the resonant
wavelength. At the resonant wavelength, most energy
coupled into the circular resonator from the bus waveguide.
As the insets show in Figure 2, at the wavelength of
1.576 m, most energy transmitted through the bus
waveguide without coupling into the circular resonator. But at
the wavelength of 1.476 m, most energy coupled into the
circular resonator and very little energy transmitted
through the bus waveguide. The energy resonated in the
circular resonator is sensitive to the refractive index
variations of the analyte in the circular resonator, so when the
refractive index of the analyte was changed, the resonant
wavelength in the transmission spectrum shifted which is
demonstrated in Figure 2. Thus, the above is the sensing
mechanism of this plasmonic refractive index sensor.
Transmission spectra of refractive index 1.35 for values
of R varying from 280 to 320 nm are demonstrated in
Figure 3a. The transmission dip shifts towards a longer
wavelength with incremental R. The wavelength difference
between each resonant wavelength is about 35 nm. For
each transmission spectrum, the shift of the resonant
wavelength can be explained via the standing-wave
condition, NN = 2neffL, N = (1, 2, 3 ). For a specific N, larger
radius of the circular resonator causes the red shift of
resonant wavelength, while shorter radius of the circular
Figure 3 Sensing properties as functions of R. (a) Transmission
spectra of refractive index 1.35 as functions of R. (b) Shifting
wavelengths corresponding to the dips in the transmission spectra
for different R. (c) Sensitivities of the plasmonic refractive index
sensors for different R.
resonator causes the blue shift of resonant wavelength.
The resonant wavelength versus refractive index of analyte
for different R values is demonstrated in Figure 3b. All the
resonant wavelengths increase linearly as the refractive
index increases, and slopes of the five lines are similar.
The sensitivity of the plasmonic sensor was calculated
using S(nm/RIU) = |dpeak/dna|, and shown in Figure 3c.
The sensitivity of the plasmonic refractive index sensor
has a positive correlation with incremental R in a range
from 900 to 1,010 nm/RIU. The maximum sensitivity is
1,010 nm/RIU and its corresponding sensing resolution is
9.9 105 RIU. Thus, the radius of the circular resonator
influences not only the resonant wavelength but also the
sensitivity. However, the influence of the radius of the
circular resonator on the sensitivity of the plasmonic
refractive index sensor is very small and can be neglected,
the variation of sensitivity is in a range of 110 nm/RIU
around 950 nm/RIU (fluctuation is about 6%).
Figure 4 Sensing properties as functions of H. (a) Transmission
spectra of index 1.35 for H varying from 80 to 120 nm. (b) Shifting
resonant wavelengths for H varying from 80 to 120 nm. (c) Sensitivities
of the plasmonic sensors for H varying from 80 to 120 nm.
Figure 5 Sensing properties as functions of W. (a) Transmission
spectra of index 1.35 for W varying from 80 to 120 nm. (b) Shifting
resonant wavelengths for W varying from 80 to 120 nm. (c) Sensitivities
of the plasmonic sensors for W varying from 80 to 120 nm.
Next, we analyzed the impact of different H on sensing
properties of the plasmonic refractive index sensor.
Transmission spectra of index 1.35 for values of H varying from
80 to 120 nm are demonstrated in Figure 4a. With
incremental H, the resonant wavelength shifts towards a longer
wavelength in a small range from 1.414 to 1.444 m. The
wavelength difference between each resonant wavelength
is about 6 nm. This shift can be explained by associating
with the above standing-wave condition of the F-P
resonator. The incremental H actually increases the length of
the F-P resonator, leading to the shift of the resonant
wavelength towards a longer wavelength. The resonant
wavelength versus the refractive index of analyte for
different H values is demonstrated in Figure 4b. All the
resonant wavelengths increase linearly as the refractive index of
analyte increases, and the slopes of the five lines are
similar. The sensitivity of the plasmonic sensor as a function
of H is shown in Figure 4c. With incremental H, the
sensitivity of the plasmonic refractive index sensor gradually
increases in a small range from 942 to 973 nm/RIU
around 960 nm/RIU (fluctuation is about 1.8%). Thus, the
height of gap H influences only the resonant wavelength.
The little influence of the height of the gap between the
circular resonator and the bus waveguide on the sensitivity
of the plasmonic refractive index sensor can be neglected.
The impact of different W on sensing properties of the
plasmonic refractive index sensor was investigated, and
transmission spectra of index 1.35 for values of W
varying from 80 to 120 nm are demonstrated in Figure 5a.
With the incremental W, the transmission dip shifts
towards a shorter wavelength in a small range from 1.414
to 1.448 m, which is contrary to the relation between
transmission dip shift and H, and the wavelength
difference between each resonant wavelength is about 7 nm.
This shift can also be explained by associating with the
above standing-wave condition of the F-P resonator.
Widening W equivalently decreases the length of the
FP resonator, leading to the shift of the resonant wavelength
towards a shorter wavelength. The resonant wavelength
versus the refractive index of analyte for different W values
is demonstrated in Figure 5b. All the resonant wavelengths
increase linearly as the refractive index of analyte increases,
and the slopes of the five lines are similar. The sensitivity of
the plasmonic sensor as a function of W is shown in
Figure 5c. With incremental W, the sensitivity of the
plasmonic refractive index sensor gradually decreases in a small
range from 940 to 975 nm/RIU around 960 nm/RIU
(fluctuation is about 2%). Thus, the height of gap W influences
only the resonant wavelength. The little influence of the
width of the gap between the circular resonator and the
bus waveguide on the sensitivity of the plasmonic refractive
index sensor can be neglected.
At last, we will discuss the wavelength-selective
characteristic of this plasmonic structure and indicate its
application as a filter. As shown in Figure 2, the
transmittance at the dip of the transmission spectrum is 5%
and the central stop-wavelength shifts towards a longer
wavelength with incremental refractive index of analyte.
But the transmittance at the central stop-wavelength
keeps the same. By filling material like LiNbO3 or liquid
crystal, the central stop-wavelength can be adjustable.
As shown in Figures 3, 4, and 5, the central
stopwavelength shifts with different structure parameters
and the transmittance at the central stop-wavelength
nearly keeps unchanged. So, by designing proper
structures, the wavelength-selective characteristic can be
We have proposed a plasmonic circular resonator for
refractive index sensor and filter. With all three
dimensions below 1 m, it has a simple and ultra-compact
structure, which makes it easy to be filled with analyte
and integrate with other components. The sensing
properties of the proposed sensor are numerically analyzed
using finite elements method. The positions of
transmission dips have linear relations with the refractive index
of analyte. The maximum sensitivity is 1,010 nm/RIU, its
corresponding sensing resolution is 9.9 105 RIU. It
has a relatively high quality factor of 35. More
importantly, the sensitivity of this ultra-compact plasmonic
sensor is immune to the changes of structure
parameters. At last, we indicated that with a very low
transmittance of 5%, this plasmonic structure could be also
employed as a filter. And the transmittance keeps nearly
unchanged when the structure parameters vary. By
filling material with proper refractive index, LiNbO3 or
liquid crystal, into the circular resonator, this filter can
realize customized and adjustable wavelength-selective
WW proposed the structure of plasmonic circular resonator, calculated
properties of the proposed structure, and wrote the manuscript. XZ and XR
analyzed the data and revised the manuscript. All authors read and
approved the final manuscript.
This work was supported by the National Natural Science Foundation of
China (61376019), the National Natural Science Foundation of Beijing
(4142038), the Specialized Research Fund for the Doctoral Program of Higher
Education (20120005110011), BUPT Excellent Ph.D. Student Foundation
(CX201435), and the 111 Project of China (B07005).
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