Sensors 2011, 11, 1992-2000; doi:10.3390/s110201992
Compact on-Chip Temperature Sensors Based on
Dielectric-Loaded Plasmonic Waveguide-Ring Resonators
Thomas B. Andersen, Zhanghua Han * and Sergey I. Bozhevolnyi
Institute of Technology and Innovation, University of Southern Denmark, Niels Bohrs Alle 1,
DK-5230 Odense M, Denmark; E-Mails: email@example.com (T.B.A.); firstname.lastname@example.org (S.I.B.)
* Author to whom correspondence should be addressed; E-Mail: email@example.com;
Tel: +45-6595-8641; Fax: +45-6550-7384.
Received: 10 December 2010; in revised form: 14 January 2011 / Accepted: 30 January 2011 /
Published: 7 February 2011
Abstract: The application of a waveguide-ring resonator based on dielectric-loaded
surface plasmon-polariton waveguides as a temperature sensor is demonstrated in this
paper and the influence of temperature change to the transmission through the
waveguide-ring resonator system is comprehensively analyzed. The results show that the
roundtrip phase change in the ring resonator due to the temperature change is the major
reason for the transmission variation. The performance of the temperature sensor is also
discussed and it is shown that for a waveguide-ring resonator with the resonator radius
around 5 m and waveguide-ring gap of 500 nm which gives a footprint around 140 µm2,
the temperature sensitivity at the order of 10−2 K can be achieved with the input power
of 100 W within the measurement sensitivity limit of a practical optical detector.
Keywords: temperature sensor; dielectric-loaded surface plasmon-polariton waveguide;
Temperature sensing based on optical techniques is promising and remains an area of continuing
and intensive research interest around the World in recent years due to some advantages compared to
other temperature measurement techniques, e.g., high sensitivity, large temperature range and the
stability and immunity of optical signal to the turbulence of the environmental noises . Up till now,
fiber-optic temperature sensors constitute a major category of the optical temperature sensors, and they
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mainly employ the principles of fiber Bragg gratings  or surface plasmon resonance
(SPR) . The temperature change will introduce a noticeable shift in the central resonance
wavelength, thus people can obtain the information for the temperature with high sensitivity by
monitoring the resonance wavelength change. These fiber-optic temperature sensors can take the
advantage of the well-developed fiber-optics technique and are very favorable for constructing remote
distributed sensing networks with low propagation loss in optical fibers and wavelength division
multiplexing techniques. However, all these fiber-optic temperature sensors are bulky and can hardly
be used as chip scale temperature sensors. In addition, the measurement of resonance wavelength shift
needs an optical spectrum analyzer, which is quite expensive and can hardly be integrated into an
optical integrated circuit chip.
In this paper, we propose to realize chip scale temperature sensors based on dielectric-loaded
surface plasmon-polariton waveguide-ring resonators (WRR). Surface plasmons are the surface waves
due to the coupling of electromagnetic waves to the collective electron oscillations in the metals, and
they propagate along the interface between the metal and the dielectrics, with the field decaying
exponentially along the direction perpendicular to the interface , providing a new way of
manipulating light at the nano scale. The light energy of surface plasmons is mainly localized at the
interface between the metal and the dielectric with the major part in the dielectric, so the propagation
of surface plasmons is greatly affected by the dielectric properties, which in principle implies that the
use of surface plasmons in sensing is also quite promising. What’s more, the light field near the
metal/dielectric is greatly enhanced and this will improve the sensing sensitivity considerably. In the
literature much effort has been made to investigate the use of surface plasmons for sensing, and while
some decent results have been reported , most of them still rely on SPRs. In the meanwhile,
plasmonic waveguides have been attracting much attention in recent years owing to their ability to
spatially confine light below the diffraction limit , thereby potentially enabling photonic device
integration on a scale not accessible with conventional dielectric waveguide-based photonic integrated
circuits, and this opens up a new avenue for further miniaturization of optical components. To date,
various plasmonic waveguide structures have been proposed and investigated [7-9] for planar photonic
integration. But the use of plasmonic waveguides in on-chip sensing has been rarely explored. Among
those plasmonic waveguides proposed up till now, the dielectric-loaded surface plasmon-polariton
waveguide (DLSPPW) is quite promising due to its compactness, ease of fabrication and the
moderate propagation loss of surface plasmons in this waveguide. Some polymers, e.g.,
Poly-methylmethacrylate (PMMA), are usually employed as the dielectric material in the DLSPPW
and this makes DLSPPW a good candidate for temperature sensors due to the good thermo-optic
effects of the polymers.
Figure 1(a) gives the schematic figure for the cross section of the DLSPPW, showing that a PMMA
ridge with width 500 nm and height 550 nm is deposited onto a 60 nm thick gold film, which is
supported by a thin glass substrate. In Figure 1(b) the mode profile for the 1.5m wavelength is also
shown, from which one can see the tight lateral confinement and that the light is well confined near the
bottom of the PMMA ridge in the perpendicular direction. One main advantage of the DLSPPW is that
metal can be used as a negative-permittivity material to support the plasmonic mode, as well as part of
the electrical circuit, so that both the optical and electrical signals can propagate through the DLSPPW
at the same time. This can also be employed to heat the polymer ridges by applying some electric
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current through the metal strip so that the index of the polymer will be changed due to thermo-optical
effect. As a consequence, the mode effective index of the DLSPPW will also change in both the real
part and the imaginary part, and these two parameters will determine the power transmission through a
specific waveguide. The polymer refractive index is also dependent on the environmental temperature;
then one can analyze the temperature change by monitoring the power transmission. To further
enhance the sensitivity of the transmission to the index change, a WRR system schematically shown in
Figure 1(c) is adopted in this paper because of the high sensitivity of the transmission through the bus
waveguide to the index change in the ring for some wavelengths. In the WRR system, a straight
DLSPPW is laterally coupled to a ring resonator with a small gap between them and both the two
components are placed on a thin gold layer. These structures can be easily fabricated with deep
ultraviolet lithography or electron beam lithography techniques when the polymers can work as both
the resist and the DLSPPW core material.
Figure 1. (a) Schematic figure for the cross section of DLSPPW; (b) the mode profile for
the DLSPPW at the wavelength of 1.5 m; (c) Schematic illustration of WRR with the
dielectric-loaded surface plasmon waveguide laterally coupled to a ring resonator.
In the following section we will analyze in detail how the temperature change will affect the power
transmission through the WRR system. Some numerical results will be given in Section 3 to show the
dependence of power transmission on the temperature and the performance of this temperature sensor
is also discussed. The whole paper concludes in Section 4.
It is well known that the transmission through an all-pass ring resonator schematically shown in
Figure 1(c) is determined by the following Equation :
2 cos(( )2
12cos( ( )2
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accounts for the pure bending loss and
eff eff eff
), is the transmission coefficient in the bus waveguide through the waveguide-ring
interaction region. is the round trip phase, determined by the ring radius R and the real part of the
mode effective index
In Equation (1), the parameters and are all dependant on polymer index, so they are all
functions of temperature T when the polymer thermo-optic effect is considered. Note that the thermal
expansion is not considered here because at room temperature the linear thermal expansion coefficient of
PMMA, the polymer adopted in our calculation, is about one order of magnitude smaller (3.6 × 10−5 /K)
than the effect of temperature on refractive index (−1.05 × 10−4/K) . As for gold, its linear thermal
expansion coefficient at room temperature is even smaller (1.42 × 10−5/K) than that of PMMA, thus we
don’t take into account in our calculations the thickness change of gold due to thermal expansion.
Therefore the dimensions, including w, g, R and t, shown in Figure 1 are considered to be irrelevant to
temperature T. Under this condition
is the inner circulation factor describing the internal loss where
is the imaginary part of the mode effective index
at the free space wavelength
is the propagation constant in
rT can be written as
( ( ), ( ), ( ))
. Then the derivative
rT with respect to T is:
We will discuss each term of A, B and C separately. Using the expression for α given above one
The last factor
imaginary part of the mode effective index changes as a function of the polymer refractive index n and
dTd expresses the change in transmission when the propagation loss in the ring changes.
Transmission coefficient τ will suffer from some change when n changes with temperature since the
mode property will be affected and the transmission also depends on τ. This all together gives:
dn dT is the thermo optical coefficient of the polymer,
dNdn describes how the
When it comes to the last term C, it is related to the change in the accumulated round trip phase θ
due to variations in the real part of the mode effective index. This in turn affects the interference
between the ring and the bus waveguide and consequently changes the overall transmission. We cannot
measure directly how the transmission is affected by change in roundtrip phase, i.e.,
know from our experiments how transmission changes with wavelength
paper, we are investigating changes in transmission versus temperature at a certain wavelength
we can get:
dTd , but we
dTd . Note that in this
0 . So
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Since is a function of
0 , the connection between d and
, we obtain that
can be derived
. Because mathematically. With
4( ) /
dR dNN d
0 , it can be concluded from
.With the expression for , we also have
dNdT describing mode effective index change with temperature, we realize it’s not
possible to calculate it directly, but we can determine how the mode effective index changes with
polymer change index of refraction n and it’s known how n changes with temperature:
dNdTdNdn dn dT
. This together gives the result:
, then we have
. As for
So in principle the polymer index change due to the thermo-optic effect will cause some changes in
which further lead to the variation of power transmission
Thus the temperature change can be calculated via the Tr variation. This is the basic idea of the
temperature sensor based on dielectric-loaded plasmonic waveguide-ring resonators.
rT through the WRR.
3. Results and Discussion
In the previous section, we have shown analytically the temperature dependence of the transmission
output through a WRR system. In this section, we will discuss quantitatively the three terms of A, B
and C for a specific WRR system. That is, how the changes of and due to the change of polymer
index as a function of temperature will affect the transmission through the WRR.
We start with a specific example of a WRR with the ring radius R equaling to 5.39 m and
waveguide-ring gap g being 0.5m, whose transmission spectrum is shown in Figure 2. Here it is
assumed that the pure bending loss is 0.71 and the transmission coefficient is 0.66. In the
calculations of the mode effective index, i.e.,
have a fast and simple calculation over this wavelength range while retaining an acceptable accuracy
compared to the pure numerical method, e.g., the finite-element method (FEM) based mode solvers.
We used the
to be –2.52 × 105m−1+ 1.6138 and the power propagation length
, to be 71.2− 60.88 µm. Note that the equations for
will be dependent on the geometry of the DLSPPW show in Figure 1(a). All the assumptions are
proven to be valid because they give a good agreement between the experimental transmission result
and the analytical result from Equation (1) . From Figure 2 one can see that the transmission
exhibits period dips with extinction ratios above 10 dB and the free spectral range around 45 nm.
, effective index method  is adopted to
, which is
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Figure 2. Transmission spectrum for an all-pass ring resonator based on DLSPPW.
With this ring resonator as an example, the specific values of A, B and C in Equation (2) will be
approximately estimated for some wavelengths. We will start with C first, because it is strongly
affected by the working wavelength due to the term of dTr/dλ. Taking the derivative of Tr with respect
to a maximum of dTr/dλ with the value 7.394 × 107 is found at the wavelength around 1.5 m.
Assuming the complex refractive index of gold to be the experimental value of 0.53 + 9.51j  and
the PMMA index to be 1.493, using a commercial FEM mode solver of Comsol Multiphysics, the
mode effective index for the DLSPPW schematically shown in Figure 1(a) is found to be
1.224 + 0.00384j. For the calculation of
dN dn, the index of PMMA is changed by a small amount
∆n and FEM mode solver is used again to find the new value of
respect to temperature dn/dT is −1.05 × 10−4 /K . Then the specific value of C at around 1.5 m is
estimated to be C = 8.4 × 10−3 /K.
For the calculation of A at 1.5m, first α is found at this wavelength, with which Tr is further
calculated according to Equation (1). Using a similar approach to that described above, is changed
by a small amount ∆ and
calculation, FEM mode solver is also used twice with a small change of the PMMA index, then the
value of A is estimated as A = 9.3 × 10−6 /K. The calculation of B is not so straightforward because the
determination of transmission coefficient usually needs a full wave simulation. To have a rough
estimation of it, we switch to a simpler method. As is known, the coupling of optical power from one
straight waveguide to the other straight waveguide is determined by their interaction length l and the
coupling length Lc between the two waveguides, while the latter is the length over which the power can
be completely transferred from one waveguide to the other and Lc can be calculated using
Lc = λ / (2|ne – no|) where ne and no are the mode effective index for the even mode and the odd mode
respectively for the two-waveguide system, so the transmission coefficient can be roughly obtained
cos( / 2/)
. With the FEM mode solver and having two DLSPPW with a gap g
. The PMMA index change with
rT is calculated again, then
dTd is obtained. With respect to
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of 500 nm in the structure, both ne and no can be obtained with which Lc can be calculated at 1.5 m.
Assuming the interaction length between the straight waveguide and the ring resonator to be
l = 7.15 m, we can get the transmission coefficient to be about 0.66, which agrees quite well with
the value of used to generate Figure 2. By changing the PMMA index with a small amount and
repeating the above procedures, the dependence of on PMMA index
this method, we can roughly estimate B at the wavelength of 1.5 m to be
Having a comparison of A, B and C, one can see that A and B are 2 orders and 1 order of magnitude
smaller than C, respectively, which implies that we can ignore A and B just to simplify the analysis.
These values are obtained at a wavelength when
as sensitive to the wavelength as C is, so we can conclude that
dTd is at its maximum.
C demonstrates the dependence of transmission on the roundtrip phase of the resonator waveguide,
which is actually the dependence of transmission on the mode effective index. One can easily
understand why C is much larger than A and B because the transmission through an all-pass resonator
is actually due to the interference of light through the straight waveguide directly and the light coupled
to the straight waveguide from the resonator after one roundtrip of propagation. The interference is
very sensitive to the phase change inside the ring resonator.
So in principle the temperature sensor is mainly based on the temperature dependence of PMMA
index, which further determines the mode effective index of the ring waveguide and the roundtrip
phase of the ring. One may also raise the question about the influence of thermo-optic effect in the
gold layer to the transmission. This can be estimated using Equations (2 ~ 4) and (6),
changed to be
is the complex refractive index of gold. Our numerical calculation results show
that the influence to the transmission through the WRR system due to the thermo-optic effect of gold is
roughly two orders of magnitude smaller than that due to the thermo-optic effect of PMMA. Here the
dependence of both of the real and imaginary parts of the complex refractive index of gold is evaluated
with the temperature dependent Drude model . Then for the sake of simplicity, we can only
concentrate on the thermo-optic effect of PMMA in this paper.
From Equation (6), one can see that
dTd plays a very important part in the determination of C.
In order to have an optimum performance for the temperature sensor, one needs to have to have
dTd as large as possible.
dTd can be roughly estimated as
are the maximum and minimum transmissions respectively, and
at resonance wavelength
intrinsic quality factor of the plasmonic ring resonator, we need to have a large difference between
or in other words a large extinction ratio in order to increase
in , for plasmonic resonators, the loss in the resonators is relatively large, i.e., is quite small. In
order to have a coupling close to the critical coupling, the gap between the bus waveguide and the ring
resonator should be small enough. As for the ring radius, since it determines both the roundtrip
propagation loss inside the ring and the bending loss and there should be a compromise between the
two, one needs to design the ring resonators carefully under specific conditions.
can be calculated. Using
2.12 10 /
d is large, however. Note that A and B are not
dTdT has its maximum when
is the bandwidth
and the quality factor Q is limited by the low
dTd . As discussed
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According to the discussions shown above, the sensitivity of transmission to the temperature is on
the order of
10 / K
. In practice, the minimal detectable temperature change is affected by the optical
detector sensitivity, and can be described as:
where NEP is the Noise-equivalent power of the optical detector, B is the bandwidth of the detector,
P is the input power from the light source and
to the detector, here considered to be fiber-coupled. If we use the NEP to be 1.4
be 320 kHz, which are the characteristics of a commercially available optical detector from Thorlabs
(PDA10CS-EC), and assume
to be 3.8 × 10−2  and the input power to be 100 µW, we can find
that the minimal detectable temperature change can be as low as 2.5 × 10−2 K with the value of
dTdT equaling to
8.4 10 /K
. The sensitivity can be further increased if a lock-in-amplifier is
used. In this case B can be replaced with 1/(2τ), where τ is the integration time. For τ equaling to 60 s,
the sensitivity becomes as low as 4.0 × 10−6 K. Note the optical detector for the DLSPPW can also be
replaced with a power monitor that was proposed for the long range surface plasmon polariton
waveguides , then both the temperature sensor and the power monitor can be integrated on a
Although the change in power transmission is monitored in this temperature sensor, we can also
compare the refractive index sensitivity with other temperature sensors measuring the resonance
wavelength shift. Using the data in Section 3, we can find the refractive index sensitivity to be
d dnd dN dNdnN dN dn
alone only has a footprint of around 140 µm2 and is quite compact.
characterizes the power loss from the light source
10 W Hz
and B to
. And note that the sensing part
We have demonstrated in this paper the application of a WRR based on DLSPPW as a temperature
sensor. The temperature dependence of transmission coefficient in the bus waveguide through the
waveguide-ring interaction region, the intrinsic loss and the roundtrip phase inside the ring, as well as
the influence of these parameters to the transmission through the WRR are analyzed. Theoretical
calculations also show that for a WRR with the resonator radius around 5 m and waveguide-ring gap
of 500 nm, the temperature sensitivity at the order of 10−2 K can be achieved with the input power
of 100 W within the sensitivity limit of a practical photodetector. This temperature sensor is very
promising as an on-chip sensor of temperature due to the compact size and high sensitivity. We believe
that it will find broad applications in many areas.
This work was supported by FTP-project No. 09-072949 ANAP.
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