Page 1

Sensors 2011, 11, 1992-2000; doi:10.3390/s110201992

sensors

ISSN 1424-8220

www.mdpi.com/journal/sensors

Article

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: tbsa@iti.sdu.dk (T.B.A.); seib@iti.sdu.dk (S.I.B.)

* Author to whom correspondence should be addressed; E-Mail: zhh@iti.sdu.dk;

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;

waveguide-ring resonator

1. Introduction

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 [1]. Up till now,

fiber-optic temperature sensors constitute a major category of the optical temperature sensors, and they

OPEN ACCESS

Page 2

Sensors 2011, 11

1993

mainly employ the principles of fiber Bragg gratings [2] or surface plasmon resonance

(SPR) [3]. 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 [4], 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 [5], 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 [6], 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

Page 3

Sensors 2011, 11

1994

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.

2. Principle

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 [10]:

22'

22

22

22'

2

2cos(( )2

)

2

2

cos( )

cos( )

2

1

12cos( ( )2

)

eff

r

eff

NR

T

NR

(1)

w

g

(c)

t

(a)

(b)

PMMA

Gold

Glass

R

Page 4

Sensors 2011, 11

1995

in which

accounts for the pure bending loss and

(

effeffeff

NN jN

), 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

eff

N

free space.

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) [11]. 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

of

"

eff

0

exp( 2

)

Rk N

is the inner circulation factor describing the internal loss where

"

eff

N

is the imaginary part of the mode effective index

eff

N

'"

'( )

at the free space wavelength

0

2 /

k

is the propagation constant in

rT can be written as

( ( ), ( ), ( ))

TT

rr

TTT

. Then the derivative

rT with respect to T is:

rrrr

dT

dT

dT

d

dT

d

dT

d

d

dT

d

dT

d

dT

ABC

(2)

We will discuss each term of A, B and C separately. Using the expression for α given above one

obtains:

"

eff

"

eff

00

"

eff

"

eff

22

00

( 2

)( 2

)

Rk N

Rk N

rrr

dN

dT

dN

dn dT

dT

d

dT

d

dT

d

d

dT

dn

ARk e

Rk e

(3)

The last factor

imaginary part of the mode effective index changes as a function of the polymer refractive index n and

/

r

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,

"/

eff

dNdn describes how the

rr

dT

d

dT

d

d

dT

d

dn dT

dn

B

(4)

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:

/

r

dTd , but we

/

r

dTd . Note that in this

0 . So

00

'

0T

0

'

1

()()

eff

rr

d

d

eff

dN

dT

dT

d

dT

d

d

dT

d

C

d

d

dN

(5)

Page 5

Sensors 2011, 11

1996

Since is a function of

'

eff

N

at

0 , the connection between d and

, we obtain that

'

eff

dN

can be derived

. Because mathematically. With

d

at

2'

4/

eff

RN

2''2

4() /

effeff

0

dR dNN d

0

0 , it can be concluded from

4/

eff

RN

.With the expression for , we also have

the term

/

eff

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:

''

/(/)(/)

effeff

dNdTdNdn dn dT

. This together gives the result:

2'

4/

eff

RN

that

'

eff

dN

, then we have

2'2

/

dd

0

'2

/4/

eff

ddNR

. As for

'

'

'

eff

r

eff

dN

dn dT

dT

d

dn

C

N

(6)

So in principle the polymer index change due to the thermo-optic effect will cause some changes in

and or

eff

N

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.,

eff

N

and

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

eff

N

to be –2.52 × 105m−1+ 1.6138 and the power propagation length

defined as

( ) /(4)

sp eff

LN

, 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) [13]. 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.

'"

eff

N

, effective index method [12] is adopted to

'

( )

, which is

and

L

sp

L

N

"'

eff

( )

sp

Page 6

Sensors 2011, 11

1997

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 [14] 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

/

eff

dNdn, 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 [11]. 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

by

cos( / 2/)

c

l L

[15]. With the FEM mode solver and having two DLSPPW with a gap g

'

'

eff

N

. The PMMA index change with

rT is calculated again, then

/

r

dTd is obtained. With respect to

"/

eff

dNdn

Page 7

Sensors 2011, 11

1998

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

r

dT

as sensitive to the wavelength as C is, so we can conclude that

/

r

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),

with

dndNeff/

,

dndNeff/

,

dnd /

, and

dTdn/

changed to be

, where

Au

n

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 [16]. 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

/

r

dT d 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

/

r

dT d as large as possible.

/

r

dT d can be roughly estimated as

rT

and

min

are the maximum and minimum transmissions respectively, and

at resonance wavelength

m

. Since

/

FWHM

intrinsic quality factor of the plasmonic ring resonator, we need to have a large difference between

and

min

or in other words a large extinction ratio in order to increase

in [17], 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.

/

B

d dn

can be calculated. Using

4

2.12 10 /

K

.

/

d is large, however. Note that A and B are not

/

r

dT dT has its maximum when

'"

Aueff

dndN

/

'

,

Aueff

dndN

/

"

,

Au

dn d /

, and

dTdnAu/

maxmin

0.5()/

rr FWHM

TT

where

max

rT

FWHM

is the bandwidth

m Q

and the quality factor Q is limited by the low

max

rT

rT

/

r

dTd . As discussed

Page 8

Sensors 2011, 11

1999

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:

3

min

/()

r

in loss

P k

dT

dt

dTNEPB

(6)

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

loss

k

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

loss

k

to be 3.8 × 10−2 [18] 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

/

r

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 [19], then both the temperature sensor and the power monitor can be integrated on a

single chip.

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

''''

/////

eff effeff eff

ddn ddNdN dnN dN dn

alone only has a footprint of around 140 µm2 and is quite compact.

in

characterizes the power loss from the light source

12

10 W Hz

and B to

3

1090/

nm RIU

. And note that the sensing part

4. Conclusions

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.

Acknowledgements

This work was supported by FTP-project No. 09-072949 ANAP.

References

1. Childs, P.R.N.; Greenwood, J.R.; Long, C.A. Review of temperature measurement. Rev. Sci.

Instrum. 2000, 71, 2959-2978.

Page 9

Sensors 2011, 11

2000

2. Lee, B. Review of the present status of optical fiber sensors. Opt. Fiber Technol. 2003, 9, 57-79.

3. Sharma, A.K.; Jha, R.; Gupta, B.D. Fiber-optic sensors based on surface plasmon resonance: A

comprehensive review. IEEE Sens. J. 2007, 7, 1118-1129.

4. Raether, H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings; Springer: Berlin,

Germany, 1988.

5. Shao. L.; Shevchenko, Y.; Albert. J. Intrinsic temperature sensitivity of tilted fiber Bragg grating

based surface plasmon resonance sensors. Opt. Express 2010, 18, 11464-11471.

6. Gramotnev, D.K.; Bozhevolnyi, S.I. Plasmonics beyond the diffraction limit. Nat. Photonic. 2010,

4, 83-91.

7. Bozhevolnyi, S.I.; Volkov, V.S.; Devaux, E.; Laluet, J.-Y.; Ebbesen, T.W. Channel plasmon

subwavelength waveguide components including interferometers and ring resonators. Nature

2006, 440, 508-511.

8. Holmgaard, T.; Bozhevolnyi, S.I.; Markey, L.; Dereux, A. Dielectric-loaded surface

plasmon-polariton waveguides at telecommunication wavelengths: Excitation and characterization.

Appl. Phys. Lett. 2008, 92, 011124:1-011124:3.

9. Han, Z.; Elezzabi, A.Y.; Van, V. Experimental realization of subwavelength plasmonic slot

waveguides on a silicon platform. Opt. Lett. 2010, 35, 502-504.

10. Yariv, A. Universal relations for coupling of optical power between microresonators and dielectric

waveguides. Electron. Lett. 2000, 36, 321-322.

11. Weber, M.J. Handbook of Optical Materials; CRC Press: Boca Raton, FL, USA, 2003; Chapter 3.

12. Holmgaard, T.; Bozhevolnyi, S.I. Theoretical analysis of dielectric-loaded surface

plasmon-polariton waveguides. Phys. Rev. B 2007, 75, 245405:1-245405:12.

13. Holmgaard, T.; Chen, Z.; Bozhevolnyi, S.I.; Markey, L.; Dereux, A. Dielectric-loaded plasmonic

waveguide-ring resonators. Opt. Express 2009, 17, 2968-2975.

14. Palik, E.D. Handbook of Optical Constants of Solids; Academic Press: New York, NY, USA,

1985.

15. Saleh, B.E.A.; Teich, M.C. Fundamentals of Photonics; Wiley: New York, NY, USA, 1991;

Chapter 7.

16. Ozdemir, S.K.; Turhan-Sayan, G. Temperature effects on surface plasmon resonance: Design

considerations for an optical temperature sensor. J. Lightwave Technol. 2003, 21, 805-814.

17. Han, Z. Ultracompact plasmonic racetrack resonators in metal-insulator-metal waveguides.

Photonics Nanostruct. Fundam. Appl. 2010, 8, 172-176.

18. Gosciniak, J.; Volkov, V.S.; Bozhevolnyi, S.I.; Markey, L.; Massenot, S.; Dereux, A.

Fiber-coupled dielectric-loaded plasmonic waveguides. Opt. Express 2010, 18, 5314-5319.

19. Bozhevolnyi, S.I.; Nikolajsen, T; Leosson, K. Integrated power monitor for long-range surface

plasmon polaritons. Opt. Commun. 2005, 255, 51-56.

© 2011 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article

distributed under the terms and conditions of the Creative Commons Attribution license

(http://creativecommons.org/licenses/by/3.0/).