Refractive index sensor utilizing thermo-optic effect of silicon waveguide

Optik 127 (2016) 6407–6411

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Optik journal homepage: www.elsevier.de/ijleo

Original research article

Refractive index sensor utilizing thermo-optic effect of silicon waveguide Haishi Wang ∗ , Tianbao Wang Collaborative Innovation Center of Integrated Computation and Chip Security, Chengdu University of Information technology, Chengdu, Sichuan, China

a r t i c l e

i n f o

Article history: Received 2 March 2016 Accepted 20 April 2016 Keywords: Refractive index sensor Directional coupler Silicon waveguide Thermo-optic effect

a b s t r a c t We propose a refractive index sensor based on thermo-optic (TO) effect in directional coupler (DC) with silicon waveguide to detect physiological concentrations of glucose in water. A temperature compensation method is used to realize a refractive index sensor with high sensitivity. The coupling length of the DC with silicon waveguide is calculated by coupledmode theory. Different silicon width and separation distance of DC have great influence on the sensitivity and resolution to refractive index change of glucose water. Based on simulation results, a sensor with a size of 119.5 ␮m × 10 ␮m can be obtained with a resolution of about 1.49 × 10−6 and a sensitivity of 867 K/RIU for glucose concentration less than 1000 mg/dL using highly sensitive detectors with a noise equivalent power (NEP) of picowatt. We also give the equivalent circuit for the refractive index sensor in order to realized opto-electronic integration. © 2016 Elsevier GmbH. All rights reserved.

1. Introduction Refractive index detection is widely researched for a number of applications including monitoring of chemical processes, label-free monitoring of bio-molecular interactions on surfaces and plane-ness detector in precision processing, which promises real-time results and minimal sample preparation with no fluorescent labeling required [1,2]. For an ideal refractive index sensor, it must show a very high sensitivity, quick response, small size, portability and low cost. Many optical methods have been developed to meet these demands, such as photonic crystal structure [3], planar waveguide ring resonator [4], directional coupler (DC) [5], Mach-Zehnder interferometry [6]. However, tiny refractive index detection is difficult in the above methods as it may bring an undetectable physical parameter. Therefore the sensitivity of the sensor will be greatly reduced by use of other technology. Silicon-on-insulator (SOI) waveguide structures are very promising in the application areas which are characterized by small optical losses over communication wavelengths and fully compatible with CMOS technology and micromechanical devices [7,8]. Silicon is available in large size, good quality and low price, and its technology is highly developed. As silicon’s thermo-optic (TO) effect [9] is significantly larger than its electro-optic effect [10], it is an attractive method to modulate the refractive index in SOI waveguides. A number of different silicon-based TO devices have been reported to date.

∗ Corresponding author. E-mail address: [email protected] (H. Wang). http://dx.doi.org/10.1016/j.ijleo.2016.04.111 0030-4026/© 2016 Elsevier GmbH. All rights reserved.

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Fig. 1. The schematic diagram of refractive index sensor with a DC structure.

Coupling Length (μm)

33.4

33.2

33

32.8

32.6 1.35

1.4

1.45

nG

1.5

0

10

20

30

ΔT(K)

Fig. 2. Coupling length for different sample index and modulation temperature.

In this paper, we propose a refractive index sensor based on TO effect in a DC with silicon waveguide. A temperature compensation method is used to realize a refractive index sensor with high sensitivity. The influences of silicon width and separation distance of DC on the sensitivity and resolution to refractive index change of glucose water are discussed. 2. Sensing mechanism, simulation results and discussion In a refractive index sensor with a DC structure as shown in Fig. 1, the sample (n0 ) to be measured is injected into the sensing area, and the temperature of one silicon (n1 ) waveguide can be modulated by the heater. Here we make use of d1 and d2 to denote the width of silicon waveguides and the separation distance between them. The coupling effect of the DC can be analyzed by interference phenomena between the even mode and odd mode, and the electric field in the directional coupler can be approximated by the summation of even mode and odd mode when high-order modes are neglected. The corresponding mode-coupling coefficient of DC is =

ˇe − ˇo 2

(1)

in which we make use of ˇe and ˇo to denote the propagation constant of the even mode and odd mode, respectively. The coupling length of the five-layer waveguide can be written as Lc =

  = 2 ˇe − ˇo

(2)

In this case, the output power can be defined as Pout1 = cos2 (z) Pin 2

Pout2 = sin (z) Pin

(3) (4)

We set the coupling length of the DC as that with water (n0 = 1.333) in sensing area and in this case the incident light is totally coupled into Port 2, which means Pout1 is zero and Pout2 is maximum. As samples with different glucose concentration bring changes of coupling length in DC, the output of Port 1 (Pout1 ) is nonzero. By accurately modulation the temperature of silicon waveguides with the heater, the refractive index of silicon can be changed. Thus the coupling length can be modulated by the silicon temperature and it is possible to adjust it back to the original value and keep Pout1 remains zero. We call this phenomenon as the thermal-optic compensation effect in the proposed structure. In this method, a relationship between the refractive index of sample and the modulated temperature can be obtained. Based on the relation between the refractive index and the glucose concentration [8], different modulated temperature determines the glucose concentration in water. In our sensor, we choose the length of the DC as the coupling length with water in sensing area. The input power will be totally coupled into Pout2 and the photo-detector cannot detect any power in Pout1 . In fact the coupling length can be

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Table 1 The coupling length (␮m) for different d1 (␮m) and d2 (␮m). d1

d2

0.2 0.3 0.4 0.5 0.6

0.2

0.3

0.4

0.5

0.6

2.2 5.5 13.9 28.0 49.0

3.5 13.5 40.8 89.3 163.0

5.7 33.0 119.5 284.0 542.2

9.2 80.9 350.4 904.0 1804.0

14.8 198.5 1027.0 2877.0 6001.0

0.2

0.3

0.4

0.5

0.6

0.008 – 0.055 0.03 0.028

– – 0.035 0.025 0.022

– 0.17 0.029 0.022 0.02

– 0.09 0.026 0.021 0.019

– 0.07 0.024 0.02 0.018

Table 2 The maximum n0 for different d1 (␮m) and d2 (␮m). d1

d2

0.2 0.3 0.4 0.5 0.6

1.50 1.48 1.46

nG

1.44 1.42 1.40 1.38 1.36 1.34 0

5

10

15

20

25

30

ΔT (K) Fig. 3. The relation between modulated temperature and detected refractive index.

modulated by setting different waveguide width (d1 ) and the distance (d2 ) between the two waveguide. In Table 1, we give some calculated coupling length when n0 = 1.333 and n1 = 3.48. When a sample of glucose with different concentration is measured, the coupling length of the directional coupler will be changed. As the refractive index of silicon will change with temperature, the n0 induced by glucose can be compensated by the TO effect of silicon to ensure the coupling length is unchanged. By properly modulation the temperature of the silicon waveguide, the output of Port 1 remains zero. Here we choose the TO coefficient of silicon asdn1 /dT = 1.87 × 10−4 /K. Therefore, there must be a relation between the modulated temperature T and the refractive index change n0 . For a fixed temperature change T , n0 can be determined by solving the following equations





ˇt d12 1 + wt2 v2t  8u2t wt2 ut = atan d

 2d 2

exp −

d1

 wt

w 





=



ˇ0 d12 1 + w02 v20  8u20 w02

 2d 2

exp −

t

d1

 w0

(5a)

(5b)

ut d



dn

where ut = 21 n21t k02 − ˇt2 , wt = 21 ˇt2 − n20t k02 , n1t = n1 + T × dT1 andn0t = n0 + n0 . While the sensing range of refractive index varies with different structure of the device, including the waveguide width (d1 ) and the distance (d2 ) between the two waveguides. In Table 2, we give the maximum refractive index change for a fixed structure where the “-” means Eq. (5) does not have a solution. Here we also choose n0 = 1.333, n1 = 3.48 and dn1 /dT = 1.87 × 10−4 /K. We can find when d1 = 0.3 ␮m, d2 = 0.4 ␮m, the maximum n0 is about 0.17. In this case, the detectable maximum refractive index is about 1.503. As the glucose with concentration of 10000 mg/dL is about 1.47185 [8], this detection range is completely large enough for measurement of glucose concentration smaller than 10,000 mg/dL. We give the curves about T , n0 and coupling length in Fig. 2. We can find that with the increase of nG , the coupling length decreases, while the increase of temperature enlarges the coupling length. For the sake of convenience, we give the relation of T and nG in Fig. 3. In this figure, the refractive index for water with different glucose concentration can be obtained.

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Fig. 4. Equivalent circuit of the refractive index sensing system. Table 3 The |dLc /dnG | for different d1 (␮m) and d2 (␮m). d1

d2

0.2 0.3 0.4 0.5 0.6

0.2

0.3

0.4

0.5

0.6

– – 1.5 6 14.1

– – 11.5 35.5 74.4

– 1.4 51.7 160.1 338.9

– 10.8 204.5 658.5 1400.0

– 44.6 800.0 2600.0 5733.3

At last, we discuss the resolution of the proposed sensor. In order to construct a highly sensitive biosensing system, we choose a photodetector which can measure optical power as low as picowatt which means its noise equivalent power (NEP) is 10−12 W. In the following, we calculate the resolution of the proposed refractive index sensor. When we choose n0 = 1.333, n1 = 3.48, d1 = 0.3 ␮m and d2 = 0.4 ␮m the coupling length Lc is about 33 ␮m, as shown in Table 1. For the glucose sample of different concentration with refractive index of nG , the coupling length change is Lc . Here we assume the minimum power can be detected by photodetector is about 1 pW, and the corresponding refractive index change nG is the resolution of the sensor. According to Eq. (3), the output power of Port1 can be written as





Pout2 = sin2 Lc /2 (Lc − Lc ) + /2 Pin

(6)

If we assume the input power is 1 W, the output power induced by refractive index change of glucose water is





Pout2 = sin2 Lc / (Lc − Lc ) × /2



(7)



As the small refractive index change of glucose water, we have Lc  Lc and sin Lc / (Lc − Lc ) × /2 ≈ Lc / (Lc − Lc ) × /2.Therefore Eq. (7) can be simplified as Lc / (Lc − Lc ) × /2 = 10−6

(8)

The Lc can be obtained as Lc = 6.4 × 10





nG min = Lc / |dLc /dnG | × 6.4 × 10

−7

Lc , and the minimum nG can be derived as

−7





(9)

To get smaller nGmin , we must take measures to achieve a smaller Lc / |dLc /dnG | . As we have demonstrate the coupling length for different parameters in Table 1, in the following we give |dLc /dnG | as shown in Table 3. We can find that with the increase of the device dimension, the resolution of the sensor will be greatly improved as small as ∼6 × 10−7 . It can be explained as that the enlarged sensing area collects more information about the sample index, therefore improves the sensing resolution. However, we must take into account miniaturization of the device as well as the resolution. There must be a tradeoff between the two factors. In addition, for small refractive index change, the sensing resolution should be improved. Therefore we may choose a structure with d1 = d2 = 0.4 ␮m and Lc = 119.5 ␮m for small concentration detection (<1000 mg/dL), the sensing resolution of refractive index is about 1.49 × 10−6 . Here we define the sensitivity of the refractive index sensor as SRIU = dT/dnG

(10)

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Based on the calculation results of the nG ∼T relation, the sensitivity can be obtained as 867 K/RIU. But by contrast, if we directly detect the output power in Port 2 to measure the refractive index change, which is about 1.1 × 10−7 watt, and the sensitivity of dPout2 /dnG is only 1.1 × 10−3 W/RIU. Therefore we can come to a conclusion that by use of the TO effect of silicon waveguide, the sensitivity of the refractive index sensor can be greatly improved. 3. Equivalent circuit In this section, we design an equivalent circuit for the refractive index system as shown in Fig. 4. Here we assume the output power of Port 1 is Paux and that of Port 2 is Pout . When glucose water to be detected is filled in the sensing area, some energy is coupled into Paux and Pout is lower than Pin . If Pout is lower than Pref (maximum of Pout ), the voltage Vs is lower than Vr , then thermal source is open to heat sensing area to change refractive index to make Pout equaling to max (Pout ). After Pout and temperature of sensing area are regulated, read temperature through a temperature to voltage converting circuit and an A/D converter. 4. Conclusion In conclusion, we propose a DC refractive index sensor to detect physiological concentrations of glucose in water based on the TO effect of silicon waveguide. The sensing mechanism is by accurate temperature modulation of silicon the refractive index change induced by glucose concentration can be compensated to keep the coupling length of DC unchanged. Thus the output power in Port 2 remains the same as before and a relationship between the temperature and refractive index can be obtained. We discuss the design principles based on the coupled-mode theory of DC and deduce the conditions for a valid refractive index sensor model. We give some examples to present the coupling length, the detectable refractive index range and the sensing resolution for different silicon width and separation distance in the DC. Calculation results show that with the increase of device length, the sensing resolution can be greatly improved. By a tradeoff between the coupling length and resolution of refractive index for glucose concentration detection ( < 1000 mg/dL), we can obtain a refractive index sensor with a size of 119.5 ␮m × 10 ␮m which shows a resolution of about 1.49 × 10−6 and a sensitivity of 867 K/RIU by use of highly sensitive detectors with NEP of picowatt. At last, we give the equivalent circuit of the refractive index sensing system in order to realize opto-electronic integration. Acknowledgement This work is supported by National Social Science Foundation Grant No. 61504014 to the author. References [1] Yi Wang, Chun-Jen Huang, Ulrich Jonas, Tianxin Wei, Jakub Dostalek, Wolfgang Knolla, Refractive index sensor based on hydrogel optical waveguide spectroscopy, Refract. Index Sens. Bioelectron. 25 (7) (2010) 1663–1668. [2] R. Slavík, J. Homola, Optical multilayers for LED-based surface plasmon resonance sensors, Appl. Opt. 45 (2006) 3752–3759. [3] L. Rindorf, J.B. Jensen, M. Dufva, L.H. Pedersen, P.E. Hoiby, O. Bang, Photoniccrystal fiber longperiod gratings for biochemical sensing, Opt. Express 14 (2006) 8224–8231. [4] S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, F. Vollmer, Shift of whispering-gallery modes in microspheres by protein adsorption, Opt. Lett. 28 (2003) 272–274. [5] Tingting Tang, Wenying Ma, Wenli Liu, Xiujun He, Sensing of refractive index based on mode interference in a five-layer slab waveguide, Opt. Commun. (2015) 294–297. [6] J. Feng, V.S. Siu, A. Roelke, et al., Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing, Nano Lett. 12 (2) (2012) 602–609. [7] P. Dainesi, A. Küng, M. Chabloz, A. Lagos, Ph. Flückiger, A. Ionescu, P. Fazan, Ph. Declerq, Ph. Renaud, Ph. Robert, CMOS compatible fully integrated Mach–Zehnder interferometer in SOI technology, IEEE Photon. Technol. Lett. 12 (2000) 660–662. [8] W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, D. Van Thourhout, Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology, J. Lightwave Technol. 23 (2005) 401–412. [9] G. Cocorullo, I. Rendina, Thermo-optical modulation at 1.5 ␮m in silicon etalon, Electron. Lett. 28 8 (1992) 3–85. [10] R.A. Soref, B.R. Bennett, Electro optical effects in silicon, IEEE J. Quantum Electron. QE 23 (1987) 123–129.