- Email: [email protected]
Refractive index sensor of Mach–Zehnder interferometer based on thermo-optic effect of SOI waveguide
Optik 127 (2016) 6366–6370
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Refractive index sensor of Mach–Zehnder interferometer based on thermo-optic effect of SOI waveguide Tingting Tang ∗ , Li Luo Information Materials and Device Applications Key Laboratory of Sichuan Provincial Universities, Chengdu University of Information Technology, Chengdu 610225, China
a r t i c l e
i n f o
Article history: Received 7 March 2016 Accepted 25 April 2016 Keywords: Refractive index sensor Mach–Zehnder interferometry Thermo-optic effect
a b s t r a c t We propose a Mach–Zehnder interferometry (MZI) refractive index sensor based on thermo-optic effect of silicon-on-insulator (SOI) waveguide to detect refractive index of liquid. By modulating silicon temperature the phased shift induced by the sample index change is compensated to ensure the output power is unchanged. The phase-matching conditions for a valid refractive index sensor are discussed to direct the design for lengths of sensing and heating areas. Meanwhile the sensitivity and resolution of the refractive index sensor are also analyzed. The proposed thermo-optic compensation method shows noticeable advantages compared with refractive index sensor by directly detecting the output power. Based on these discussions, a refractive index sensor with a compact size of 2 mm × 1.5 mm can be realized with a sensitivity of 48,000K/RIU and a resolution of 2 × 10−6 can be realized. © 2016 Elsevier GmbH. All rights reserved.
1. Introduction Modern biosensors have attracted more and more interest in the past several decades. It should be not only highly selective and sensitive, but should also be small and easy to operate. Biosensors hold great promise to develop fast, inexpensive, portable biomedical devices for point-of-care detection in medical and environmental applications [1–5]. Moreover, labon-chip systems are desired to implement a large number of highly integrated probes to enable a high degree of parallel measurements in pharmacy or biotechnology. For an ideal biosensor, 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 optical fiber [6], directional coupler (DC) [7], Mach–Zehnder interferometry (MZI) [8], ring resonators [9], and surface plasmon resonance (SPR) [10]. Among the various techniques, MZI has been one of the widely useful methods in the development of biochemical sensors in recent years. A MZI can convert small changes in the local refractive index caused by biomolecular binding into spectral shifts in the extinction spectra [11] or the output power [10]. This allows real-time label-free detection of the biomolecular interactions using simple and inexpensive transmission spectroscopy or power. The mentioned MZI work by other groups focuses on plasmonic sensors, which require a metal layer. As metal is lossy, the sensitivity is reduced by the absorption of metal layer. So far the reported sensors have shown a resolution as low as 10−5 [12], to get higher resolution and sensitivity, new biosensing mechanism should be developed. In 2013, Dante demonstrated a MZI refractive
∗ Corresponding author. E-mail address: [email protected] (T. Tang). http://dx.doi.org/10.1016/j.ijleo.2016.04.134 0030-4026/© 2016 Elsevier GmbH. All rights reserved.
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
6367
Fig. 1. Schematic of the proposed refractive index sensor based on MZI, (a) top-view and (b) the profile in the middle of sensing area. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
index sensor whose phase is tuned by modulating the emission wavelength of low-cost commercial laser diodes by changing their output power [13]. This simple phase modulation scheme renders in a sensor with a detection limit of 1.9 × 10−7 RIU. Silicon-on-insulator (SOI) waveguide structures are very promising in several application areas, such as optical interconnects in high-speed microprocessors and on-chip control circuits with optoelectronics for wavelength division multiplexing. They are characterized by small optical losses over communication wavelengths and fully compatible with CMOS technology and micromechanical devices [14,15]. As silicon’s thermo-optic effect is significantly larger than its electro-optic effect, it is an attractive way to modulate the refractive index in SOI waveguides. A number of different silicon-based thermo-optic devices have been reported to date. MZI switches with rise-/fall times of a few microseconds have been demonstrated with heating powers in the range of 100 mW [16]. As devices and components based on thermo-optic effect show low transmission loss, low cost, high stability, low power consumption and very large scale of integration, the thermo-optic effect becomes a new prosperous method to design optoelectronic devices with silicon waveguide. In this paper, we propose a MZI refractive index sensor to detect the refractive index of liquid based on thermo-optic effect of silicon waveguide. The phase shift induced by sample can be compensated by the thermo-optic effect of SOI waveguide, thus the power distribution remains the same as a reference liquid in sensing area. Moreover the sensitivity and resolution of the refractive index sensor are also discussed. 2. Sensing mechanism, theoretical analysis and discussion In a refractive index sensor with a MZI structure in Fig. 1, the top-view (a) and the profile at the middle of sensing area (b) are shown. The two silicon waveguides are surrounded by the silica with index n0 (yellow area). The sample with index nS (green area) to be measured is injected into the sensing area, and the temperature of one silicon (n1 ) waveguide can be modulated by the heater in heating area (red area). The temperature in heating arm can be controlled by a top aluminium heater, 0.5 m thick, lying on the surface of the silicon [17]. Here we make use of d1 and d0 to denote the width of silicon waveguides and the separation distance between them. By properly modulating the length of sensing area, the phase different of the two arms can be integral multiples of 2. In this case the output power is maximum. As different samples bring changes of MZI phase difference in two arms, the output is reduced. By accurately modulation the temperature of silicon waveguide with the heater, the refractive index of silicon can be changed. Thus the phase difference of MZI can be modulated by the silicon temperature and it is possible to adjust it back to be the original value and keep Pout remains maximum. 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 liquid concentration, different modulated temperature determines refractive index in sensing area to be measured. In our sensor, the temperature is modulated to keep the output power unchanged. This modulation procedure may take some time to reach a steady state which can be understood as relaxation time in thermodynamics. We call this time as the modulation time, and it may take several seconds as the slow speed of heat conduction in silicon and silica layers. In addition, the sensing mechanism is based on the temperature compensation effect. Thus we mainly focus on modulating the temperature to keep the output power unchanged no matter the output power is maximum or not. This means we do not care the light wavelength or heating through waveguide losses. Our sensor shows good tolerance on the wavelength shift or power loss in the waveguide, and is potential for applications in complicated environment. When we design the structure and parameters for the sensor, we assume the original sensing area is filled with reference liquid with refractive index nR . In the following analysis, we assume the propagation wave is TM mode. In order to keep output power is maximum, the phase shift induced by water should be an integral multiple of 2. It must be ensured by the sensing area length, thus we can get a condition of
ˇ0 − ˇR LS = 2k
(k = 1, 2, 3, 4...)
(1)
6368
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
where ˇ0 is the original propagation constant in the heating arm and ˇR are the propagation constant of sensing arm when it is filled with reference liquid (nR ). According to Eq. (1), the length of sensing area should satisfy the condition LS =
k ˇ0 − ˇR
(k = 1, 2, 3, 4...)
(2)
When a sample is measured, the phase shift induced by the additional optical path difference must be totally compensated by the thermo-optic effect of silicon waveguide. In this method the output power distribution remains as the same as that of water in sensing area. The output power can be written as Pout = P0 cos2
ϕ
(3)
2
Here ϕ is the phase difference when sample is detected, which can be expressed as
ϕ = ˇH − ˇ0 LH − ˇS − ˇR LS
(4)
In order to keep the phase shift as zero, we must ensure the phase-matching condition
ˇH − ˇ0 LH = ˇS − ˇR LS
(5)
in which ˇS is the propagation constant of silica/water/silica waveguide when the sensing area is filled with sample (nS ) and ˇH is the propagation constant when n1 = nH which can be expressed as nH = n1 + T ×
dn1 dT
(6)
As silica also possesses TO effect, the refractive index influenced by temperature is (n0 + T × dn0 /dT ). Here we assume the propagation constant change caused by sample is ˇS = ˇS − ˇR
(7)
And the propagation constant change caused by temperature change is ˇH = ˇH − ˇ0
(8)
Eq. (5) can be written as ˇH LS = LH ˇS
(9)
which shows a linear relation between ˇH and ˇS . As ˇH and ˇS are induced by the refractive index of heating arm (nH ) and sensing arm (nS ), a relationship between nS and T can be obtained by Eqs. (7)–(9). Then we give the sensitivity of the sensor as SRIU =
dT dnS
(10)
According to Eq. (9), the increase of LS /LH will decrease the detectable refractive index range. While we can find the sensitivity will be improved as the identical refractive index change brings a larger temperature change in heating arm. On the other hand, the decrease of LS /LH will increase the detectable refractive index range, while worsen the sensitivity as the identical refractive index change brings a smaller temperature change in heating arm. If we assume the temperature resolution of the heater is 0.1 K, the resolution of the refractive index sensor is RIU = 0.1/SRIU
(11)
In what following we discuss the possible ranges of modulating temperature and detectable refractive index change. To increase LS /LH , we can enlarge the length of sensing area or shorten the length of heating area. In this case, for a fixed modulating temperature range, the detectable refractive index range is reduced. Meanwhile for a fixed detectable refractive index range, a lar can be obtained. Meanwhile for a fixed detectable refractive index range, the required modulating temperature range is decreased. In what following, we choose n0 = 1.444, n1 = 3.48, nR = 1.45, dn1 /dT = 1.87 × 10−4 /K, dn0 /dT = 1.0 × 10−5 /K [17] and d1 = 1 m. Here we assume the distance between the two arms of MZI is about 1 mm to ensure the heating arm has little influence about the sensing arm. To avoid the diffusing of sensing arm this distance can be further enlarged which also causes the extension of the Y-junctions length. Based on these parameters, our sensor is used to detect liquid with refractive index ranging from 1.45 to 1.455. This is determined by the SOI waveguide in which the refractive index of silica is 1.444 when wavelength is 1550 nm. As is the core layer of silica-liquid-silica waveguide, the refractive index of liquid in the sensing area should be larger than 1.444. Therefore our sensor is suitable for liquids or solids with refractive index in the range from 1.45 to 1.455 as mentioned in Ref. [18]. The relation between nS and ˇS is shown in Fig. 2 and the relation between T and ˇH is shown in Fig. 3. In order to keep the output the same as before, the propagation constant change induced by the sample index must be compensated by
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
6369
Fig. 2. The propagation constant variation for different sample index change.
Fig. 3. The propagation constant variation for different temperature change.
the TO effect of silicon waveguide. According to the phase-matching condition in Eq. (5), the relation between ˇS and ˇH is determined by the ratio of LS /LH . Therefore once the lengths of sensing and heating areas are fixed, the sensitivity and resolution of the sensor is determined. In the following, we discuss the influence of LS /LH on the sensitivity and resolution of the sensor. When LS = LH , the sensitivity of the refractive index sensor is about 6000 K/RIU, and the corresponding resolution is about 1.67 × 10−5 . Calculation results show that if we detect the output power induced by refractive index instead of this temperature compensation method, the sensitivity is about 0.1/RIU and the corresponding resolution is about 3 × 10−4 where we assume the resolution of the power detector is 0.03%. Therefore, by the use of temperature compensation method, the resolution of refractive index sensor is increased by about 20 times. At last, we explore how to improve the sensitivity and resolution of the sensor in our model by adjusting the heating or sensing length. According to Eq. (9), we can shorten LH , which increase the temperature change for identical refractive index change. For example, if we cut the heating arm length by half, the sensitivity will be doubled and the resolution improved to 8.3 × 10−6 . To improve the resolution, we must also take measures to enlarge LS . We can find that with the increase of the sensing area length, the resolution of the sensor will be greatly improved. It can be explained as that the enlarged sensing area collects more information about the sample index, and thus a smaller change of index can be detected. However, we should take into account miniaturization of the device as well as the resolution. There must be a tradeoff between the two factors. Therefore we may choose a structure with LS /LH = 4, a sensitivity of 48,000K/RIU and a sensing resolution of 2.0 × 10−6 can be obtained. If we continue to increase LS /LH , the sensitivity and resolution can be further improved. 3. Conclusion In this paper, we propose a MZI refractive index sensor based on thermo-optic effect of SOI waveguide to detect refractive index of liquid. The sensing mechanism is analyzed and the design principle is discussed to realize a valid refractive index sensor. Moreover the sensitivity and resolution of the refractive index sensor are also discussed. At last a refractive index sensor with a compact size of 2 mm × 1.5 mm can be realized with a sensitivity of 48000K/RIU and a resolution of 2 × 10−6 . This new kind of refractive index sensor is rather prosperous for its simple structure, compact size, high sensitivity and resolution in the field of biological and chemical sensing. Compared with other refractive index sensors, the proposed sensor’s sensitivity and resolution can be adjusted and further improved by increasing the length ratio between sensing
6370
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
and heating areas, which brings great flexibility for the design and provides an effective method to improve the sensor’s performance. Acknowledgements This work is supported by National Natural Science Foundation of China under Grant No. 61505016, the scientific research fund of Chengdu University of Information Technology (No. J201417) and the project of Sichuan Provincial Department of Education (15ZA0183). References [1] K.M. Mayer, J.H. Hafner, Localized surface plasmon resonance sensors, Chem. Rev. 111 (6) (2011) 3828–3857. [2] K.A. Tetz, L. Pang, Y. Fainman, High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance, Opt. Lett. 31 (10) (2006) 1528–1530. [3] F.B. Myers, L.P. Lee, Innovations in optical microfluidic technologies for point-of-care diagnostics, Lab Chip 8 (12) (2008) 2015–2031. [4] Y. Gao, Q. Gan, Z. Xin, X. Cheng, F.J. Bartoli, Plasmonic Mach–Zehnder interferometer for ultrasensitive on-chip biosensing, ACS Nano 5 (12) (2011) 9836–9844. [5] 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. [6] J. Kou, J. Feng, Q. Wang, et al., Microfiber-probe-based ultrasmall interferometric sensor, Opt. Lett. 35 (13) (2010) 2308–2310. [7] 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. [8] 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. [9] A.M. Armani, R.P. Kulkarni, S.E. Fraser, et al., Label-free, single-molecule detection with optical microcavities, Science 317 (5839) (2007) 783–787. [10] Y. Gao, Z. Xin, B. Zeng, et al., Plasmonic interferometric sensor arrays for high-performance label-free biomolecular detection, Lab Chip 13 (24) (2013) 4755–4764. [11] W.W. Lam, L.H. Chu, C.L. Wong, et al., A surface plasmon resonance system for the measurement of glucose in aqueous solution, Sens. Actuators B 105 (2) (2005) 138–143. [12] Y. Gao, Z. Xin, Q. Gan, et al., Plasmonic interferometers for label-free multiplexed sensing, Opt. Express 21 (5) (2013) 5859–5871. [13] S. Dante, D. Duval, B. Sepúlveda, et al., All-optical phase modulation for integrated interferometric biosensors, Opt. Express 20 (7) (2012) 7195–7205. [14] G. Cocorullo, I. Rendina, Thermo-optical modulation at 1.5 m in silicon etalon, Electron. Lett. 28 (1992) 83–85. [15] R.A. Soref, B.R. Bennett, Electro optical effects in silicon, IEEE J. Quantum Electron. QE-23 (1987) 123–129. [16] Y. Li, J. Yu, S. Chen, Rearrangeable nonblocking SOI waveguide thermo optic 4 × 4 switch matrix with low insertion loss and fast response, IEEE Photon. Technol. Lett. 17 (2005) 1641–1643. [17] V. Passaro, F. Magno, A. Tsarev, Investigation of thermo-optic effect and multi-reflector tunable filter/multiplexer in SOI waveguides, Opt. Express 13 (9) (2005) 3429–3437. [18] Y. Liu, J. Kim, Numerical investigation of finite thickness metal-insulator-metal structure for waveguide-based surface plasmon resonance biosensing, Sens. Actuators B 148 (1) (2010) 23–28.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Refractive index sensor of Mach–Zehnder interferometer based on thermo-optic effect of SOI waveguide Tingting Tang ∗ , Li Luo Information Materials and Device Applications Key Laboratory of Sichuan Provincial Universities, Chengdu University of Information Technology, Chengdu 610225, China
a r t i c l e
i n f o
Article history: Received 7 March 2016 Accepted 25 April 2016 Keywords: Refractive index sensor Mach–Zehnder interferometry Thermo-optic effect
a b s t r a c t We propose a Mach–Zehnder interferometry (MZI) refractive index sensor based on thermo-optic effect of silicon-on-insulator (SOI) waveguide to detect refractive index of liquid. By modulating silicon temperature the phased shift induced by the sample index change is compensated to ensure the output power is unchanged. The phase-matching conditions for a valid refractive index sensor are discussed to direct the design for lengths of sensing and heating areas. Meanwhile the sensitivity and resolution of the refractive index sensor are also analyzed. The proposed thermo-optic compensation method shows noticeable advantages compared with refractive index sensor by directly detecting the output power. Based on these discussions, a refractive index sensor with a compact size of 2 mm × 1.5 mm can be realized with a sensitivity of 48,000K/RIU and a resolution of 2 × 10−6 can be realized. © 2016 Elsevier GmbH. All rights reserved.
1. Introduction Modern biosensors have attracted more and more interest in the past several decades. It should be not only highly selective and sensitive, but should also be small and easy to operate. Biosensors hold great promise to develop fast, inexpensive, portable biomedical devices for point-of-care detection in medical and environmental applications [1–5]. Moreover, labon-chip systems are desired to implement a large number of highly integrated probes to enable a high degree of parallel measurements in pharmacy or biotechnology. For an ideal biosensor, 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 optical fiber [6], directional coupler (DC) [7], Mach–Zehnder interferometry (MZI) [8], ring resonators [9], and surface plasmon resonance (SPR) [10]. Among the various techniques, MZI has been one of the widely useful methods in the development of biochemical sensors in recent years. A MZI can convert small changes in the local refractive index caused by biomolecular binding into spectral shifts in the extinction spectra [11] or the output power [10]. This allows real-time label-free detection of the biomolecular interactions using simple and inexpensive transmission spectroscopy or power. The mentioned MZI work by other groups focuses on plasmonic sensors, which require a metal layer. As metal is lossy, the sensitivity is reduced by the absorption of metal layer. So far the reported sensors have shown a resolution as low as 10−5 [12], to get higher resolution and sensitivity, new biosensing mechanism should be developed. In 2013, Dante demonstrated a MZI refractive
∗ Corresponding author. E-mail address: [email protected] (T. Tang). http://dx.doi.org/10.1016/j.ijleo.2016.04.134 0030-4026/© 2016 Elsevier GmbH. All rights reserved.
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
6367
Fig. 1. Schematic of the proposed refractive index sensor based on MZI, (a) top-view and (b) the profile in the middle of sensing area. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
index sensor whose phase is tuned by modulating the emission wavelength of low-cost commercial laser diodes by changing their output power [13]. This simple phase modulation scheme renders in a sensor with a detection limit of 1.9 × 10−7 RIU. Silicon-on-insulator (SOI) waveguide structures are very promising in several application areas, such as optical interconnects in high-speed microprocessors and on-chip control circuits with optoelectronics for wavelength division multiplexing. They are characterized by small optical losses over communication wavelengths and fully compatible with CMOS technology and micromechanical devices [14,15]. As silicon’s thermo-optic effect is significantly larger than its electro-optic effect, it is an attractive way to modulate the refractive index in SOI waveguides. A number of different silicon-based thermo-optic devices have been reported to date. MZI switches with rise-/fall times of a few microseconds have been demonstrated with heating powers in the range of 100 mW [16]. As devices and components based on thermo-optic effect show low transmission loss, low cost, high stability, low power consumption and very large scale of integration, the thermo-optic effect becomes a new prosperous method to design optoelectronic devices with silicon waveguide. In this paper, we propose a MZI refractive index sensor to detect the refractive index of liquid based on thermo-optic effect of silicon waveguide. The phase shift induced by sample can be compensated by the thermo-optic effect of SOI waveguide, thus the power distribution remains the same as a reference liquid in sensing area. Moreover the sensitivity and resolution of the refractive index sensor are also discussed. 2. Sensing mechanism, theoretical analysis and discussion In a refractive index sensor with a MZI structure in Fig. 1, the top-view (a) and the profile at the middle of sensing area (b) are shown. The two silicon waveguides are surrounded by the silica with index n0 (yellow area). The sample with index nS (green area) to be measured is injected into the sensing area, and the temperature of one silicon (n1 ) waveguide can be modulated by the heater in heating area (red area). The temperature in heating arm can be controlled by a top aluminium heater, 0.5 m thick, lying on the surface of the silicon [17]. Here we make use of d1 and d0 to denote the width of silicon waveguides and the separation distance between them. By properly modulating the length of sensing area, the phase different of the two arms can be integral multiples of 2. In this case the output power is maximum. As different samples bring changes of MZI phase difference in two arms, the output is reduced. By accurately modulation the temperature of silicon waveguide with the heater, the refractive index of silicon can be changed. Thus the phase difference of MZI can be modulated by the silicon temperature and it is possible to adjust it back to be the original value and keep Pout remains maximum. 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 liquid concentration, different modulated temperature determines refractive index in sensing area to be measured. In our sensor, the temperature is modulated to keep the output power unchanged. This modulation procedure may take some time to reach a steady state which can be understood as relaxation time in thermodynamics. We call this time as the modulation time, and it may take several seconds as the slow speed of heat conduction in silicon and silica layers. In addition, the sensing mechanism is based on the temperature compensation effect. Thus we mainly focus on modulating the temperature to keep the output power unchanged no matter the output power is maximum or not. This means we do not care the light wavelength or heating through waveguide losses. Our sensor shows good tolerance on the wavelength shift or power loss in the waveguide, and is potential for applications in complicated environment. When we design the structure and parameters for the sensor, we assume the original sensing area is filled with reference liquid with refractive index nR . In the following analysis, we assume the propagation wave is TM mode. In order to keep output power is maximum, the phase shift induced by water should be an integral multiple of 2. It must be ensured by the sensing area length, thus we can get a condition of
ˇ0 − ˇR LS = 2k
(k = 1, 2, 3, 4...)
(1)
6368
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
where ˇ0 is the original propagation constant in the heating arm and ˇR are the propagation constant of sensing arm when it is filled with reference liquid (nR ). According to Eq. (1), the length of sensing area should satisfy the condition LS =
k ˇ0 − ˇR
(k = 1, 2, 3, 4...)
(2)
When a sample is measured, the phase shift induced by the additional optical path difference must be totally compensated by the thermo-optic effect of silicon waveguide. In this method the output power distribution remains as the same as that of water in sensing area. The output power can be written as Pout = P0 cos2
ϕ
(3)
2
Here ϕ is the phase difference when sample is detected, which can be expressed as
ϕ = ˇH − ˇ0 LH − ˇS − ˇR LS
(4)
In order to keep the phase shift as zero, we must ensure the phase-matching condition
ˇH − ˇ0 LH = ˇS − ˇR LS
(5)
in which ˇS is the propagation constant of silica/water/silica waveguide when the sensing area is filled with sample (nS ) and ˇH is the propagation constant when n1 = nH which can be expressed as nH = n1 + T ×
dn1 dT
(6)
As silica also possesses TO effect, the refractive index influenced by temperature is (n0 + T × dn0 /dT ). Here we assume the propagation constant change caused by sample is ˇS = ˇS − ˇR
(7)
And the propagation constant change caused by temperature change is ˇH = ˇH − ˇ0
(8)
Eq. (5) can be written as ˇH LS = LH ˇS
(9)
which shows a linear relation between ˇH and ˇS . As ˇH and ˇS are induced by the refractive index of heating arm (nH ) and sensing arm (nS ), a relationship between nS and T can be obtained by Eqs. (7)–(9). Then we give the sensitivity of the sensor as SRIU =
dT dnS
(10)
According to Eq. (9), the increase of LS /LH will decrease the detectable refractive index range. While we can find the sensitivity will be improved as the identical refractive index change brings a larger temperature change in heating arm. On the other hand, the decrease of LS /LH will increase the detectable refractive index range, while worsen the sensitivity as the identical refractive index change brings a smaller temperature change in heating arm. If we assume the temperature resolution of the heater is 0.1 K, the resolution of the refractive index sensor is RIU = 0.1/SRIU
(11)
In what following we discuss the possible ranges of modulating temperature and detectable refractive index change. To increase LS /LH , we can enlarge the length of sensing area or shorten the length of heating area. In this case, for a fixed modulating temperature range, the detectable refractive index range is reduced. Meanwhile for a fixed detectable refractive index range, a lar can be obtained. Meanwhile for a fixed detectable refractive index range, the required modulating temperature range is decreased. In what following, we choose n0 = 1.444, n1 = 3.48, nR = 1.45, dn1 /dT = 1.87 × 10−4 /K, dn0 /dT = 1.0 × 10−5 /K [17] and d1 = 1 m. Here we assume the distance between the two arms of MZI is about 1 mm to ensure the heating arm has little influence about the sensing arm. To avoid the diffusing of sensing arm this distance can be further enlarged which also causes the extension of the Y-junctions length. Based on these parameters, our sensor is used to detect liquid with refractive index ranging from 1.45 to 1.455. This is determined by the SOI waveguide in which the refractive index of silica is 1.444 when wavelength is 1550 nm. As is the core layer of silica-liquid-silica waveguide, the refractive index of liquid in the sensing area should be larger than 1.444. Therefore our sensor is suitable for liquids or solids with refractive index in the range from 1.45 to 1.455 as mentioned in Ref. [18]. The relation between nS and ˇS is shown in Fig. 2 and the relation between T and ˇH is shown in Fig. 3. In order to keep the output the same as before, the propagation constant change induced by the sample index must be compensated by
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
6369
Fig. 2. The propagation constant variation for different sample index change.
Fig. 3. The propagation constant variation for different temperature change.
the TO effect of silicon waveguide. According to the phase-matching condition in Eq. (5), the relation between ˇS and ˇH is determined by the ratio of LS /LH . Therefore once the lengths of sensing and heating areas are fixed, the sensitivity and resolution of the sensor is determined. In the following, we discuss the influence of LS /LH on the sensitivity and resolution of the sensor. When LS = LH , the sensitivity of the refractive index sensor is about 6000 K/RIU, and the corresponding resolution is about 1.67 × 10−5 . Calculation results show that if we detect the output power induced by refractive index instead of this temperature compensation method, the sensitivity is about 0.1/RIU and the corresponding resolution is about 3 × 10−4 where we assume the resolution of the power detector is 0.03%. Therefore, by the use of temperature compensation method, the resolution of refractive index sensor is increased by about 20 times. At last, we explore how to improve the sensitivity and resolution of the sensor in our model by adjusting the heating or sensing length. According to Eq. (9), we can shorten LH , which increase the temperature change for identical refractive index change. For example, if we cut the heating arm length by half, the sensitivity will be doubled and the resolution improved to 8.3 × 10−6 . To improve the resolution, we must also take measures to enlarge LS . We can find that with the increase of the sensing area length, the resolution of the sensor will be greatly improved. It can be explained as that the enlarged sensing area collects more information about the sample index, and thus a smaller change of index can be detected. However, we should take into account miniaturization of the device as well as the resolution. There must be a tradeoff between the two factors. Therefore we may choose a structure with LS /LH = 4, a sensitivity of 48,000K/RIU and a sensing resolution of 2.0 × 10−6 can be obtained. If we continue to increase LS /LH , the sensitivity and resolution can be further improved. 3. Conclusion In this paper, we propose a MZI refractive index sensor based on thermo-optic effect of SOI waveguide to detect refractive index of liquid. The sensing mechanism is analyzed and the design principle is discussed to realize a valid refractive index sensor. Moreover the sensitivity and resolution of the refractive index sensor are also discussed. At last a refractive index sensor with a compact size of 2 mm × 1.5 mm can be realized with a sensitivity of 48000K/RIU and a resolution of 2 × 10−6 . This new kind of refractive index sensor is rather prosperous for its simple structure, compact size, high sensitivity and resolution in the field of biological and chemical sensing. Compared with other refractive index sensors, the proposed sensor’s sensitivity and resolution can be adjusted and further improved by increasing the length ratio between sensing
6370
T. Tang, L. Luo / Optik 127 (2016) 6366–6370
and heating areas, which brings great flexibility for the design and provides an effective method to improve the sensor’s performance. Acknowledgements This work is supported by National Natural Science Foundation of China under Grant No. 61505016, the scientific research fund of Chengdu University of Information Technology (No. J201417) and the project of Sichuan Provincial Department of Education (15ZA0183). References [1] K.M. Mayer, J.H. Hafner, Localized surface plasmon resonance sensors, Chem. Rev. 111 (6) (2011) 3828–3857. [2] K.A. Tetz, L. Pang, Y. Fainman, High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance, Opt. Lett. 31 (10) (2006) 1528–1530. [3] F.B. Myers, L.P. Lee, Innovations in optical microfluidic technologies for point-of-care diagnostics, Lab Chip 8 (12) (2008) 2015–2031. [4] Y. Gao, Q. Gan, Z. Xin, X. Cheng, F.J. Bartoli, Plasmonic Mach–Zehnder interferometer for ultrasensitive on-chip biosensing, ACS Nano 5 (12) (2011) 9836–9844. [5] 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. [6] J. Kou, J. Feng, Q. Wang, et al., Microfiber-probe-based ultrasmall interferometric sensor, Opt. Lett. 35 (13) (2010) 2308–2310. [7] 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. [8] 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. [9] A.M. Armani, R.P. Kulkarni, S.E. Fraser, et al., Label-free, single-molecule detection with optical microcavities, Science 317 (5839) (2007) 783–787. [10] Y. Gao, Z. Xin, B. Zeng, et al., Plasmonic interferometric sensor arrays for high-performance label-free biomolecular detection, Lab Chip 13 (24) (2013) 4755–4764. [11] W.W. Lam, L.H. Chu, C.L. Wong, et al., A surface plasmon resonance system for the measurement of glucose in aqueous solution, Sens. Actuators B 105 (2) (2005) 138–143. [12] Y. Gao, Z. Xin, Q. Gan, et al., Plasmonic interferometers for label-free multiplexed sensing, Opt. Express 21 (5) (2013) 5859–5871. [13] S. Dante, D. Duval, B. Sepúlveda, et al., All-optical phase modulation for integrated interferometric biosensors, Opt. Express 20 (7) (2012) 7195–7205. [14] G. Cocorullo, I. Rendina, Thermo-optical modulation at 1.5 m in silicon etalon, Electron. Lett. 28 (1992) 83–85. [15] R.A. Soref, B.R. Bennett, Electro optical effects in silicon, IEEE J. Quantum Electron. QE-23 (1987) 123–129. [16] Y. Li, J. Yu, S. Chen, Rearrangeable nonblocking SOI waveguide thermo optic 4 × 4 switch matrix with low insertion loss and fast response, IEEE Photon. Technol. Lett. 17 (2005) 1641–1643. [17] V. Passaro, F. Magno, A. Tsarev, Investigation of thermo-optic effect and multi-reflector tunable filter/multiplexer in SOI waveguides, Opt. Express 13 (9) (2005) 3429–3437. [18] Y. Liu, J. Kim, Numerical investigation of finite thickness metal-insulator-metal structure for waveguide-based surface plasmon resonance biosensing, Sens. Actuators B 148 (1) (2010) 23–28.