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Theoretical research on high sensitivity gas sensor due to slow light in slotted photonic crystal waveguide
Sensors and Actuators B 173 (2012) 505–509
Contents lists available at SciVerse ScienceDirect
Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb
Theoretical research on high sensitivity gas sensor due to slow light in slotted photonic crystal waveguide Ya-Nan Zhang, Yong Zhao ∗ , Di Wu, Qi Wang Northeastern University, College of Information Science and Engineering, Shenyang 110819, China
a r t i c l e
i n f o
Article history: Received 11 May 2012 Received in revised form 3 July 2012 Accepted 9 July 2012 Available online 21 July 2012 Keywords: Gas sensor Fiber-optic sensor Slotted photonic crystal waveguide Structure optimization Slow light
a b s t r a c t A miniature and sensitivity gas sensor based on slotted photonic crystal waveguide (SPCW) was presented, in which the correlation spectroscopy method was applied for signal processing and the SPCW was used for the gas cell. To enhance the system sensitivity, the structure of the SPCW was optimized to possess extremely high group index and very large light confinement in the slot. Simulation results indicated that the measuring resolution of acetylene gas of 1 ppm was achieved with good temperature stability. Additionally, the active region was only 1 mm long, which could be of great advantage in the use of the limited space. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Photonic crystal is a periodic dielectric structure with the capability of guiding and manipulating light at the scale of optical wavelength [1]. Since first proposed in 1987 [2], photonic crystal has been studied extensively both theoretically and experimentally. Photonic crystal waveguide (PCW) shows highly dispersive characteristics so that the group velocity varies enormously near the band edge. Particularly, by using proper materials and adjusting geometrical parameters, the PCW can be used to realize high sensitivity and miniature sensors due to the advantages of working under room temperature, great potential bandwidth, and realizing slow light in arbitrary wavelength [3]. Recently, it has been found that PCW could enhance light–matter interaction because of the enormously low group velocity near the band edge of PCW, which could be used to realize high sensitivity and miniature gas sensor [4]. However, in conventional PCW, slow light is usually confined to the high index medium, which is a major drawback in this application where the interaction with the test gas is weak due to poor overlap. At the same time, with the development of silicon based photonics technology, researchers found that the slotted photonic crystal waveguide (SPCW) can combine the ability to confine light in the low-index slot with the slow light enhancement available from PCW [5]. At present, compact and high sensitivity sensors based on nanocavity in SPCW have been studied intensively, such
∗ Corresponding author. Tel.: +86 24 83687266. E-mail address: [email protected] (Y. Zhao). 0925-4005/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.snb.2012.07.051
as displacement sensor [6], biochemical sensor [7,8] and refractive sensor [9,10]. However, there is a need for further researchers to open up the slow light property of SPCW for sensor application, in which the structure optimization of SPCW is a key technology for SPCW to be applied much better in high sensitivity sensor. In recent years, many waveguide structures have been studied to improve the slow light properties of SPCW [11–16]. In Refs. [13,14], the holes radius adjacent to the slot were adjusted, and the largest group index was about 40. However, Li et al. [17] indicated that it was difficult to control the holes size of a photonic lattice accurately and reproducibly from the aspect of fabrication processes. In Ref. [15], the Bragg-like corrugation of wide slot was introduced to optimize the slow light property. Numerical results showed that slow light with group index of 140 and 90 over 1.5 nm and 2 nm bandwidths were achieved. Though the properties of slow light were well improved, the comb in this case included a series of 90-degree angles, whose size and shape were difficult to control, thus adds to the difficulty of SPCW preparation. This paper firstly analyzes the working principle of gas sensor based on SPCW. By theoretically exploring the dependence of slow light properties of SPCW on the interaction of slow light with the test gas, a method to enhance the sensitivity of gas sensor is offered. Then the structure of SPCW is optimized by properly shifting the first two rows of air holes adjacent to the slot, simulation results indicate that a very high group index of 105 could be achieved and the enhancement factor of the electric field would reaches to 12 with good temperature stability. Although similar results have been published [15], this method is much simpler and it is much easier from the aspect of fabrication processes. Combined with
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Y.-N. Zhang et al. / Sensors and Actuators B 173 (2012) 505–509
Fig. 1. The structure of schematic design and the inset shows the structure of SPCW cell.
correlation spectroscopy and differential absorption method for signal processing, a compact and high sensitivity gas sensor based on the designed SPCW is presented. 2. Theory model The schematic diagram of SPCW based acetylene gas detection system is shown in Fig. 1, whose signal processing method is the correlation spectroscopy and differential absorption. A distributed feedback Bragg laser diode (DFB-LD) was subjected to the modulation of sinusoidal signal with an appropriate frequency. After the absorption of test gas in SPCW, the transmitted light would be equally divided into two parts with the help of a coupler. The first part would be sent into a reference gas cell that the type of the filling gas is similar to the test gas but the concentration is constant and known, and it would be detected by a photodetector after the fixed gas absorption. The other part would be detected directly by another photodetector. Then the two output electric signals would be sent into the lock-in amplifier to get the harmonic components and to compute the difference between two signals. At last, the data would be processed and displayed by the computer. The output light signal I∗ , after passage through the SPCW based gas cell, is given by [18–20]: ∗
I = I + I
(1)
where I is the unknown light fluctuation that would be interfered with the external environment, and I is attenuated following the Lambert–Beer law [19,20]: I = I0 · exp(− · ˛CL)
(2)
where I0 is the intensity of the input light, C is the gas concentration, ˛ is the absorption coefficient, L is the absorption length and equals to the length of SPCW in this work, is the absorption enhancement factor determined by slow light enhance light–matter interaction.
Montensen and Xiao [21] have theoretically demonstrated that: = f · c/vg = f · ng
(3)
where f is the filling factor of the optical field in the test medium, c is the velocity of light in vacuum, vg , ng are the group velocity and group index in the test medium respectively. After gas absorption, the two output signals received by the lockin amplifier would be: I1 = 0.5 · (ˇ · I + I)
(4)
I2 = 0.5 · (I + I)
(5)
where ˇ is the attenuation coefficient of the gas in the reference gas cell and it is a constant in this system. The output expression of this system is given by: ID = I2 − I1 =
(1 − ˇ) · I (1 − ˇ) · I0 · exp(− · ˛CL) = 2 2
(6)
Therefore the sensitivity of this sensor could be expressed by:
(1 − ˇ)I0 ˛L (1 − ˇ)I0 ˛L ID = f · ng · =· 2 2 C
S=
(7)
The detection limit of this system could be determined by: C =
ID /I0 f · ng · (1 − ˇ) · ˛L/2
(8)
where ID /I0 is the smallest fractional change in the output that can be detected by photodetector. From Eq. (6), it is found that the proposed system could not only eliminates fluctuation in light intensity due to the interference gas in the test gas, but also decreases the impact of the environment [22], which is benefited from the signal processing method of the correlation spectroscopy and differential absorption. Meanwhile, Eqs. (7) and (8) show the sensitivity and detection limit of the proposed system. It can be found that the sensitivity and detection limit of the sensor based on slow light in SPCW are related to the group index and the filling factor of the optical field in the test gas,
Y.-N. Zhang et al. / Sensors and Actuators B 173 (2012) 505–509
507
180 160
Group Index-ng
140
T=280 K T=300 K
120 100 80 60 40
Fig. 2. The structure of slotted photonic crystal waveguide.
20 0.2695
which can be improved by the combination of slow light effect and optical confinement in SPCW. Thus the structure of SPCW needs to be designed to possess extremely high group index and very large light confinement in the slot. As well known, the refractive index of silicon is thermal dependence, thus will change the properties of the optical sensor, and the influence of temperature will be enhanced when the slow light phenomenon is introduced to improve the light–matter interaction. So the temperature stability and bandwidth of slow light in SPCW should be considered in the practical application of gas sensor. Besides, the coupling loss between the ridge waveguide and the SPCW should also be resolved before its practical application. 3. Simulation optimization and results discussion Fig. 2 shows the basic structure of SPCW, which is constructed in a silicon-on-insulator (SOI) substrate (n = 3.48) by replacing the central row of air holes in the triangular lattice photonic crystal with a narrow slot, where the test gas can be infiltrated into the holes and the slot. The properties of SPCW are numerically investigated by using the MIT photonic band (MPB) package [23] and finite-difference time-domain (FDTD) method [24]. In numerical simulations, the effective index of 2.87 is used for the 220 nm thick slab [17], the radius of air holes r = 0.32a, the slot width ω = 0.3a, where a is the lattice constant. According to Ref. [25], the band diagrams of PCW are the combination of the index-guided mode at the small wavevector region and the gap-guided mode at the large wavevector region. The properly optimized structure parameters would enlarge the gap-guided mode area, which is indication of enhancing the slow light modes since the large group index is only obtained in the gap-guided mode part. In this study, the method of changing the positions of the first
0.27
0.2705
0.271
0.2715
Normalized Frequency-ωa/2πc Fig. 4. The group index curves of the designed SPCW for temperatures, T = 290 K and T = 300 K.
and second rows of air holes adjacent to the slot was adopted to improve the slow light properties of SPCW, which has been widely used in conventional W1 waveguide and has been demonstrated as a simple method [17]. The dashed lines in Fig. 2 illustrate the displacement of the first two rows, and the parameters P1 and P2 denote the shift distance of each row from their original positions. Fig. 3(a) and (b) shows the dependence of the dispersion characteristics on the shift distance of P1 and P2 respectively, while other structure parameters are identical with the original structure. It is obvious that the higher P1 will shift the whole dispersion diagrams to the lower frequency and the slope decreases, while the higher P2 will shift the whole dispersion diagrams to the lower frequency and then to the higher frequency in the small wavevector with P2 = 0.1a as a turning point. By properly increasing P1 to decrease the slope of the tail of the diagram near the band edge and adjusting suitable P2 to decrease the slope of the dispersion diagram at the middle of the band, the slow light would be maximized over a wide bandwidth. For P1 = 0.06a and P2 = 0.115a, Fig. 4 illustrates the group index curves of SPCW when the temperature T = 280 K and T = 300 K, respectively. It is shown that a very high group index of 105 is achieved while still retaining a respectable bandwidth, and the optimized SPCW possesses good temperature stability in the range of 20 K, which can guarantees the practical application of SPCW. The y-component electric field (Ey ) distribution of the TE mode is shown in Fig. 5(a) while the operating frequency of input light is chosen near 0.2705ωa/2c, for which the group index is 105. It indicates that just a small part of light energy leaks out, on the contrary, most of the energy could be confined in the slot as the light
Fig. 3. (a) Dispersion diagrams with different shift of P1 from −0.04a to 0.04a with P2 = 0; (b) dispersion diagrams with different shift of P1 from −0.04a to 0.04a with P2 = 0.
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Y.-N. Zhang et al. / Sensors and Actuators B 173 (2012) 505–509
Fig. 5. (a) Calculated electric field (Ey ) distribution of the optimized SPCW; (b) electric field amplitude of TE mode in the section area S, the side view (left) and the three-view image (right) is shown respectively.
propagating forward. Fig. 5(b) shows the normalized Ey amplitude of the section area S, which demonstrates a significant enhancement of the electric field intensity in the narrow low-index slot by nearly a factor of 12, thus it can enhance the interaction between slow light and the test gas effectively. As well known, the effectively coupling of light from ridge waveguide to slow light waveguide is a crucial point before its application. In this study, to reduce coupling loss, the suitable resonant structures are added at both ends of the SPCW, which is inspired by Ref. [26]. The parameters of the resonate structure are shown in the inset of Fig. 6, for which the optimized parameters are r0 = 0.56a, s = 2.9a and ω0 = 4.9a. By placing defects near the crystal edge, the interference effects between multiple beams produce a
self-collimated beaming effect, and the high transmission and low ripple can be obtained. A nearly flat transmission spectrum with 20 dB enhancement in the overall guide band could be achieved. The Fabry–Perot ripples in the slow light region still exist due to the finite length of the slot (15a in this paper), which causes a finite remaining reflectivity at the interface. For the optimized structure of SPCW, the lattice constant was set to a = 413.9 nm to make the device operates at the wavelength of 1530 nm, which is the spectral absorption peak of acetylene gas [27]. From the above simulations, a very high group index of 105 could be achieved and the enhancement factor of the electric field would reach to 12 with good temperature stability. According to Eqs. (7) and (8), the system sensitivity can be increased by 1260 times due to slow light in SPCW. In our measurement, ID /I0 = 5 × 10-4 is the smallest fractional change in light intensity that can be detected by photodetector. ˛ = 0.86/cm is the absorption coefficient of acetylene gas at 1530 nm. L is assumed to be 1 mm. ˇ = 0.1165 when the concentration of the fixed acetylene gas is 100% and the absorption length is 25 cm. Then the expected detection limit of our designed system would down to 1 ppm, and the introduction of slow light managed to improve detection limit by 1260 times than without slow light. It is worth noting that the group index as well as the absorption enhancement factor increases slightly with the temperature, while the absorption coefficient of acetylene gas would decreases slightly. Moreover, as the length of SPCW, namely, the absorption length is only 1 mm, the thermal stability of the designed sensor system can therefore be greatly enhanced compare to the conventional gas sensor.
4. Conclusion
Fig. 6. The transmission curves of SPCW with and without resonate coupling structure. The parameters of the resonate structure are shown in the inset, for which the optimized parameters are r0 = 0.56a, s = 2.9a and ω0 = 4.9a.
Above all, a high sensitivity gas sensor based on the designed SPCW was proposed. Due to the combination of low group velocity and large light confinement in SPCW, the detection limit of this simple and compact sensor could reach about 1 ppm, which has the potential to build on-chip devices for in situ measurement with
Y.-N. Zhang et al. / Sensors and Actuators B 173 (2012) 505–509
high sensitivity. Besides, this technology could be applied to the sensing of other fluids directly. Acknowledgements This work was supported in part by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20100042110029, and the Fundamental Research Funds for the Central Universities under Grants 110204002, 100404006 and 110804003. References [1] S.A. Schulz, L.O. Faolain, D.M. Beggs, et al., Dispersion engineered slow light in photonic crystals: a comparison, Journal of Optics 12 (10) (2010) 104004. [2] S. John, Strong localization of photons in certain disordered dielectric superlattices, Physical Review Letters 58 (23) (1987) 2486–2489. [3] T. Baba, Slow light in photonic crystals, Nature Photonics 2 (8) (2008) 465–473. [4] Y. Zhao, Y.N. Zhang, Q. Wang, Research advances of photonic crystal gas and liquid sensors, Sensors and Actuators B 160 (1) (2011) 1288–1297. [5] J.D. Ryckman, S.M. Weiss, Localized field enhancements in guided and defect modes of a periodic slot waveguide, IEEE Photonics Journal 3 (6) (2011) 986–995. [6] D.Q. Yang, H.P. Tian, Y.F. Ji, Microdisplacement sensor based on high-Q nanocavity in slot photonic crystal, Optical Engineering 50 (5) (2011) 054402. [7] M.G. Scullion, A. Di Falco, T.F. Krauss, Slotted photonic crystal cavities with integrated microfluidics for biosensing applications, Biosensors and Bioelectronics 27 (1) (2011) 101–105. [8] A. Di Falco, L. O’Faolain, T.F. Krauss, Chemical sensing in slotted photonic crystal heterostructure cavities, Applies Physics Letters 94 (6) (2009) 063503. [9] J. Jágerská, H. Zhang, Z.L. Diao, et al., Refractive index sensing with an air-slot photonic crystal nanocavity, Optics Letters 35 (15) (2010) 2523–2525. [10] B.W. Wang, M.A. Dündar, R. Nötzel, et al., Photonic crystal slot nanobeam slow light waveguides for refractive index sensing, Applied Physics Letters 97 (15) (2010) 151105. [11] A. Di Falco, L. O’Faolain, T.F. Krauss, Dispersion control and slow light in slotted photonic crystal waveguides, Applied Physics Letters 92 (8) (2008) 082501. [12] J.M. Brosi, C. Koos, L.C. Andreani, et al., High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide, Optics Express 16 (6) (2008) 4177–4199. [13] J. Wu, C. Peng, Y.P. Li, et al., Slow light in tapered slot photonic crystal waveguide, Chinese Science Bulletin 54 (20) (2009) 3074–3078. [14] H. Aghababaeian, M.H. Vadjed-Samiei, N. Granpayeh, Temperature stabilization of group index in silicon photonic crystal waveguides, Journal of the Optical Society of Korea 15 (4) (2011) 398–402. [15] C. Caer, X.L. Roux, V.K. Do, et al., Dispersion engineering of wide slot photonic crystal waveguides by Bragg-like corrugation of the slot, IEEE Photonics Technology Letters 23 (18) (2011) 1298–1300. [16] W.C. Lai, S. Chakravarty, X.L. Wang, et al., On-chip methane sensing by near-IR absorption signatures in a photonic crystal slot waveguide, Optics Letters 36 (6) (2011) 984–986. [17] J. Li, T.P. White, L.O. Faolain, et al., Systematic design of flat band slow light in photonic crystal waveguides, Optical Express 16 (9) (2008) 6227–6232. [18] X.T. Lou, G. Somesfalean, Z.G. Zhang, Gas detection by correlation spectroscopy employing a multimode diode laser, Applied Optics 47 (13) (2008) 2392–2398. [19] K.L. Yu, C.Q. Wu, Z. Wang, Optical methane sensor based on a fiber loop at 1665 nm, IEEE Sensors Journal 10 (3) (2010) 728–731. [20] H. Ding, J.Q. Liang, J.H. Cui, et al., A novel fiber Fabry–Perot filter based mixedgas sensing system, Sensors and Actuators B: Chemical 138 (1) (2009) 154–159.
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[21] N.A. Mortensen, S.S. Xiao, Slow-light enhancement of Beer–Lambert–Bouguer absorption, Applied Physics Letters 90 (14) (2007) 141108. [22] B. Wang, G. Somesfalean, L. Mei, et al., Detection of gas concentration by correlation spectroscopy using a multi-wavelength fiber laser, Progress in Electromagnetics Research 114 (2011) 469–479. [23] http://ab-initio.mit.edu/wiki/index.php/MIT Photonic Bands. [24] A.F. Oskooi, D. Roundy, M. Ibanescu, et al., Meep: a flexible free-software package for electromagnetic simulations by the FDTD method, Computer Physics Communications 181 (3) (2010) 687–702. [25] K. Yamada, H. Morita, A. Shinya, et al., Improved line-defect structures for photonic crystal waveguides with high group velocity, Optics Communications 198 (4–6) (2001) 395–402. [26] M.G. Scullion, T.F. Krauss, A. Di Falco, High efficiency interface for coupling into slotted photonic crystal waveguides, IEEE Photonics Journal 3 (2) (2011) 203–208. [27] L.S. Rothman, I.E. Gordon, A. Barbe, et al., The HITRAN 2008 molecular spectroscopic database, Journal of Quantitative Spectroscopy & Radiative Transfer 110 (9–10) (2009) 533–572.
Biographies
Yong Zhao received his M.A. and Ph.D. degrees, respectively, in precision instrument & automatic measurement with laser and fiber-optic techniques from the Harbin Institute of Technology, China, in 1998 and 2001. He was awarded a first prize scholarship in 2000 by the China Instrument and Control Society and the Sintered Metal Corporation (SMC) scholarship in Japan. He was a postdoctor in the Department of Electronic Engineering of Tsinghua University from 2001 to 2003, and then worked as an associate professor in the Department of Automation, Tsinghua University of China. In 2006, he was a visiting scholar of University of Illinois in Urbana and Champagne, USA. In 2008, he was awarded as the “New Century Excellent Talents in University” by the Ministry of Education of China. In 2009, he was awarded as the “Liaoning Bai-Qian-Wan Talents” by Liaoning Province. In 2011, he was awarded by the Royal Academy of Engineering as an academic researcher of City University London. Now he is working in Northeastern University as a full professor. As a leader of his research group, his current research interests are the development of fiber-optic sensors and device, fiber Bragg grating sensors, novel sensor materials and principles, slow light and sensor technology, optical measurement technologies. He has authored and co-authored more than 130 scientific papers and conference presentations, 7 patents, and 4 books. He is a member in the Editorial Boards of the International Journals of Sensor Letters, Instrumentation Science & Technology, Journal of Sensor Technology, and Advances in Optical Technologies. Qi Wang was born in Liaoning, China, in 1982. He received his Ph.D. degree in 2009 from the School of Physics and Optoelectronic Technology, Dalian University of Technology (DUT), Dalian, China. He is currently working in the College of Information Science and Engineering at Northeast University, China. His research interests are new photonic devices, fiber-optic sensors, optoelectronic measurement technology and system, and their industrial applications. He has authored and co-authored more than 20 scientific papers, patents and conference presentations.
Contents lists available at SciVerse ScienceDirect
Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb
Theoretical research on high sensitivity gas sensor due to slow light in slotted photonic crystal waveguide Ya-Nan Zhang, Yong Zhao ∗ , Di Wu, Qi Wang Northeastern University, College of Information Science and Engineering, Shenyang 110819, China
a r t i c l e
i n f o
Article history: Received 11 May 2012 Received in revised form 3 July 2012 Accepted 9 July 2012 Available online 21 July 2012 Keywords: Gas sensor Fiber-optic sensor Slotted photonic crystal waveguide Structure optimization Slow light
a b s t r a c t A miniature and sensitivity gas sensor based on slotted photonic crystal waveguide (SPCW) was presented, in which the correlation spectroscopy method was applied for signal processing and the SPCW was used for the gas cell. To enhance the system sensitivity, the structure of the SPCW was optimized to possess extremely high group index and very large light confinement in the slot. Simulation results indicated that the measuring resolution of acetylene gas of 1 ppm was achieved with good temperature stability. Additionally, the active region was only 1 mm long, which could be of great advantage in the use of the limited space. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Photonic crystal is a periodic dielectric structure with the capability of guiding and manipulating light at the scale of optical wavelength [1]. Since first proposed in 1987 [2], photonic crystal has been studied extensively both theoretically and experimentally. Photonic crystal waveguide (PCW) shows highly dispersive characteristics so that the group velocity varies enormously near the band edge. Particularly, by using proper materials and adjusting geometrical parameters, the PCW can be used to realize high sensitivity and miniature sensors due to the advantages of working under room temperature, great potential bandwidth, and realizing slow light in arbitrary wavelength [3]. Recently, it has been found that PCW could enhance light–matter interaction because of the enormously low group velocity near the band edge of PCW, which could be used to realize high sensitivity and miniature gas sensor [4]. However, in conventional PCW, slow light is usually confined to the high index medium, which is a major drawback in this application where the interaction with the test gas is weak due to poor overlap. At the same time, with the development of silicon based photonics technology, researchers found that the slotted photonic crystal waveguide (SPCW) can combine the ability to confine light in the low-index slot with the slow light enhancement available from PCW [5]. At present, compact and high sensitivity sensors based on nanocavity in SPCW have been studied intensively, such
∗ Corresponding author. Tel.: +86 24 83687266. E-mail address: [email protected] (Y. Zhao). 0925-4005/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.snb.2012.07.051
as displacement sensor [6], biochemical sensor [7,8] and refractive sensor [9,10]. However, there is a need for further researchers to open up the slow light property of SPCW for sensor application, in which the structure optimization of SPCW is a key technology for SPCW to be applied much better in high sensitivity sensor. In recent years, many waveguide structures have been studied to improve the slow light properties of SPCW [11–16]. In Refs. [13,14], the holes radius adjacent to the slot were adjusted, and the largest group index was about 40. However, Li et al. [17] indicated that it was difficult to control the holes size of a photonic lattice accurately and reproducibly from the aspect of fabrication processes. In Ref. [15], the Bragg-like corrugation of wide slot was introduced to optimize the slow light property. Numerical results showed that slow light with group index of 140 and 90 over 1.5 nm and 2 nm bandwidths were achieved. Though the properties of slow light were well improved, the comb in this case included a series of 90-degree angles, whose size and shape were difficult to control, thus adds to the difficulty of SPCW preparation. This paper firstly analyzes the working principle of gas sensor based on SPCW. By theoretically exploring the dependence of slow light properties of SPCW on the interaction of slow light with the test gas, a method to enhance the sensitivity of gas sensor is offered. Then the structure of SPCW is optimized by properly shifting the first two rows of air holes adjacent to the slot, simulation results indicate that a very high group index of 105 could be achieved and the enhancement factor of the electric field would reaches to 12 with good temperature stability. Although similar results have been published [15], this method is much simpler and it is much easier from the aspect of fabrication processes. Combined with
506
Y.-N. Zhang et al. / Sensors and Actuators B 173 (2012) 505–509
Fig. 1. The structure of schematic design and the inset shows the structure of SPCW cell.
correlation spectroscopy and differential absorption method for signal processing, a compact and high sensitivity gas sensor based on the designed SPCW is presented. 2. Theory model The schematic diagram of SPCW based acetylene gas detection system is shown in Fig. 1, whose signal processing method is the correlation spectroscopy and differential absorption. A distributed feedback Bragg laser diode (DFB-LD) was subjected to the modulation of sinusoidal signal with an appropriate frequency. After the absorption of test gas in SPCW, the transmitted light would be equally divided into two parts with the help of a coupler. The first part would be sent into a reference gas cell that the type of the filling gas is similar to the test gas but the concentration is constant and known, and it would be detected by a photodetector after the fixed gas absorption. The other part would be detected directly by another photodetector. Then the two output electric signals would be sent into the lock-in amplifier to get the harmonic components and to compute the difference between two signals. At last, the data would be processed and displayed by the computer. The output light signal I∗ , after passage through the SPCW based gas cell, is given by [18–20]: ∗
I = I + I
(1)
where I is the unknown light fluctuation that would be interfered with the external environment, and I is attenuated following the Lambert–Beer law [19,20]: I = I0 · exp(− · ˛CL)
(2)
where I0 is the intensity of the input light, C is the gas concentration, ˛ is the absorption coefficient, L is the absorption length and equals to the length of SPCW in this work, is the absorption enhancement factor determined by slow light enhance light–matter interaction.
Montensen and Xiao [21] have theoretically demonstrated that: = f · c/vg = f · ng
(3)
where f is the filling factor of the optical field in the test medium, c is the velocity of light in vacuum, vg , ng are the group velocity and group index in the test medium respectively. After gas absorption, the two output signals received by the lockin amplifier would be: I1 = 0.5 · (ˇ · I + I)
(4)
I2 = 0.5 · (I + I)
(5)
where ˇ is the attenuation coefficient of the gas in the reference gas cell and it is a constant in this system. The output expression of this system is given by: ID = I2 − I1 =
(1 − ˇ) · I (1 − ˇ) · I0 · exp(− · ˛CL) = 2 2
(6)
Therefore the sensitivity of this sensor could be expressed by:
(1 − ˇ)I0 ˛L (1 − ˇ)I0 ˛L ID = f · ng · =· 2 2 C
S=
(7)
The detection limit of this system could be determined by: C =
ID /I0 f · ng · (1 − ˇ) · ˛L/2
(8)
where ID /I0 is the smallest fractional change in the output that can be detected by photodetector. From Eq. (6), it is found that the proposed system could not only eliminates fluctuation in light intensity due to the interference gas in the test gas, but also decreases the impact of the environment [22], which is benefited from the signal processing method of the correlation spectroscopy and differential absorption. Meanwhile, Eqs. (7) and (8) show the sensitivity and detection limit of the proposed system. It can be found that the sensitivity and detection limit of the sensor based on slow light in SPCW are related to the group index and the filling factor of the optical field in the test gas,
Y.-N. Zhang et al. / Sensors and Actuators B 173 (2012) 505–509
507
180 160
Group Index-ng
140
T=280 K T=300 K
120 100 80 60 40
Fig. 2. The structure of slotted photonic crystal waveguide.
20 0.2695
which can be improved by the combination of slow light effect and optical confinement in SPCW. Thus the structure of SPCW needs to be designed to possess extremely high group index and very large light confinement in the slot. As well known, the refractive index of silicon is thermal dependence, thus will change the properties of the optical sensor, and the influence of temperature will be enhanced when the slow light phenomenon is introduced to improve the light–matter interaction. So the temperature stability and bandwidth of slow light in SPCW should be considered in the practical application of gas sensor. Besides, the coupling loss between the ridge waveguide and the SPCW should also be resolved before its practical application. 3. Simulation optimization and results discussion Fig. 2 shows the basic structure of SPCW, which is constructed in a silicon-on-insulator (SOI) substrate (n = 3.48) by replacing the central row of air holes in the triangular lattice photonic crystal with a narrow slot, where the test gas can be infiltrated into the holes and the slot. The properties of SPCW are numerically investigated by using the MIT photonic band (MPB) package [23] and finite-difference time-domain (FDTD) method [24]. In numerical simulations, the effective index of 2.87 is used for the 220 nm thick slab [17], the radius of air holes r = 0.32a, the slot width ω = 0.3a, where a is the lattice constant. According to Ref. [25], the band diagrams of PCW are the combination of the index-guided mode at the small wavevector region and the gap-guided mode at the large wavevector region. The properly optimized structure parameters would enlarge the gap-guided mode area, which is indication of enhancing the slow light modes since the large group index is only obtained in the gap-guided mode part. In this study, the method of changing the positions of the first
0.27
0.2705
0.271
0.2715
Normalized Frequency-ωa/2πc Fig. 4. The group index curves of the designed SPCW for temperatures, T = 290 K and T = 300 K.
and second rows of air holes adjacent to the slot was adopted to improve the slow light properties of SPCW, which has been widely used in conventional W1 waveguide and has been demonstrated as a simple method [17]. The dashed lines in Fig. 2 illustrate the displacement of the first two rows, and the parameters P1 and P2 denote the shift distance of each row from their original positions. Fig. 3(a) and (b) shows the dependence of the dispersion characteristics on the shift distance of P1 and P2 respectively, while other structure parameters are identical with the original structure. It is obvious that the higher P1 will shift the whole dispersion diagrams to the lower frequency and the slope decreases, while the higher P2 will shift the whole dispersion diagrams to the lower frequency and then to the higher frequency in the small wavevector with P2 = 0.1a as a turning point. By properly increasing P1 to decrease the slope of the tail of the diagram near the band edge and adjusting suitable P2 to decrease the slope of the dispersion diagram at the middle of the band, the slow light would be maximized over a wide bandwidth. For P1 = 0.06a and P2 = 0.115a, Fig. 4 illustrates the group index curves of SPCW when the temperature T = 280 K and T = 300 K, respectively. It is shown that a very high group index of 105 is achieved while still retaining a respectable bandwidth, and the optimized SPCW possesses good temperature stability in the range of 20 K, which can guarantees the practical application of SPCW. The y-component electric field (Ey ) distribution of the TE mode is shown in Fig. 5(a) while the operating frequency of input light is chosen near 0.2705ωa/2c, for which the group index is 105. It indicates that just a small part of light energy leaks out, on the contrary, most of the energy could be confined in the slot as the light
Fig. 3. (a) Dispersion diagrams with different shift of P1 from −0.04a to 0.04a with P2 = 0; (b) dispersion diagrams with different shift of P1 from −0.04a to 0.04a with P2 = 0.
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Fig. 5. (a) Calculated electric field (Ey ) distribution of the optimized SPCW; (b) electric field amplitude of TE mode in the section area S, the side view (left) and the three-view image (right) is shown respectively.
propagating forward. Fig. 5(b) shows the normalized Ey amplitude of the section area S, which demonstrates a significant enhancement of the electric field intensity in the narrow low-index slot by nearly a factor of 12, thus it can enhance the interaction between slow light and the test gas effectively. As well known, the effectively coupling of light from ridge waveguide to slow light waveguide is a crucial point before its application. In this study, to reduce coupling loss, the suitable resonant structures are added at both ends of the SPCW, which is inspired by Ref. [26]. The parameters of the resonate structure are shown in the inset of Fig. 6, for which the optimized parameters are r0 = 0.56a, s = 2.9a and ω0 = 4.9a. By placing defects near the crystal edge, the interference effects between multiple beams produce a
self-collimated beaming effect, and the high transmission and low ripple can be obtained. A nearly flat transmission spectrum with 20 dB enhancement in the overall guide band could be achieved. The Fabry–Perot ripples in the slow light region still exist due to the finite length of the slot (15a in this paper), which causes a finite remaining reflectivity at the interface. For the optimized structure of SPCW, the lattice constant was set to a = 413.9 nm to make the device operates at the wavelength of 1530 nm, which is the spectral absorption peak of acetylene gas [27]. From the above simulations, a very high group index of 105 could be achieved and the enhancement factor of the electric field would reach to 12 with good temperature stability. According to Eqs. (7) and (8), the system sensitivity can be increased by 1260 times due to slow light in SPCW. In our measurement, ID /I0 = 5 × 10-4 is the smallest fractional change in light intensity that can be detected by photodetector. ˛ = 0.86/cm is the absorption coefficient of acetylene gas at 1530 nm. L is assumed to be 1 mm. ˇ = 0.1165 when the concentration of the fixed acetylene gas is 100% and the absorption length is 25 cm. Then the expected detection limit of our designed system would down to 1 ppm, and the introduction of slow light managed to improve detection limit by 1260 times than without slow light. It is worth noting that the group index as well as the absorption enhancement factor increases slightly with the temperature, while the absorption coefficient of acetylene gas would decreases slightly. Moreover, as the length of SPCW, namely, the absorption length is only 1 mm, the thermal stability of the designed sensor system can therefore be greatly enhanced compare to the conventional gas sensor.
4. Conclusion
Fig. 6. The transmission curves of SPCW with and without resonate coupling structure. The parameters of the resonate structure are shown in the inset, for which the optimized parameters are r0 = 0.56a, s = 2.9a and ω0 = 4.9a.
Above all, a high sensitivity gas sensor based on the designed SPCW was proposed. Due to the combination of low group velocity and large light confinement in SPCW, the detection limit of this simple and compact sensor could reach about 1 ppm, which has the potential to build on-chip devices for in situ measurement with
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high sensitivity. Besides, this technology could be applied to the sensing of other fluids directly. Acknowledgements This work was supported in part by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20100042110029, and the Fundamental Research Funds for the Central Universities under Grants 110204002, 100404006 and 110804003. References [1] S.A. Schulz, L.O. Faolain, D.M. Beggs, et al., Dispersion engineered slow light in photonic crystals: a comparison, Journal of Optics 12 (10) (2010) 104004. [2] S. John, Strong localization of photons in certain disordered dielectric superlattices, Physical Review Letters 58 (23) (1987) 2486–2489. [3] T. Baba, Slow light in photonic crystals, Nature Photonics 2 (8) (2008) 465–473. [4] Y. Zhao, Y.N. Zhang, Q. Wang, Research advances of photonic crystal gas and liquid sensors, Sensors and Actuators B 160 (1) (2011) 1288–1297. [5] J.D. Ryckman, S.M. Weiss, Localized field enhancements in guided and defect modes of a periodic slot waveguide, IEEE Photonics Journal 3 (6) (2011) 986–995. [6] D.Q. Yang, H.P. Tian, Y.F. Ji, Microdisplacement sensor based on high-Q nanocavity in slot photonic crystal, Optical Engineering 50 (5) (2011) 054402. [7] M.G. Scullion, A. Di Falco, T.F. Krauss, Slotted photonic crystal cavities with integrated microfluidics for biosensing applications, Biosensors and Bioelectronics 27 (1) (2011) 101–105. [8] A. Di Falco, L. O’Faolain, T.F. Krauss, Chemical sensing in slotted photonic crystal heterostructure cavities, Applies Physics Letters 94 (6) (2009) 063503. [9] J. Jágerská, H. Zhang, Z.L. Diao, et al., Refractive index sensing with an air-slot photonic crystal nanocavity, Optics Letters 35 (15) (2010) 2523–2525. [10] B.W. Wang, M.A. Dündar, R. Nötzel, et al., Photonic crystal slot nanobeam slow light waveguides for refractive index sensing, Applied Physics Letters 97 (15) (2010) 151105. [11] A. Di Falco, L. O’Faolain, T.F. Krauss, Dispersion control and slow light in slotted photonic crystal waveguides, Applied Physics Letters 92 (8) (2008) 082501. [12] J.M. Brosi, C. Koos, L.C. Andreani, et al., High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide, Optics Express 16 (6) (2008) 4177–4199. [13] J. Wu, C. Peng, Y.P. Li, et al., Slow light in tapered slot photonic crystal waveguide, Chinese Science Bulletin 54 (20) (2009) 3074–3078. [14] H. Aghababaeian, M.H. Vadjed-Samiei, N. Granpayeh, Temperature stabilization of group index in silicon photonic crystal waveguides, Journal of the Optical Society of Korea 15 (4) (2011) 398–402. [15] C. Caer, X.L. Roux, V.K. Do, et al., Dispersion engineering of wide slot photonic crystal waveguides by Bragg-like corrugation of the slot, IEEE Photonics Technology Letters 23 (18) (2011) 1298–1300. [16] W.C. Lai, S. Chakravarty, X.L. Wang, et al., On-chip methane sensing by near-IR absorption signatures in a photonic crystal slot waveguide, Optics Letters 36 (6) (2011) 984–986. [17] J. Li, T.P. White, L.O. Faolain, et al., Systematic design of flat band slow light in photonic crystal waveguides, Optical Express 16 (9) (2008) 6227–6232. [18] X.T. Lou, G. Somesfalean, Z.G. Zhang, Gas detection by correlation spectroscopy employing a multimode diode laser, Applied Optics 47 (13) (2008) 2392–2398. [19] K.L. Yu, C.Q. Wu, Z. Wang, Optical methane sensor based on a fiber loop at 1665 nm, IEEE Sensors Journal 10 (3) (2010) 728–731. [20] H. Ding, J.Q. Liang, J.H. Cui, et al., A novel fiber Fabry–Perot filter based mixedgas sensing system, Sensors and Actuators B: Chemical 138 (1) (2009) 154–159.
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Biographies
Yong Zhao received his M.A. and Ph.D. degrees, respectively, in precision instrument & automatic measurement with laser and fiber-optic techniques from the Harbin Institute of Technology, China, in 1998 and 2001. He was awarded a first prize scholarship in 2000 by the China Instrument and Control Society and the Sintered Metal Corporation (SMC) scholarship in Japan. He was a postdoctor in the Department of Electronic Engineering of Tsinghua University from 2001 to 2003, and then worked as an associate professor in the Department of Automation, Tsinghua University of China. In 2006, he was a visiting scholar of University of Illinois in Urbana and Champagne, USA. In 2008, he was awarded as the “New Century Excellent Talents in University” by the Ministry of Education of China. In 2009, he was awarded as the “Liaoning Bai-Qian-Wan Talents” by Liaoning Province. In 2011, he was awarded by the Royal Academy of Engineering as an academic researcher of City University London. Now he is working in Northeastern University as a full professor. As a leader of his research group, his current research interests are the development of fiber-optic sensors and device, fiber Bragg grating sensors, novel sensor materials and principles, slow light and sensor technology, optical measurement technologies. He has authored and co-authored more than 130 scientific papers and conference presentations, 7 patents, and 4 books. He is a member in the Editorial Boards of the International Journals of Sensor Letters, Instrumentation Science & Technology, Journal of Sensor Technology, and Advances in Optical Technologies. Qi Wang was born in Liaoning, China, in 1982. He received his Ph.D. degree in 2009 from the School of Physics and Optoelectronic Technology, Dalian University of Technology (DUT), Dalian, China. He is currently working in the College of Information Science and Engineering at Northeast University, China. His research interests are new photonic devices, fiber-optic sensors, optoelectronic measurement technology and system, and their industrial applications. He has authored and co-authored more than 20 scientific papers, patents and conference presentations.