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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5897–5909
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A refractive index sensor design based on grating-assisted coupling between a strip waveguide and a slot waveguide

Qing Liu, Jack Sheng Kee, and Mi Kyoung Park  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 5897-5909 (2013)
http://dx.doi.org/10.1364/OE.21.005897


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Abstract

In this paper, we present a design of a refractive index sensor based on grating-assisted light coupling between a strip waveguide and a slot waveguide. The slot waveguide serves as the sensing waveguide while the strip waveguide is used for light launching and detection. The wavelength at which the light is coupled from the strip waveguide to the slot waveguide serves as a measure of the refractive index of the external medium. The sensitivity of the sensor is ~1.46 × 103 nm/RIU (refractive index unit) and can be almost doubled by isolating the strip waveguide from the external medium. The effects of the slot-waveguide parameters on the sensitivity have also been investigated. In particular, it is found that the sensor can achieve extraordinarily high sensitivity (on the order of 105 nm/RIU) when the group indices of two waveguides are close. The temperature dependence of the sensor is also investigated and a sensor with very low temperature dependence can be achieved with a polymer isolation layer.

© 2013 OSA

1. Introduction

Optical refractive index (RI) sensors have been extensively investigated for a number of applications and play a prominent role in biochemical analysis [1

1. X. D. Fan, I. M. White, S. I. Shopova, H. Y. Zhu, J. D. Suter, and Y. Z. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]

]. Among the existing biochemical RI sensors, those based on integrated optical waveguides are of great interest because of their high sensitivity, small size, and high scale integration. For a resonance-based RI sensor, a wavelength shift of the transmission spectrum of the sensor is usually used to quantify the measured refractive index change. An important figure of merit of a sensor is its detection limit which is decided by the ratio of the smallest detectable wavelength shift and the sensitivity of the sensor [1

1. X. D. Fan, I. M. White, S. I. Shopova, H. Y. Zhu, J. D. Suter, and Y. Z. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]

]. One way to achieve low detection limit is by using a resonator sensor with narrow resonance peaks (i.e., small detectable wavelength shift). For example, a ring resonator sensor in Ref [2

2. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]

]. has a minimal detectable refractive index change of ~10−5 RIU (refractive index unit). The sensor has a narrow resonance peak with a 3-dB bandwidith of 75 pm, and a not exceptionally high sensitivity of 70 nm/RIU. However, in order to monitor such a small refractive index change, an optical spectrum analyzer (OSA) with a resolution as high as ~5pm is required. An alternative way to measure this small wavelength shift is by using the combination of a photodetector and a high-precision tunable laser. Both high-resolution OSA and high-precision tunable laser are very expensive and cumbersome, which are not suitable for situation when a low-cost, portable and highly sensitive sensing is required. Another way of achieving low detection limit is by increasing the sensitivity of the sensor [1

1. X. D. Fan, I. M. White, S. I. Shopova, H. Y. Zhu, J. D. Suter, and Y. Z. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]

]. There is always a tradeoff between the sensitivity and bandwidth [3

3. Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express 19(11), 10029–10040 (2011). [CrossRef] [PubMed]

]. A sensor has a high sensitivity, also has a large bandwidth [3

3. Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express 19(11), 10029–10040 (2011). [CrossRef] [PubMed]

]. Compared with sensors having low sensitivity and small bandwidth, the detection limit of sensors with high sensitivity and large bandwidth is in fact comparable [1

1. X. D. Fan, I. M. White, S. I. Shopova, H. Y. Zhu, J. D. Suter, and Y. Z. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]

,3

3. Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express 19(11), 10029–10040 (2011). [CrossRef] [PubMed]

]. However sensor with high sensitivity is sometime more preferred since it relaxes the requirements for high-precision tunable laser and high-resolution spectrum analyzer used in the sensing system [3

3. Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express 19(11), 10029–10040 (2011). [CrossRef] [PubMed]

].

Recently, RI sensors based on slot waveguide have attracted significant interest due to the slot waveguide’s remarkable property to provide high optical intensity in a subwavelength-size low refractive index region (slot region) sandwiched between two high refractive index strips [4

4. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]

,5

5. C. A. Barrios, “Optical slot-waveguidde based biochemical sensors,” Sensors (Basel Switzerland) 9(6), 4751–4765 (2009). [CrossRef]

]. Using the slot as sensing region, larger light-analyte interaction, and hence higher sensitivity, can be obtained as compared to conventional waveguides. Up to now, slot waveguide sensors based on ring resonator [6

6. C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007). [CrossRef] [PubMed]

8

8. T. Claes, J. G. Molera, K. De Vos, E. Schacht, R. Baets, and P. Bienstman, “Label-free biosensing with a slot-waveguide-based ring resonator in silicon on insulator,” IEEE Photon. J. 1(3), 197–204 (2009). [CrossRef]

], Mach-Zehnder interferometer [9

9. X. Tu, J. F. Song, T.-Y. Liow, M. K. Park, J. Q. Yiying, J. S. Kee, M. B. Yu, and G. Q. Lo, “Thermal independent silicon-nitride slot waveguide biosensor with high sensitivity,” Opt. Express 20(3), 2640–2648 (2012). [CrossRef] [PubMed]

], Bragg grating [10

10. A. S. Jugessur, M. Yagnyukova, J. Dou, and J. S. Aitchison, “Bragg-grating air-slot optical waveguide for label-free sensing,” Proc. SPIE 8231, 82310N (2012). [CrossRef]

] and directional coupler [11

11. V. M. N. Passaro, F. Dell’olio, C. Ciminelli, and M. N. Armenise, “Efficient chemical sensing by coupled slot SOI waveguides,” Sensors (Basel) 9(2), 1012–1032 (2009). [CrossRef] [PubMed]

] have been reported. It has been both theoretically and experimentally verified that the slot-waveguide ring resonator sensor exhibits a sensitivity more than two times larger (~212 nm/RIU) than that of ring resonator sensors based on conventional strip waveguides [5

5. C. A. Barrios, “Optical slot-waveguidde based biochemical sensors,” Sensors (Basel Switzerland) 9(6), 4751–4765 (2009). [CrossRef]

,6

6. C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007). [CrossRef] [PubMed]

].

In this paper, we propose and design a highly sensitive RI sensor based on grating-assisted light coupling between a strip waveguide and a slot waveguide. Grating-assisted directional coupler is a basic guided-wave component that has found numerous applications, such as wavelength-division multiplexing [12

12. J. M. Senior and S. D. Cusworth, “Devices for wavelength multiplexing and demultiplexing,” Proc. Inst. Electr. Eng. 136, 183–202 (1989).

], optical wavelength filtering [13

13. L. L. Buhl, R. C. Alferness, U. Koren, B. I. Miller, M. G. Young, T. L. Koch, C. A. Burrus, and G. Raybon, “Grating assisted vertical coupler/filter for extended tuning range,” Electron. Lett. 29(1), 81–82 (1993). [CrossRef]

] and input and output coupling [14

14. G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Dual grating-assisted directional coupling between fibers and thin semiconductor waveguides,” IEEE Photon. Technol. Lett. 15(10), 1395–1397 (2003). [CrossRef]

]. However, it has rarely been reported for sensing application. Meanwhile, surface grating coupler which shares many characteristics with grating-assisted directional coupler has been extensively studied and demonstrated for sensor application [15

15. K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sens. Actuators B Chem. 91(1-3), 241–251 (2003). [CrossRef]

]. Recently, a compact broadband polarization beam splitter has been proposed utilizing the evanescent coupling between strip and slot waveguides [16

16. M. A. Komatsu, K. Saitoh, and M. Koshiba, “Design of miniaturized silicon wire and slot waveguide polarization splitterbased on a resonant tunneling,” Opt. Express 17(21), 19225–19233 (2009). [CrossRef] [PubMed]

,17

17. D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011). [CrossRef] [PubMed]

]. Quasi-TM polarization is coupled to the cross port while the coupling for quasi-TE polarization is depressed because two waveguides have very different effective indices (i.e., phase mismatch) for quasi-TE polarization [16

16. M. A. Komatsu, K. Saitoh, and M. Koshiba, “Design of miniaturized silicon wire and slot waveguide polarization splitterbased on a resonant tunneling,” Opt. Express 17(21), 19225–19233 (2009). [CrossRef] [PubMed]

,17

17. D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011). [CrossRef] [PubMed]

]. Here we introduce a grating to induce co-directional light coupling between a silicon nitride (Si3N4) strip waveguide and a Si3N4 slot waveguide for the quasi-TE polarization and utilize its resonance wavelength for sensing. We show that the sensitivity of sensor is ~1.46 × 103 nm/RIU and can be almost doubled by isolating the strip waveguide from the external medium. In particular, an extraordinarily high sensitivity on the order of 105 nm/RIU can be achieved in this sensing structure as the group indices of two waveguides become close. Furthermore, by applying a polymer isolation layer on the strip waveguide, the sensor achieves very low temperature dependence. The paper is organized as follows: in Section 2, we describe the working principle of the sensor and the grating analysis equations based on the coupled mode theory. In Section 3, the equation for sensitivity calculation is derived and discussed. The strip waveguide isolation is introduced to enhance the sensitivity and the effects of slot waveguide parameters on the sensitivity are investigated. Then the grating period, grating strength and transmission spectrum are analyzed in Section 4. In Section 5, the extraordinarily high sensitivity region is investigated and discussed. Its dual-resonance spectral feature is also studied. In Section 6, we study the temperature dependency of the sensor and an athermal design is presented with the use of a polymer isolation layer. Discussion and concluding remarks are given in Section 7.

2. Working principle and grating analysis

Figures 1(a) and (b)
Fig. 1 (a) Schematic diagram and (b) cross section of the proposed sensor.
show the schematic diagram and cross section of our proposed RI sensor which consists of a Si3N4 slot waveguide and a Si3N4 strip waveguide placed side by side on a silicon dioxide (SiO2) substrate. A corrugation grating is formed on the surface of the strip waveguide. The separation between the slot waveguide and the strip waveguide is s. The strip waveguide and the slot waveguide have the same total height h and slab thickness t (slab layer is not shown in Fig. 1(a)). The strip waveguide width, slot waveguide width and gap are W, Ws and g, respectively. The refractive indices of Si3N4, SiO2 and external medium are denoted as nSi3N4, nSiO2 and nex, respectively.

Since the slot waveguide and strip waveguide have very different effective indices (i.e., not synchronous in phase) for the quasi-TE polarization [16

16. M. A. Komatsu, K. Saitoh, and M. Koshiba, “Design of miniaturized silicon wire and slot waveguide polarization splitterbased on a resonant tunneling,” Opt. Express 17(21), 19225–19233 (2009). [CrossRef] [PubMed]

,17

17. D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011). [CrossRef] [PubMed]

], no evanescent light coupling occurs between them. However, phase matching between these two waveguides can be achieved with a grating [18

18. D. Marcuse, “Directional coupler made of nonidentical asymmetric slabs. Part II: Garting-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987). [CrossRef]

]. When a grating period Λ is appropriately chosen, the light will be transferred from one guide to the other and the strongest coupling occurs at a particular wavelength λ0 (resonance wavelength) where the phase-matching condition [18

18. D. Marcuse, “Directional coupler made of nonidentical asymmetric slabs. Part II: Garting-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987). [CrossRef]

]
λ0=(NeffstripNeffslot)Λ=ΔNeffΛ,
(1)
is satisfied. NeffstripandNeffslotare the effective indices of the strip waveguide and the slot waveguide, respectively. According to Eq. (1), the grating coupler is wavelength-selective. When a broad-band light is launched into the strip waveguide, the light at the resonance wavelength λ0 is coupled to the slot waveguide and thereby produces a band-rejection spectrum in the launching strip waveguide while a band-pass spectrum in the neighboring slot waveguide. The slot waveguide serves as the sensing waveguide while the strip waveguide is used for optical light launching and detection. As the refractive index of the external medium nex changes, the effective indices of the slot waveguide and strip waveguide change accordingly, resulting in a change of ΔNeff and a resonance wavelength shift in the output spectrum. Therefore, by monitoring this resonance wavelength shift, the refractive index change can be measured. The band-rejection spectrum at the output of the strip waveguide can be obtained with [19

19. H. Kogelnik, Theory of optical waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer, 1990).

]
T(λ)=1κ2κ2+δ24sin2κ2+δ24L,
(2)
where
δ=2πλΔNeff2πΛ.
(3)
L is the grating length and κ is the coupling coefficient used to characterize the grating strength and is obtained with the coupled mode theory (CMT) [19

19. H. Kogelnik, Theory of optical waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer, 1990).

],
κ=2(nSi3N42nex2)λcμ0Aestripeslot*dA,
(4)
where c and μ0 are the speed of light in free space and the vacuum permeability, nSi3N42nex2is the refractive index perturbation, and A is the grating perturbation area. The overlap integral in Eq. (4) is calculated over the cross section of an equivalent unperturbed waveguide structure containing a grating region of depth Δhh is the etch depth of the grating). The equivalent unperturbed composite waveguide structure is similarly shown in Fig. 1(b), where the height of the strip waveguide equals to the average between perturbed and unperturbed waveguide height, i.e., hh/2 [18

18. D. Marcuse, “Directional coupler made of nonidentical asymmetric slabs. Part II: Garting-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987). [CrossRef]

,20

20. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21(12), 3399–3405 (2003). [CrossRef]

]. estripand eslotare the normalized fields of the equivalent unperturbed waveguide. Noted from Eq. (2), when κL = π/2 and δ = 0, 100% coupling occurs at the resonance wavelength λ0.

3. Sensitivity investigation

The waveguide structure shown in Fig. 1(b) supports both quasi-TE and quasi-TM modes, and only the quasi-TE polarization is considered in the following analysis. Both waveguides are single-mode waveguides. Sstrip and Sslot are numerically obtained by varying the external medium refractive index nex in a small range and finding the relevant change of the effective index Neff. The group indices are found similarly by varying the wavelength. The waveguide parameters used in the following calculation are nSi3N4 = 2.0, nex = 1.333 (water), nSiO2 = 1.444, h = 400 nm, g = 200 nm, s = 1 μm, W = 1 μm, Ws = 450 nm, and t = 0 nm. Wavelength is fixed at 1550 nm. The refractive indices nSi3N4, nSiO2, and the total waveguide thickness h are fixed throughout the paper. We analyze the modes of the composite structure shown in Fig. 1(b) with a full-vectorial finite difference mode solver (Lumerical Mode Solutions). The electric field (Ex) distributions for the stripe and slot waveguides are shown in Figs. 2(a)
Fig. 2 Electric field (Ex) distributions for the (a) strip waveguide and (b) slot waveguide in a sensor with g = 200nm, Ws = 450nm, W = 1μm, s = 1μm, and t = 0nm.
and 2(b), respectively, which correspond to the first and second quasi-TE modes of the composite structure. The sensitivity calculation results are shown in Table 1

Table 1. Calculation of the sensitivity for the sensor shown in Fig. 1(b).

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and the sensitivity is as large as −1461.0 nm/RIU. The negative sign indicates that the resonance wavelength shifts to shorter wavelength as the external refractive index increases. This sensitivity value is ~seven times larger than that of a slot-waveguide ring resonator sensor [5

5. C. A. Barrios, “Optical slot-waveguidde based biochemical sensors,” Sensors (Basel Switzerland) 9(6), 4751–4765 (2009). [CrossRef]

,6

6. C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007). [CrossRef] [PubMed]

].

3.1 Silicon dioxide isolation

3.2 Slot waveguide parameters

In this section, we study the effects of slot waveguide parameters, including slot width Ws, slot waveguide gap g, and slab height t, on the sensor sensitivity. Generally, since Sstrip < Sslot, ΔS is a negative value. For simplicity, only the magnitudes of ΔS and sensitivity will be shown in the following figures. As shown in Fig. 4(a)
Fig. 4 Variation of (a) the sensitivity difference ΔS, the group index difference ΔNg and (b) the sensitivity as a function of slot waveguide width Ws. The parameters are g = 200nm, W = 1μm, s = 1μm, and t = 0nm.
, for both sensors without and with SiO2 isolation, ΔS decreases as slot waveguide width Ws increases. The group index difference ΔNg also decreases because the group index of slot waveguide Ngslotincreases while the group index of strip waveguide remains unchanged. ΔNg decreases faster than ΔS as Ws increases, resulting in an increase in sensitivity as shown in Fig. 4(b). Sensitivities as high as 1625 and 4400 nm/RIU can be achieved for sensors without and with SiO2 isolation when Ws is 650 nm. Fabrication tolerance can be evaluated with Fig. 4(b). For Ws = 450 nm, ± 10% variation in the slot width results in ± 15% relative change in sensitivity for the sensor with SiO2 isolation. On the other hand, for the sensor without SiO2 isolation, the same variation in Ws introduces −9.4% and + 6.5% relative changes in sensitivity.

Figure 5(a)
Fig. 5 Variation of (a) the sensitivity difference ΔS, the group index difference ΔNg and (b) the sensitivity as a function of slot waveguide gap g. The parameters are Ws = 450nm, W = 1μm, s = 1μm, and t = 0nm.
shows the variation of ΔS and ΔNg with the slot waveguide gap g. As the gap size increases, the group index of the slot waveguide decreases and ΔNg increases. As shown in Fig. 5(a), ΔS increases first as the gap increases and become insensitive to gap size as the gap is larger than 200 nm. It is seen from Fig. 5(b) that the sensitivity decreases as the gap increases which are the results of decrease of ΔS and increase of ΔNg. The sensitivities obtained at g = 50 nm are 2000 nm/RIU and 5000 nm/RIU respectively for sensors without and with SiO2 isolation. For g = 200 nm, ± 10% variation in the slot gap introduces −2.5%, + 4.3% and −2.9%, + 1.9% relative changes in sensitivity for sensors with and without SiO2 isolation, respectively.

The effects of the slab height on ΔS and ΔNg are shown in Fig. 6(a)
Fig. 6 Variation of (a) the sensitivity difference ΔS, the group index difference ΔNg and (b) the sensitivity as a function of slab height t. The parameters are Ws = 450nm, g = 200nm, s = 1μm, and W = 1μm.
, both of which are found to decrease as the slab height increases. Noted from Fig. 6(b) that the sensitivity depends relatively weakly on the slab height t as compared with slot waveguide width Ws and gap g. With ± 10% variation in the slab height, the relative changes in sensitivity for both sensors with and without SiO2 isolation are within ± 1% range.

4. Grating period, coupling coefficient and transmission spectrum

The grating period is chosen according to the phase-matching condition Eq. (1). Figure 7(a)
Fig. 7 (a) Variation of the grating period as a function of wavelength and (b) dependence of the coupling coefficient and required grating length for achieving 100% coupling on the grating etch depth for three different values of separation distance s. The parameters are g = 200nm, W = 1μm, Ws = 450nm, and t = 0nm.
shows its variation as a function of wavelength for sensors with g = 200 nm, s = 1 μm, W = 1 μm, Ws = 450 nm, and t = 0 nm. As shown in Fig. 7(a), the grating period increases linearly with the wavelength and the sensor without SiO2 isolation requires a longer grating period to achieve the same resonance wavelength as compared with the one with SiO2 isolation.

We evaluate the coupling coefficient with the coupled mode theory, which is efficient and accurate for the analysis of a weak grating [19

19. H. Kogelnik, Theory of optical waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer, 1990).

,20

20. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21(12), 3399–3405 (2003). [CrossRef]

]. The coupling coefficient can be controlled by the grating etch depth on the top of the strip waveguide. Figure 7(b) shows the dependence of the coupling coefficient as a function of the etch depth for sensors with three different values of separation distance s at wavelength 1550nm. The coupling coefficient increases as the etch depth increases. Smaller separation distance results in larger coupling coefficient at the same etch depth. The coupling coefficient for sensor with SiO2 isolation is also calculated (not shown in Fig. 7(b)) and the results are similar. This is because refractive index change from 1.333 to 1.444 only introduces very small index perturbation and field distribution changes due to the large refractive index of silicon nitride. According to Eq. (2), a rejection band with a maximum contrast at the resonance wavelength λ0 is produced in the transmission spectrum when κL = π/2. The corresponding grating lengths required for achieving κL = π/2 are also shown in Fig. 7(b). In practice, an appropriate combination of grating length and etch depth should be chosen so that the coupling strength of the grating is equal to κL ~π/2. If a long grating is used, the required etch depth could become so small that makes the etching process difficult to control. Meanwhile, a too short grating requires a large etch depth, which can introduce serious scattering loss to the strip waveguide. In addition, since the bandwidth of resonance is inversely proportional to the number of grating periods [18

18. D. Marcuse, “Directional coupler made of nonidentical asymmetric slabs. Part II: Garting-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987). [CrossRef]

,19

19. H. Kogelnik, Theory of optical waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer, 1990).

], a short grating results in a large bandwidth which lowers the resolution for wavelength shift measurement. Here, we chosen a grating length of L = 2000μm, so that the coupling coefficient required for achieving a maximum contrast for s = 1μm is given by κ = π/2L = 7.85 × 102 m−1, which, according to Fig. 7(b), requires an etch depth of ~21nm (~5% of the thickness of the total waveguide height). This small etch depth is achievable by the etching process and does not introduce serious scattering loss to the strip waveguide. In addition, the variation of the etch depth has strong influence on the coupling efficiency. In this example, a variation of ± 20% in the etch depth changes the coupling strength of the grating by ~ ± 10% (i.e., κL = 0.4π and 0.6π). This change decreases the coupling efficiency to 90% according to Eq. (2). It should be noted that, due to the large refractive index difference between silicon nitride and water/SiO2, as the etch depth becomes larger, the grating can no longer be treated as a perturbation and the coupling coefficient obtained from CMT (Eq. (4)) becomes less accurate. However, for smaller grating etch depth, Eq. (4) can still provide accurate results.

A broad-band light is launched into the strip waveguide and a rejection band is produced in the launching strip waveguide. The resonance wavelength shift is used for the measurement of the external medium refractive index change. The transmission spectra at the output of the strip waveguide for sensors without and with SiO2 isolation at different values of external refractive index nex are calculated from Eqs. (2) and (3) and shown in Fig. 8(a)
Fig. 8 (a) Transmissions spectra at the output of the stripe waveguide for sensors without and with SiO2 isolation at different values of external refractive index nex. (b) Variation of the resonance wavelengths as a function of external refractive index nex. The parameters are g = 200nm, W = 1μm, Ws = 450nm, s = 1μm, and t = 0nm.
. The grating periods are 12.8 and 10.9 μm for sensors without and with SiO2 isolation, respectively, both of which produce resonance peak at 1550nm for nex = 1.333. The grating lengths for both sensors are 2000 μm and κLπ/2 (0.498π). For both sensors, the resonance wavelength shifts to shorter wavelength as the external refractive index nex increases which agrees with the negative sign of the sensor sensitivity shown in Tables 1 and 2. As expected, the sensor with SiO2 isolation is more sensitive than the one without SiO2 isolation. The dependences of the resonance wavelengths on the external refractive index are shown in Fig. 8(b). The sensitivities are linearly fitted to be −1.46 × 103 nm/RIU and −2.70 × 103 nm/RIU, which agree well with those calculated from Eq. (5) (Table 1 and Table 2).

5. Extraordinary sensitivity

As mentioned afore, the sensitivity can be extraordinarily high as ΔNg approaches zero (i.e., two waveguides have close group index). Figure 9(a)
Fig. 9 Variation of (a) the group index difference (ΔNg) and (b) the sensitivity as a function of strip waveguide width W. The parameters are Ws = 650nm, g = 200nm, s = 1μm, and t = 0nm.
shows the variation of ΔNg with the strip waveguide width W. A slot waveguide with Ws = 650nm and g = 200nm is assumed in the calculation. Only the sensor with SiO2 isolation is considered here. It is clearly seen that ΔNg changes sign from negative to positive as W increases and equals to zero when W is ~585nm. As shown in Fig. 9(b), the sensitivity increases dramatically and can be extraordinarily high when the group indices of the slot waveguide and strip waveguide become close to each other. For example, as W decreases from 1000 nm to 590 nm, ΔNg decreases from 0.11 to 0.0037 and the sensitivity increases from 4.4 × 103 nm/RIU to 1.2 × 105 nm/RIU. Therefore, a wide range of sensitivity is achievable through tuning of the strip waveguide width W. In practice, in order to achieve sensitivity larger than 105 nm/RIU, the variation in the strip waveguide width should be controlled within ± 10 nm around 585 nm. The fabrication tolerance is significantly relaxed for achieving sensitivity in the range of 104 nm/RIU, which is ± 64 nm around 585 nm and easily manufacturable with existing CMOS technologies. The sensitivity becomes infinitely large when ΔNg = 0, which is due to the presence of a singularity in Eq. (5). This extraordinary sensitivity has also been observed in long-period fiber/waveguide grating devices (light is coupled from the core mode to the cladding mode through the grating) [20

20. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21(12), 3399–3405 (2003). [CrossRef]

,23

23. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002). [CrossRef]

] and surface plasmon resonance sensor [3

3. Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express 19(11), 10029–10040 (2011). [CrossRef] [PubMed]

], where two modes or multiple modes are involved in the coupling [3

3. Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express 19(11), 10029–10040 (2011). [CrossRef] [PubMed]

].

The grating performance of the sensor with extraordinarily high sensitivity can be analyzed similarly. The relationship between grating period and wavelength for a sensor with Ws = 650nm, g = 200nm, W = 585nm and t = 0 nm is shown in Fig. 10(a)
Fig. 10 (a) Variation of the grating period as a function of the wavelength. (b) Transmission spectra at the output of the stripe waveguide for sensors with SiO2 isolation at different values of external refractive index nex. (c) Variations of the dual resonance wavelengths as a function of external refractive index nex. The parameters are Ws = 650nm, g = 200nm, W = 585nm, s = 1μm, and t = 0nm.
. Only the sensor with SiO2 isolation is considered here. In Fig. 10(a), the dependence is no longer linear and there is a turning point along the curve which indicates two resonance wavelengths can be produced with the same grating period. The turning point is located at 1550nm, where ΔNg equals to zero (i.e., dΛ/0 = ΔNg/(ΔNeff)2 = 0). This dual-resonance phenomenon is verified by the spectra at different values of nex shown in Fig. 10(b), where a 2000 μm long grating with a period of 51.57 μm is used. From Fig. 10(b), as nex increases, the two resonance dips shift towards each other. This feature is also observed in long-period fiber gratings and has been demonstrated for high sensitivity sensing [23

23. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002). [CrossRef]

25

25. S. M. Topliss, S. W. James, F. Davis, S. P. J. Higson, and R. P. Tatam, “Optical fibre long period grating based selective vapour sensing of volatile organic compounds,” Sens. Actuators B Chem. 143(2), 629–634 (2010). [CrossRef]

]. The changes of the dual resonance wavelengths with the external refractive index are summarized in Fig. 10(c). The sensitivities of the two resonance dips are fitted linearly to be −4.7 × 104 nm/RIU and 5.1 × 104 nm/RIU, respectively. If the separation between the dual resonance wavelengths is used as a measure for nex change, the sensitivity can be as large as 9.8 × 104 nm/RIU. It is also worth noting that the 3-dB bandwidth of the resonance dips shown in Fig. 10(b) is ~45 nm for nex = 1.335, which is much larger than those shown in Fig. 8(a), indicating a worse resolution for wavelength shift measurement. A shift of one fifteenth of the bandwidth is easily measurable [2

2. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]

], therefore a minimal detectable wavelength shift of 3 nm corresponds to a minimal detectable refractive index change of ~10−5 RIU. The detection limit is comparable to that achieved by a ring resonator sensor. However this highly sensitive sensor allows the use of a spectrometer with a low resolution on the order of nm.

6. Temperature dependence and athermal design

The temperature dependence is important for a sensor since active temperature control is usually needed if the sensor is temperature-sensitive. This need adds cost, size and complexity to the sensor. Therefore, sensors with low temperature dependence are desirable. The temperature dependence of the sensor is calculated as follows:
dλ0dT=λ0ΔNg(ΔNeffnSiO2CSiO2+ΔNeffnexCex+ΔNeffnSi3N4CSi3N4+ΔNeffnisoCiso),
(8)
where CSiO2 = 1.0 × 10−5/°C, Cex = −8.0 × 10−5/°C (for water) [26

26. C. B. Kim and C. B. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol. 15(9), 1683–1686 (2004). [CrossRef]

], CSi3N4 = 4.0 × 10−5/°C [27

27. R. Amatya, C. W. Holzwarth, H. I. Smith, and R. J. Ram, “Efficient thermal tuning for second-order silicon nitride microring resonators,” in Proceedings of IEEE Conference on Photonics in Switching (Institute of Electrical and Electronics Engineers, San Francisco, 2007), pp. 149–150.

], and Ciso are thermal-optic coefficients (TOC) for the SiO2 substrate, external analyte, Si3N4, and cover layer for isolation, respectively. Figure 11
Fig. 11 Temperature dependences of the resonance wavelength at different values of strip waveguide width W. The parameters are Ws = 450nm, g = 200nm, s = 1μm, and t = 0nm.
shows the temperature dependence of the resonance wavelength at different values of strip waveguide width. All the waveguide parameters used are the same as those used in Fig. 8. As shown in Fig. 11, the sensors without and with SiO2 isolation have a positive temperature dependence of ~200 pm/°C and ~310 pm/°C, respectively. Since the sensor has a positive temperature dependence (i.e., resonance wavelength shifts to longer wavelength as temperature increases), a polymer cover with a negative TOC can be used as an isolation layer instead of SiO2 to compensate for the temperature dependence of the sensor [28

28. J.-M. Lee, D.-J. Kim, G.-H. Kim, O.-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16(3), 1645–1652 (2008). [CrossRef] [PubMed]

]. We found that sum in parentheses in Eq. (8) can be close to zero when a polymer with an appropriate negative TOC is used. Therefore the temperature dependence of the sensor can be greatly reduced. As an example, we use a polymer with Ciso = −1.8 × 10−4/°C and niso = 1.49 (this polymer could be WIR30-490 from ChemOptics [28

28. J.-M. Lee, D.-J. Kim, G.-H. Kim, O.-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16(3), 1645–1652 (2008). [CrossRef] [PubMed]

]) to cover the stripe waveguide. As seen from Fig. 11, the magnitude of temperature dependence is greatly reduced to be < 20 pm/°C for a large range of strip waveguide width after applying a polymer isolation layer. In addition, the temperature dependence can be further reduced to zero by choosing a strip waveguide with a width of ~950 nm. With a polymer isolation layer, not only the sensitivity is enhanced, but also the temperature dependence is greatly reduced. In practice, the polymer isolation layer can be fabricated with photolithography and dry etching technology, ultraviolet (UV) lithography or e-beam lithography.

7. Discussion and conclusion

The use of silicon nitride waveguide instead of higher-index silicon allows the definition of a wider slot region while maintaining single-mode operation [5

5. C. A. Barrios, “Optical slot-waveguidde based biochemical sensors,” Sensors (Basel Switzerland) 9(6), 4751–4765 (2009). [CrossRef]

]. A wider slot region facilitates filling the slot volume with liquids for liquid-based sensing applications. Silicon nitride waveguide is usually a few hundred nanometers thick due to its high refractive index. Therefore, a direct light coupling between an optical fiber and a silicon nitride waveguide is difficult. In practical application of the sensor, the light can be coupled from a standard single-mode fiber to a silicon nitride strip waveguide with a vertical grating coupler, which allows higher alignment tolerance. This approach also avoids cleaving of the sample, and enables wafer-scale testing. Recently, a wide-band silicon nitride grating coupler with a peak coupling efficiency of −4.2 dB has been demonstrated [29

29. C. R. Doerr, L. Chen, Y.-K. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett. 22(19), 1461–1463 (2010). [CrossRef]

]. The silicon nitride strip and slot waveguides designed in this paper can be readily fabricated using standard CMOS processes and the propagation losses can be as low as ~0.6 dB/cm and ~0.9 dB/cm, respectively, as demonstrated very recently in Ref [9

9. X. Tu, J. F. Song, T.-Y. Liow, M. K. Park, J. Q. Yiying, J. S. Kee, M. B. Yu, and G. Q. Lo, “Thermal independent silicon-nitride slot waveguide biosensor with high sensitivity,” Opt. Express 20(3), 2640–2648 (2012). [CrossRef] [PubMed]

].

We propose an integrated-optic refractive index sensor based on grating-assisted light coupling between a strip waveguide and a slot waveguide. We analyze in detail the sensitivity of the sensor and discuss the effects of the key slot-waveguide parameters on the performance of the sensor. The grating period, grating strength and the spectrum are analyzed with the coupled mode theory. The extraordinarily high sensitivity and dual-resonance wavelength phenomenon of the sensor are investigated and its performance is also studied. Furthermore, it is found that an isolation layer on the strip waveguide cannot only enhance the sensitivity but also help to achieve a sensor with very low temperature-dependence.

Acknowledgments

This work was supported by the Agency for Science Technology and Research (A*STAR) Joint Council Office (JCO) grant (1234e00018), Singapore.

References and links

1.

X. D. Fan, I. M. White, S. I. Shopova, H. Y. Zhu, J. D. Suter, and Y. Z. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]

2.

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]

3.

Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express 19(11), 10029–10040 (2011). [CrossRef] [PubMed]

4.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]

5.

C. A. Barrios, “Optical slot-waveguidde based biochemical sensors,” Sensors (Basel Switzerland) 9(6), 4751–4765 (2009). [CrossRef]

6.

C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007). [CrossRef] [PubMed]

7.

C. A. Barrios, M. J. Bañuls, V. González-Pedro, K. B. Gylfason, B. Sánchez, A. Griol, A. Maquieira, H. Sohlström, M. Holgado, and R. Casquel, “Label-free optical biosensing with slot-waveguides,” Opt. Lett. 33(7), 708–710 (2008). [CrossRef] [PubMed]

8.

T. Claes, J. G. Molera, K. De Vos, E. Schacht, R. Baets, and P. Bienstman, “Label-free biosensing with a slot-waveguide-based ring resonator in silicon on insulator,” IEEE Photon. J. 1(3), 197–204 (2009). [CrossRef]

9.

X. Tu, J. F. Song, T.-Y. Liow, M. K. Park, J. Q. Yiying, J. S. Kee, M. B. Yu, and G. Q. Lo, “Thermal independent silicon-nitride slot waveguide biosensor with high sensitivity,” Opt. Express 20(3), 2640–2648 (2012). [CrossRef] [PubMed]

10.

A. S. Jugessur, M. Yagnyukova, J. Dou, and J. S. Aitchison, “Bragg-grating air-slot optical waveguide for label-free sensing,” Proc. SPIE 8231, 82310N (2012). [CrossRef]

11.

V. M. N. Passaro, F. Dell’olio, C. Ciminelli, and M. N. Armenise, “Efficient chemical sensing by coupled slot SOI waveguides,” Sensors (Basel) 9(2), 1012–1032 (2009). [CrossRef] [PubMed]

12.

J. M. Senior and S. D. Cusworth, “Devices for wavelength multiplexing and demultiplexing,” Proc. Inst. Electr. Eng. 136, 183–202 (1989).

13.

L. L. Buhl, R. C. Alferness, U. Koren, B. I. Miller, M. G. Young, T. L. Koch, C. A. Burrus, and G. Raybon, “Grating assisted vertical coupler/filter for extended tuning range,” Electron. Lett. 29(1), 81–82 (1993). [CrossRef]

14.

G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Dual grating-assisted directional coupling between fibers and thin semiconductor waveguides,” IEEE Photon. Technol. Lett. 15(10), 1395–1397 (2003). [CrossRef]

15.

K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sens. Actuators B Chem. 91(1-3), 241–251 (2003). [CrossRef]

16.

M. A. Komatsu, K. Saitoh, and M. Koshiba, “Design of miniaturized silicon wire and slot waveguide polarization splitterbased on a resonant tunneling,” Opt. Express 17(21), 19225–19233 (2009). [CrossRef] [PubMed]

17.

D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett. 36(13), 2590–2592 (2011). [CrossRef] [PubMed]

18.

D. Marcuse, “Directional coupler made of nonidentical asymmetric slabs. Part II: Garting-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987). [CrossRef]

19.

H. Kogelnik, Theory of optical waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer, 1990).

20.

Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21(12), 3399–3405 (2003). [CrossRef]

21.

F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007). [CrossRef] [PubMed]

22.

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006). [CrossRef]

23.

X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002). [CrossRef]

24.

X. Shu, X. Zhu, S. Jiang, W. Shi, and D. Huang, “High sensitivity of dual resonant peaks of long-period fibre grating to surrounding refractive index changes,” Electron. Lett. 35(18), 1580–1581 (1999). [CrossRef]

25.

S. M. Topliss, S. W. James, F. Davis, S. P. J. Higson, and R. P. Tatam, “Optical fibre long period grating based selective vapour sensing of volatile organic compounds,” Sens. Actuators B Chem. 143(2), 629–634 (2010). [CrossRef]

26.

C. B. Kim and C. B. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol. 15(9), 1683–1686 (2004). [CrossRef]

27.

R. Amatya, C. W. Holzwarth, H. I. Smith, and R. J. Ram, “Efficient thermal tuning for second-order silicon nitride microring resonators,” in Proceedings of IEEE Conference on Photonics in Switching (Institute of Electrical and Electronics Engineers, San Francisco, 2007), pp. 149–150.

28.

J.-M. Lee, D.-J. Kim, G.-H. Kim, O.-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16(3), 1645–1652 (2008). [CrossRef] [PubMed]

29.

C. R. Doerr, L. Chen, Y.-K. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett. 22(19), 1461–1463 (2010). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(130.6010) Integrated optics : Sensors
(230.7390) Optical devices : Waveguides, planar

ToC Category:
Integrated Optics

History
Original Manuscript: October 18, 2012
Revised Manuscript: November 20, 2012
Manuscript Accepted: November 20, 2012
Published: March 4, 2013

Citation
Qing Liu, Jack Sheng Kee, and Mi Kyoung Park, "A refractive index sensor design based on grating-assisted coupling between a strip waveguide and a slot waveguide," Opt. Express 21, 5897-5909 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5897


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References

  1. X. D. Fan, I. M. White, S. I. Shopova, H. Y. Zhu, J. D. Suter, and Y. Z. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta620(1-2), 8–26 (2008). [CrossRef] [PubMed]
  2. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express15(12), 7610–7615 (2007). [CrossRef] [PubMed]
  3. Z. Yu and S. Fan, “Extraordinarily high spectral sensitivity in refractive index sensors using multiple optical modes,” Opt. Express19(11), 10029–10040 (2011). [CrossRef] [PubMed]
  4. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett.29(11), 1209–1211 (2004). [CrossRef] [PubMed]
  5. C. A. Barrios, “Optical slot-waveguidde based biochemical sensors,” Sensors (Basel Switzerland)9(6), 4751–4765 (2009). [CrossRef]
  6. C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett.32(21), 3080–3082 (2007). [CrossRef] [PubMed]
  7. C. A. Barrios, M. J. Bañuls, V. González-Pedro, K. B. Gylfason, B. Sánchez, A. Griol, A. Maquieira, H. Sohlström, M. Holgado, and R. Casquel, “Label-free optical biosensing with slot-waveguides,” Opt. Lett.33(7), 708–710 (2008). [CrossRef] [PubMed]
  8. T. Claes, J. G. Molera, K. De Vos, E. Schacht, R. Baets, and P. Bienstman, “Label-free biosensing with a slot-waveguide-based ring resonator in silicon on insulator,” IEEE Photon. J.1(3), 197–204 (2009). [CrossRef]
  9. X. Tu, J. F. Song, T.-Y. Liow, M. K. Park, J. Q. Yiying, J. S. Kee, M. B. Yu, and G. Q. Lo, “Thermal independent silicon-nitride slot waveguide biosensor with high sensitivity,” Opt. Express20(3), 2640–2648 (2012). [CrossRef] [PubMed]
  10. A. S. Jugessur, M. Yagnyukova, J. Dou, and J. S. Aitchison, “Bragg-grating air-slot optical waveguide for label-free sensing,” Proc. SPIE8231, 82310N (2012). [CrossRef]
  11. V. M. N. Passaro, F. Dell’olio, C. Ciminelli, and M. N. Armenise, “Efficient chemical sensing by coupled slot SOI waveguides,” Sensors (Basel)9(2), 1012–1032 (2009). [CrossRef] [PubMed]
  12. J. M. Senior and S. D. Cusworth, “Devices for wavelength multiplexing and demultiplexing,” Proc. Inst. Electr. Eng.136, 183–202 (1989).
  13. L. L. Buhl, R. C. Alferness, U. Koren, B. I. Miller, M. G. Young, T. L. Koch, C. A. Burrus, and G. Raybon, “Grating assisted vertical coupler/filter for extended tuning range,” Electron. Lett.29(1), 81–82 (1993). [CrossRef]
  14. G. Z. Masanovic, V. M. N. Passaro, and G. T. Reed, “Dual grating-assisted directional coupling between fibers and thin semiconductor waveguides,” IEEE Photon. Technol. Lett.15(10), 1395–1397 (2003). [CrossRef]
  15. K. Cottier, M. Wiki, G. Voirin, H. Gao, and R. E. Kunz, “Label-free highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips,” Sens. Actuators B Chem.91(1-3), 241–251 (2003). [CrossRef]
  16. M. A. Komatsu, K. Saitoh, and M. Koshiba, “Design of miniaturized silicon wire and slot waveguide polarization splitterbased on a resonant tunneling,” Opt. Express17(21), 19225–19233 (2009). [CrossRef] [PubMed]
  17. D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett.36(13), 2590–2592 (2011). [CrossRef] [PubMed]
  18. D. Marcuse, “Directional coupler made of nonidentical asymmetric slabs. Part II: Garting-assisted couplers,” J. Lightwave Technol.5(2), 268–273 (1987). [CrossRef]
  19. H. Kogelnik, “Theory of optical waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer, 1990).
  20. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol.21(12), 3399–3405 (2003). [CrossRef]
  21. F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express15(8), 4977–4993 (2007). [CrossRef] [PubMed]
  22. A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron.12(1), 148–155 (2006). [CrossRef]
  23. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol.20(2), 255–266 (2002). [CrossRef]
  24. X. Shu, X. Zhu, S. Jiang, W. Shi, and D. Huang, “High sensitivity of dual resonant peaks of long-period fibre grating to surrounding refractive index changes,” Electron. Lett.35(18), 1580–1581 (1999). [CrossRef]
  25. S. M. Topliss, S. W. James, F. Davis, S. P. J. Higson, and R. P. Tatam, “Optical fibre long period grating based selective vapour sensing of volatile organic compounds,” Sens. Actuators B Chem.143(2), 629–634 (2010). [CrossRef]
  26. C. B. Kim and C. B. Su, “Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fibre optic Fresnel ratio meter,” Meas. Sci. Technol.15(9), 1683–1686 (2004). [CrossRef]
  27. R. Amatya, C. W. Holzwarth, H. I. Smith, and R. J. Ram, “Efficient thermal tuning for second-order silicon nitride microring resonators,” in Proceedings of IEEE Conference on Photonics in Switching (Institute of Electrical and Electronics Engineers, San Francisco, 2007), pp. 149–150.
  28. J.-M. Lee, D.-J. Kim, G.-H. Kim, O.-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express16(3), 1645–1652 (2008). [CrossRef] [PubMed]
  29. C. R. Doerr, L. Chen, Y.-K. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010). [CrossRef]

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