On-chip temperature compensation in an integrated slot-waveguide ring
resonator refractive index sensor array

doi:10.1364/OE.18.003226

On-chip temperature compensation in an integrated slot-waveguide ring resonator refractive index sensor array

Kristinn B. Gylfason, Carl F. Carlborg, Andrzej Kazmierczak, Fabian Dortu, Hans Sohlström, Laurent Vivien, Carlos A. Barrios, Wouter van der Wijngaart, and Göran Stemme »View Author Affiliations

Optics Express, Vol. 18, Issue 4, pp. 3226-3237 (2010)
http://dx.doi.org/10.1364/OE.18.003226

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Abstract

We present an experimental study of an integrated slot-waveguide refractive index sensor array fabricated in silicon nitride on silica. We study the temperature dependence of the slot-waveguide ring resonator sensors and find that they show a low temperature dependence of −16.6 pm/K, while at the same time a large refractive index sensitivity of 240 nm per refractive index unit. Furthermore, by using on-chip temperature referencing, a differential temperature sensitivity of only 0.3 pm/K is obtained, without individual sensor calibration. This low value indicates good sensor-to-sensor repeatability, thus enabling use in highly parallel chemical assays. We demonstrate refractive index measurements during temperature drift and show a detection limit of 8.8 × 10⁻⁶ refractive index units in a 7 K temperature operating window, without external temperature control. Finally, we suggest the possibility of athermal slot-waveguide sensor design.

1. Introduction

Refractive index sensing is widely used for real-time monitoring of chemical processes and, when used in combination with separation techniques such as liquid chromatography or capillary electrophoresis, universal solute detection systems can by created [1

D. Markov, D. Begari, and D. J. Bornhop, “Breaking the 10^-7 Barrier for RI Measurements in Nanoliter Volumes,” Anal. Chem. 74, 5438–5441 (2002). URL http://dx.doi.org/10.1021/ac020403c. [CrossRef] [PubMed]

]. Refractive index sensing is also used for label-free monitoring of bio-molecular interactions on surfaces, for example in the commercially successful surface plasmon resonance (SPR) based sensors [2

R. Karlsson, A. Michaelsson, and L. Mattsson, “Kinetic analysis of monoclonal antibody-antigen interactions with a new biosensor based analytical system,” J. Immunol. Methods 145, 229–240 (1991). URL http://dx.doi.org/10.1016/0022-1759(91)90331-9. [CrossRef] [PubMed]

]. Most commercial separation tools and SPR sensors are built from bulky discrete components and placed in centralized laboratories, but integrated planar lightwave circuit technology holds great promise for the development of mobile low cost sensor arrays for highly parallel real time analysis. For use in such integrated systems, planar waveguide ring resonator sensors are interesting for their small footprint, high quality factors, and ease of integration with other on-chip optical and fluidic functions.

To be of analytical relevance [3

Z. Wang and D. J. Bornhop, “Dual-Capillary Backscatter Interferometry for High-Sensitivity Nanoliter-Volume Refractive Index Detection with Density Gradient Compensation,” Anal. Chem. 77, 7872–7877 (2005). URL http://dx.doi.org/10.1021/ac050752h. [CrossRef] [PubMed]

] and present a viable alternative to current technology [4

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta 620, 8–26 (2008). URL http://dx.doi.org/10.1016/j.aca.2008.05.022. [CrossRef] [PubMed]

], novel sensors need to achieve a detection limit of the order of 10^-6 refractive index units (RIU) or less. When considering that commonly used waveguide materials, and the liquid samples of interest, have thermo-optic coefficients of magnitudes 10^-5-10^-4 RIU/K, it is clear that minimizing temperature interference is a fundamental aspect of refractive index sensor design. Any uncompensated sensor would require external temperature stabilization to the order of 10–100 mK to reach the required detection limit.

Three approaches have been used for thermal noise reduction: active temperature control, athermal waveguide design, and temperature drift compensation by on chip referencing [4

The first approach, active control of system temperature, is commonly implemented with external Peltier heat pumps. Given a suitable thermal and electronic design, temperature stability in the 10 mK range is feasible. However, the required components add to the cost, size, and complexity of the the sensor system, and limit the cost benefits gained by employing silicon micro-fabrication. We note, however, that for measuring chemical reaction rates, absolute temperature control is required, since rate constants are temperature dependent.

In the second approach, athermal waveguide sensors are designed by taking advantage of the different polarity of the thermo-optic coefficients of liquid samples and solid waveguide materials. For example, water has a negative thermo-optic coefficient of κ H₂O = -10^-4 RIU/K [5

A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised Formulation for the Refractive Index of Water and Steam as a Function of Wavelength, Temperature and Density,” Journal of Physical and Chemical Reference Data 27, 761–774 (1998). URL http://dx.doi.org/10.1063/1.556029. [CrossRef]

], while silicon nitride and oxide have a positive value of κ Si₃N₄ = κSiO₂ = 10^-5 RIU/K [6

H. Takashashi, “Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,” Appl. Opt. 34, 667+ (1995). URL http://www.opticsinfobase.org/abstract.cfm?id=45986. [CrossRef] [PubMed]

, 7

L. Eldada, “Advances in telecom and datacom optical components,” Opt. Eng. 40, 1165–1178 (2001). URL http://dx.doi.org/10.1117/1.1372703. [CrossRef]

]. By balancing the fraction of light propagating in each material, the temperature dependence of the waveguide effective index can be eliminated. Since athermal waveguides are intrinsically temperature compensated, the compensation is not frequency limited by the thermal time constants of the sensor chip. The main drawbacks are that the design is often very sensitive to chip-to-chip fabrication variation and is solvent dependent, since thermo-optic coefficients of liquid solvents vary significantly.

Athermal planar waveguide wavelength filters with solid polymer top cladding have been studied for almost two decades [8

Y. Kokubun, N. Funato, and M. Takizawa, “Athermal waveguides for temperature-independent lightwave devices,” IEEE Photon. Technol. Lett. 5, 1297–1300 (1993). URL http://ieeexplore.ieee.org/xpls/abs all.jsp?arnumber=250049. [CrossRef]

], but we are not aware of any report of integrated refractive index sensors using athermal planar waveguides. Recently, however, Suter et al. [9

J. D. Suter, I. M. White, H. Zhu, and X. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007). URL http://dx.doi.org/10.1364/AO.46.000389. [CrossRef] [PubMed]

] reported on non-integrated athermal ring resonator refractive index sensors using liquid filled silica capillaries with air cladding. In this case, the capillary wall is the waveguide core and light is coupled in via a manually positioned optical fiber taper.

Fig. 1. A schematic cross section of the coupling region of a slot-waveguide ring resonator refractive index sensor. To the left is the straight bus waveguide and to the right the bent ring waveguide. The opposite polarity of the thermo-optic coefficients κ of the solid waveguide materials and the liquid sample, utilized in athermal sensor design, is indicated on the ring waveguide end face.

A possible explanation for the absence of reports on athermal planar sensors is that the low refractive index of liquid samples, compared to that of the solid waveguide materials, makes conventional strip sensor waveguides more asymmetric than polymer clad filter waveguides. Thus, the technique of thinning the waveguide core to push power up into the polymer top cladding, as employed in filter design, when employed to sensors, mostly pushes power down into the solid substrate. Furthermore, since the thin-core waveguides operate close to cut-off, the athermal operation point is sensitive to fabrication variances.

This limitation can be overcome by use of the recently developed slot-waveguides [10

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Optics Letters 29, 1209–1211 (2004). URL http://dx.doi.org/10.1364/OL.29.001209. [CrossRef] [PubMed]

], in which an adjustable fraction of the optical mode can be confined in the liquid top cladding by adjusting the slot width. This new design parameter enables the design of athermal single mode waveguides without thinning the core and has already been applied to wavelength filter design in [11

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, 1645–1652 (2008). URL http://dx.doi.org/10.1364/OE.16.001645. [CrossRef] [PubMed]

]. Figure 1 shows a schematic cross section of the coupling region of a slot-waveguide ring resonator refractive index sensor. To the left is the straight bus waveguide and to the right the bent ring sensor waveguide.

In the third approach, temperature drift compensation by on-chip references, multiple identical sensors in good thermal contact with each other are integrated on the same substrate. If the fluidic system allows injecting the sample of interest to one sensor, and a reference sample to another, differential measurements can be made. Such designs are solvent independent and tolerant to chip-to-chip fabrication variation. However, for highly parallel operation, the fabrication method must yield repeatable sensor-to-sensor thermal sensitivity within each chip, so that time consuming thermal calibration of each sensor can be avoided. Furthermore, the temperature compensation is limited in frequency by the thermal time constants of the sensor chip.

A sensor system might employ all or any mix of the three temperature interference reduction methods discussed. For example, active temperature control can compensate for a residual temperature sensitivity of an athermal waveguide design. However, to deliver on the promise of compact, low cost, integrated optics for refractive index sensing, active temperature control is best avoided, and on on-chip temperature compensation techniques pursued instead.

Here, we present an integrated slot-waveguide refractive index sensor array, designed for high refractive index sensitivity and temperature compensation by on-chip referencing. Our experiments include, to our knowledge, the first reported thermal sensitivity study of slot-waveguide refractive index sensors and the first reported implementation of a slot-waveguide sensor array thermally compensated by on-chip referencing. We demonstrate the ability of the sensor system to operate during temperature drift and verify that our fabrication process yields sufficiently repeatable temperature sensitivity for on-chip compensation without individual sensor calibration. Furthermore, we discuss the possibility of trading refractive index sensitivity in exchange for fully athermal slot-waveguide sensors.

2. Sensor chip design

Figure 2 is a top view of the layout of the optical circuit, occupying a chip area of 3 × 7 mm². Light enters at a 10° angle to the surface normal, via the surface grating coupler (c). We use a fully etched grating designed for a high coupling efficiency, a large coupling angle tolerance, and simple fabrication [12

G. Maire, L. Vivien, G. Sattler, A. Kaźmierczak, B. Sanchez, K. B. Gylfason, A. Griol, D. Marris-Morini, E. Cas-san, D. Giannone, H. Sohlström, and D. Hill, “High efficiency silicon nitride surface grating couplers,” Opt. Express 16, 328–333 (2008). URL http://dx.doi.org/10.1364/OE.16.000328. [CrossRef] [PubMed]

]. The propagating light is then split, by a multi-mode interference splitter (b), into eight channels: REF1, which has no sensor and is used for alignment and laser amplitude compensation, REF2, which is coupled to a reference slot-waveguide ring resonator covered with silicon dioxide top cladding, and channels M1 to M6, containing the sensing sites, where openings are etched in the silicon dioxide top cladding to allow liquid sample access down to the slot-waveguide ring resonators (a).

The optical devices are etched into a silicon nitride film of thickness t _c = 300 nm (refer to Fig. 1). The distribution network consists of 900 nm wide channel waveguides, and channel-slot mode converters [13

J. Blasco and C. A. Barrios, “Compact slot-waveguide/channel-waveguide mode-converter,” in Conference on Lasers and Electro-Optics Europe 2005 , p. 607 (2005). URL http://dx.doi.org/10.1109/CLEOE.2005.1568383. [CrossRef]

] are used for conversion between the two waveguide types before and after the ring resonator coupling regions, where the bus slot-waveguides have rail widths of w _r = 400 nm and a slot width of w _s = 200 nm. The coupling gap is w _g = 350 nm. In the sensing ring we employ asymmetric slot-waveguides [14

P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202 (2006). URL http://www.opticsinfobase.org/abstract.cfm?id=114595. [CrossRef] [PubMed]

] with the inner rail widened to w′_r = 550 nm [15

C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Optics Letters 32, 3080–3082 (2007). URL http://www.opticsinfobase.org/abstract.cfm?id=144251. [CrossRef] [PubMed]

], for high optical confinement in the slot and low bending loss.

The pitch between the channels is 750 μm and each waveguide output is focused onto a single pixel of an InGaAs photo-diode array at the output edge [16

A. Kaźmierczak, F. Dortu, O. Schrevens, D. Giannone, L. Vivien, D. M. Morini, D. Bouville, E. Cas-san, K. B. Gylfason, H. Sohlströom, B. Sanchez, A. Griol, and D. Hill, “Light coupling and distribution for Si₃N₄/SiO₂ integrated multichannel single-mode sensing system,” Opt. Eng. 48, 14, 401+ (2009). URL http://dx.doi.org/10.1117/1.3067875.

]. The orientation of the input grating and splitter, perpendicular to the output edge, minimizes stray light illumination of the detector array.

For sample delivery, a microfluidic channel network in poly(dimethylsiloxane) (PDMS), with a separate fluid channel to each sensor, is bonded on top of the silicon chip [17

C. F. Carlborg, K. B. Gylfason, A. Kaźmierczak, F. Dortu, M. J. Bañuls, A. M. Catala, G. M. Kresbach, H. Sohlström, T. Moh, L. Vivien, J. Popplewell, G. Ronan, C. A. Barrios, G. Stemme, and W. van der Wijngaart, “A packaged optical slot-waveguide ring resonator sensor array for multiplex label-free assays in labs-on-chips,” Lab on a Chip 10, 281–290 (2010). URL http://dx.doi.org/10.1039/b914183a. [CrossRef] [PubMed]

]. The total silicon chip area is 15 × 40 mm², most of which is used as support for the fluidic channels and connections in the PDMS layer. The overall size of the optical circuit, i.e. the pitch between the sensors and the distance of the sensors from the output edge, is also determined by the need for sufficient spacing between fluidic channels, to avoid cross channel leakage, and a minimum channel width, to allow manual alignment of the microfluidics to the optics under a microscope.

3. Sensor chip fabrication

The integrated optical components of the sensor chip are fabricated by standard silicon micro-fabrication methods. First, a bottom cladding layer of thickness t _b = 3.26 μm was grown by wet thermal oxidation of a silicon substrate at 1100°C. A 300 nm thick silicon nitride film was then deposited by low pressure chemical vapor deposition (LPCVD) at 800°C from NH₃ and SiH₂Cl₂ precursors. Then, the optical device layer was patterned in the silicon nitride film, by electron beam lithography and dry etching. We employed a negative electron beam resist (ma N 2403, Micro Resist Technology GmbH, Germany), exposed with a Raith-150 electron beam writer using a 10 μm aperture at an acceleration voltage of 25 kV, as a mask for etching in a CHF₃/CF₄/O₂ plasma.

Fig. 2. A top view of the layout of the optical chip: Light is injected at the surface grating coupler (c) and split, by the multi-mode interference splitter (b), to the six sensing channels M1–M6 and the two reference channels REF1 and REF2. Inset are an optical micro-graph of the splitter (b); and electron micro-graphs of the grating coupler (c), and a slot-waveguide ring resonator (a), with an enlargement of the coupling region.

A negative electron beam resist is particularly well suited for electron beam patterning of narrow optical waveguides, since only a small fraction of the surface needs to be exposed. Previously, we employed a positive resist (PMMA) and an additional lift-off step to the same effect [15

], but we found the simplified process more repeatable, even though the patterning resolution achievable with the negative resist is only just sufficient for our purpose. Since the smallest feature of our design is the 200 nm wide waveguide slot, standard deep UV lithography could be used for mass-production [18

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luys-saert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography,” IEEE Photon. Technol. Lett. 16, 1328–1330 (2004). URL http://dx.doi.org/10.1109/LPT.2004.826025. [CrossRef]

A dense top cladding layer of a suitable refractive index is needed to protect the optical distribution network and cover the input grating coupler. Our choice of LPCVD tetraethyl orthosilicate (TEOS) deposited at 720°C is dictated by the need for void free filling of the through-etched input grating groves (with an aspect ratio of 3/5). A top cladding thickness of 530 nm, in combination with the 3.26 μm bottom cladding, was previously shown to give optimum input coupling efficiency [12

]. Openings in the top cladding down to the sensors were patterned by optical lithography and wet etching in buffered hydrofluoric acid. The thermally oxidized bottom cladding provides a suitable etch stop, since the etch rate selectivity to non densified TEOS is about 1:8.

The process is finalized by dicing the substrate. To avoid particle contamination of the sensors, the chip surface was covered with a protective layer of photoresist during dicing. From a mass production perspective, it is important that no polishing of the output edge is needed after dicing. This is achieved by limiting the divergence of the output beams by inverted waveguide tapers at the output edge [19

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, “Efficient coupling of a semiconductor laser to an optical fiber by means of a tapered waveguide on silicon,” Appl. Phys. Lett. 55, 2389–2391 (1989). URL http://dx.doi.org/10.1063/1.102290. [CrossRef]

] and by a proper choice of lens and detector array in the detector optics [16

]. Since handling of individual sensor chips is avoided, they can be mass produced at low cost using standard silicon micro-fabrication.

4. Experiments

Light from a mechanically tunable, external cavity, diode laser (TSL-210V, Santec, Japan) was coupled into the chip from free space optics above the surface. The minimum wavelength step of the laser is 1 pm and the tuning range is 1260 – 1360 nm. TE polarized light was selected by an in-line fiber polarization controller between the laser and the free space optics. After passing through the chip, light is collected from the diced chip edge by a lens focusing the eight outputs onto a linear photo-diode array (XLIN-1.9-016-TE0, Xenics, Belgium) — each output onto a single pixel. The silicon sensor chip is clamped to an aluminum platform with a Peltier heat pump attached to its back side. The temperature of the system is read out by a Pt1000 platinum resistance thermometer attached to the aluminum platform, and temperature stability to within 0.1 K is achieved by a feed-back amplifier driving the Peltier heat pump. A detailed description of the optical setup has been published in [16

Liquid flow was controlled by off-chip syringe pumps, one for each flow channel. During operation, the pumps supply a continuous flow of deionized (DI) water to the chip, and samples are injected into the flow using in-line injection valves. A detailed description of the fluidic setup has been published in [17

To determine the refractive index limit of detection of the sensor array, three experiments were performed:

In the first experiment, we determined the temperature sensitivity of the slot waveguide sensors operating in still standing DI water. Using the Peltier heat pump, we raised the temperature of the chip from 23.0°C to 33.0°C, in steps of 2.0 K, and then straight back to 23.0°C, while monitoring the sensor resonance wavelength. We tracked the response of both sensor M1 and M2, to study the temperature compensation ability of the system, when referencing one sensor against the other. The laser continuously swept a wavelength range of 2.1 nm with a 20 pm wavelength step.

In the second experiment, we determined the refractive index sensitivity, by injecting a dilution series of ethanol in DI water into channel M1. The shift of each dilution from the refractive index of pure water is obtained from [20

D. R. Lide, ed., CRC handbook of chemistry and physics . (CRC ; Taylor & Francis [distributor], 2008). URL http://www.worldcat.org/oclc/219996604.

] and listed in Table 1. During injections, thermal drift was monitored by a DI water filled reference channel (M4). The laser swept a wavelength range of 4 nm with a 10 pm step.

Table 1. Mass percentage (mass of ethanol/total mass of solution) of the injected ethanol calibration solutions and the corresponding shift from pure water refractive index.

Mass percentage	Refractive index shift
5.97	0.0037
3.98	0.0024
1.99	0.0012
0.994	0.0006
0.500	0.0003

In the third experiment, we raised the temperature of the chip from 22.5°C to 31.5°C in steps of 3.0 K, while repeatedly injecting 2% ethanol plugs, to demonstrate the ability of the system to compensate for temperature variations during measurement.

The simple mode structure of the single mode ring resonators allows us to use the Levenberg-Marquardt algorithm1 to fit a Lorentzian model to the data points around resonance, and thereby reduce the effective wavelength error of the measurement well below the wavelength step of the laser [21

H. Sohlström and M. Öberg, “Refractive index measurement using integrated ring resonators,” in The 8th European Conference on Integrated Optics , pp. 322–325 (1997).

]. Furthermore, we can reduce the interfering influence of reflections from waveguide discontinuities on the estimated resonance wavelength, by cascading a Fabry-Perot cavity model [22

C. A. Barrios, B. Sánchez, K. B. Gylfason, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Demonstration of slot-waveguide structures on silicon nitride / silicon oxide platform,” Opt. Express 15, 6846–6856 (2007). URL http://www.opticsinfobase.org/abstract.cfm?id=134979. [CrossRef] [PubMed]

] to the Lorentzian resonator model. The presence of such parasitic reflections is well documented in previous experimental work, and particularly visible in the spectra published in [23

J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16, 4296–4301 (2008). URL http://dx.doi.org/10.1364/OE.16.004296. [CrossRef] [PubMed]

], where end-fire light coupling at the chip edge is employed. The problem is less apparent in [24

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 Photonics Journal 1, 197–204 (2009). URL http://dx.doi.org/10.1109/JPHOT.2009.2031596. [CrossRef]

], where surface grating couplers are employed at both input and output.

To isolate the contribution of the parasitic reflections, we first collected transmission spectra of dry ring resonators, since no light is coupled to the rings when operating in air. The spectra indicated that two parasitic Fabry-Perot cavities contribute. The extracted model parameters for the shorter cavity fit well to the length of the output waveguide from the edge of the opening in the top cladding, at the sensing ring, to the output edge of the chip. We suspect that the longer cavity corresponds to the section from the input grating coupler to the edge of the sensor opening, however, due to the complicated lightwave circuit in this section this hypothesis is difficult to confirm. Figure 3 shows example spectra, the fitted combined models, and the extracted ring resonance wavelengths of sensor M1 operating in DI water at two different chip temperatures.

5. Results

Figure 4(a) and (b) show ring resonance wavelengths as functions of time during temperature stepping, for channels M1 and M2, respectively. In Fig. 4(c) and (d) we plot the same data sets as functions of temperature, to quantify the temperature sensitivity of the two sensors. Linear regression yields temperature sensitivities of -16.7±0.2 pm/K and -16.4±0.1 pm/K for channels M1 and M2, respectively. The larger standard error on the estimate of the M1 temperature sensitivity is due to the somewhat poorer linearity of the M1 response. This poorer linearity is in turn due to a poorer fit of the combined ring resonator and Fabry-Perot cavity model to the M1 spectra, yielding a larger error in the ring resonance wavelength estimate. The random scatter in both channels is, however, dominated by the limited temperature stability (0.1 K) of the temperature controller, and averages out in the regression. From this measurement, we find that the differential temperature sensitivity for slow temperature drift, without individual sensor calibration, is only of the order of 0.3 pm/K, that is a 55 times improvement.

Figure 5(a) shows the resonance wavelength shifts of sensor M1, and the reference M4, as functions of time during injections of the dilution series of ethanol into a running buffer of DI water in M1. The mass percentage of each injection is indicated above the corresponding peak. The three lines represent channels: M1; M4; and M1 – M4, that is M1 compensated by subtracting from it the drift observed in M4.

The inset of Fig. 5(a) shows a magnification of the measured baseline noise of the compensated signal M1 – M4. The standard deviation of the measured total system noise is only σ = 0.7 pm, even though the laser wavelength step is 10 pm in this measurement. This significant noise reduction is due to the model fitting employed, which averages out wavelength and amplitude errors. We noticed that a further decrease of the wavelength step did not significantly reduce the noise level, indicating that other noise sources also contribute to the system noise.

Figure 5(b) shows the corresponding resonance wavelength shifts observed in M1-M4 as a function of the refractive index shift of the injected solutions. As expected, the ring resonance shift is proportional to the refractive index shift and the slope of the line fitted yields the refractive index sensitivity of the sensor: S = 240±10 nm/RIU.

Figure 5 (c) demonstrates the ability of the system to compensate for temperature variation during measurement. The figure shows the resonance wavelength shift of sensors M1 and M2 as a function of time, with the DI water filled M2 serving as a temperature reference. Repeated shots of 2% ethanol are injected in M1, while the temperature of the chip is varied from 22.5°C to 31.5°C.

Fig. 3. Example transmission spectra of sensor M1 operating in DI water at two different temperatures. The wavelength step in this particular measurement was 20 pm. The solid line is a combined Lorentzian and double cavity Fabry-Perot model. The obtained quality factor of this device was 3000 and the arrows indicate the extracted resonance wavelengths. The inset shows an enlargement of the region around resonance at 33°C

6. Discussion

The measured negative temperature sensitivity of the slot-waveguide ring resonators confirms the ability of slot-waveguides to guide and confine a significant mode fraction in the low index slot. A comparison of the thermo-optic coefficients of water, silicon nitride, and silicon oxide shows that, to obtain a negative temperature coefficient, more than 10% of the mode power must propagate in the liquid sample. Indeed, numerical simulations of the design have indicated that 27% of the optical power of the slot-waveguide quasi-TE mode should propagate in the sample [25

C. A. Barrios, “Analysis and modeling of a silicon nitride slot-waveguide microring resonator biochemical sensor,” in Optical Sensors 2009, F. Baldini, J. Homola, and R. A. Lieberman, eds., vol. 7356, pp. 735,605+ (SPIE, 2009). URL http://dx.doi.org/10.1117/12.820172.

]. The high refractive index sensitivity of 240 nm/RIU obtained in our measurements also indicates that a large mode fraction propagates in the liquid sample.

Even though our waveguide design was optimized for high refractive index sensitivity rather than athermal operation, the obtained absolute temperature sensitivity of -16.6 pm/K, on average, is still rather low. In fact, the negative sign indicates that, from an athermal design perspective, the waveguides are slightly overcompensated, and that by reducing the amount of power propagating in the liquid sample, by adjusting the slot width, a fully athermal design could be accomplished. For comparison, the athermal capillary based ring resonator sensors reported by Suter et al. [9

] show temperature sensitivities from 17.2 pm/K down to 5.4 pm/K, while at the same time a refractive index sensitivity of only 3.6 nm/RIU, two orders of magnitude lower than presented here. In contrast, the planar polymer ring resonator sensors reported in [26

M.-S. Kwon and W. H. Steier, “Microring-resonator-based sensor measuring both the concentration and temperature of a solution,” Opt. Express 16, 9372–9377 (2008). URL http://dx.doi.org/10.1364/OE.16.009372. [CrossRef] [PubMed]

], show a much larger magnitude of temperature sensitivity of -80 pm/K, since the polymer core and the liquid cladding have thermo-optic coefficients of the same polarity and thus do not compensate each other.

Fig. 4. The left panels show the resonance wavelengths of (a) channel M1, and (b) channel M2, as functions of time during temperature stepping from 23.0°C to 33.0°C and a jump back to 23.0°C. The right panels show the corresponding resonance wavelengths of (c) channel M1, and (d) channel M2, as functions of temperature. The slopes of the fitted lines yield the temperature sensitivities of the sensors.

In Fig. 5(a), we note that the baseline of M1 red shifts slightly with each injection, while the reference M4 blue shifts 14 pm during the same period. We attribute the red shift of the M1 baseline to the known solvent absorption of PDMS [27

J. N. Lee, C. Park, and G. M. Whitesides, “Solvent Compatibility of Poly(dimethylsiloxane)-Based Microfluidic Devices,” Anal. Chem. 75, 6544–6554 (2003). URL http://dx.doi.org/10.1021/ac0346712. [CrossRef] [PubMed]

]. During each injection, a small fraction of the ethanol is absorbed, which then slowly diffuses out again during the subsequent DI water flush and lifts the baseline. To avoid any effect of the PDMS solvent absorption on the refractive index sensitivity calibration, care was taken to reach a plateau level in each injection. Furthermore, the slope of the refractive index sensitivity is drawn through the plateau levels of the injections, and not referred to the drifting base line. The good linearity of the observed response and the close agreement with the refractive index sensitivity of 210 nm/RIU reported in [15

], for a resonator of the same design but with no PDMS layer, further supports the validity of the calibration. The slightly higher sensitivity observed in this work is most likely due to deviations in waveguide dimensions as a result of changes in the lithography process (from lift-off in [15

] to negative resist in this work). The blue shift of M4 corresponds to a sensor temperature increase of 0.8 K, and is most likely due to an increase in ambient temperature during measurement.

Fig. 5. (a) The resonance wavelength shifts of sensors M1, M4, and their difference, as functions of time during injections of a dilution series of ethanol into a running buffer of DI water in M1. The inset shows a magnification of the measured baseline noise of the differential signal. (b) The corresponding shifts observed in M1 – M4 as a function of the refractive index shift of the injected solution. (c) Resonance wavelength shifts of channels M1, M2, and their difference, for repeated injections of 2% ethanol in M1 during a 9 K temperature transient. The dashed line M2' indicates an interpolated M2 signal with cross talk from the injections in M1 removed.

Following the convention of using three standard deviations of the total system noise as a measure of the sensor resolution [28

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008). URL http://www.opticsinfobase.org/abstract.cfm?id=148904. [CrossRef] [PubMed]

], we obtain a refractive index limit of detection of

D = \frac{3 σ}{S} = \frac{2.1 pm}{240 nm / RIU} = 8.8 \times 10^{- 6} RIU,

(1)

without calibration or active temperature control. Since the differential temperature sensitivity is only 0.3 pm/K, we have a temperature operating window of 7 K, in which the system noise is dominated by other factors than temperature. If on-chip referencing would not be employed, the operating window would be only 0.1 K.

Due to the higher index contrast between silicon and water than between silicon nitride and water, higher refractive index sensitivities can be obtained in silicon slot-waveguide sensors [29

F. Dell’Olio and V. M. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15, 4977–4993 (2007). URL http://dx.doi.org/10.1364/OE.15.004977. [CrossRef] [PubMed]

]. For example, numerical calculations have predicted silicon slot-waveguide sensor sensitivities of 348 nm/RIU for a 104 nm slot width [24

], and 490 nm/RIU for a 40 nm slot width [23

]. However, from a sensing point of view, the obtainable detection limit of the sensing system is a more relevant figure of merit [28

], and as evident from (1) above it depends both on the refractive index sensitivity and on the total system noise, which in turn depends strongly on the quality factor of the sensing resonator [28

]. Thus, even though the silicon slot-waveguide reported in [24

] experimentally showed a refractive index sensitivity of 298 nm/RIU, the low observed quality factor (330) of the sensing ring resonator yielded a detection limit of 4.2 × 10^-5 RIU, almost five times that of the silicon nitride device in this work. We note, though, that high quality silicon slot-waveguide ring resonators with solid polymer top cladding have been demonstrated in [30

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081,101+ (2005). URL http://dx.doi.org/10.1063/1.1871360. [CrossRef]

], and given appropriate design adjustments for a liquid water top cladding such devices should be able to improve on the refractive index limit of detection presented here.

As seen in Fig. 5(c), an increase in temperature yields a common mode blue shift of both channels that is effectively canceled in the differential signal, while the injection of a high refractive index sample in M1 yields a clear differential red shift, as expected. We notice, however, that the injection in M1 creates slight cross-talk in M2. We believe this effect is due to the solvent absorption of PDMS, as discussed above, and the close proximity of reference channel M2 to the measurement channel M1 in this experiment (in contrast to reference channel M4 in Fig. 5(a)). To avoid these cross-talk effects on the differential signal, we interpolate the reference signal over the injection time, before subtracting it from M1 for compensation. The interpolation is indicated by the dashed line M2′ in the figure.

7. Conclusions

We have presented an integrated slot-waveguide refractive index sensor array and, to our knowledge, the first thermal sensitivity study of slot-waveguide refractive index sensors. The sensors show a temperature dependence of only -16.6 pm/K, on average, and at the same time a high refractive index sensitivity of 240 nm/RIU. Furthermore, on-chip temperature compensation, by referencing the sensors to each other, yields a differential temperature sensitivity of only 0.3 pm/K.

We demonstrated the ability of the sensor system to measure during temperature drift and showed that our fabrication process yields sufficiently repeatable sensor-to-sensor temperature sensitivity for on-chip compensation without individual sensor calibration, thus avoiding time consuming calibration and enabling use in highly parallel chemical assays.

Our main result is that a slot-waveguide refractive index sensor array, utilizing on-chip temperature referencing, can deliver a refractive index limit of detection of D = 8.8 × 10^-6 RIU in a 7 K temperature operating window, without external temperature control or individual sensor calibration.

Finally, we suggested the possibility of athermal slot-waveguide refractive index sensors, by tuning the slot width to balance the fraction of light propagating in the liquid sample. Athermal slot-waveguide sensors would be able to accurately measure liquid sample refractive index under rapid temperature variation.

Acknowledgments

K. B. Gylfason acknowledges support of the Steinmaur Foundation, Liechtenstein. This work is done within the FP6-IST-SABIO project (026554) funded by the European Commission.

References and links

1.	D. Markov, D. Begari, and D. J. Bornhop, “Breaking the 10^-7 Barrier for RI Measurements in Nanoliter Volumes,” Anal. Chem. 74, 5438–5441 (2002). URL http://dx.doi.org/10.1021/ac020403c. [CrossRef] [PubMed]
2.	R. Karlsson, A. Michaelsson, and L. Mattsson, “Kinetic analysis of monoclonal antibody-antigen interactions with a new biosensor based analytical system,” J. Immunol. Methods 145, 229–240 (1991). URL http://dx.doi.org/10.1016/0022-1759(91)90331-9. [CrossRef] [PubMed]
3.	Z. Wang and D. J. Bornhop, “Dual-Capillary Backscatter Interferometry for High-Sensitivity Nanoliter-Volume Refractive Index Detection with Density Gradient Compensation,” Anal. Chem. 77, 7872–7877 (2005). URL http://dx.doi.org/10.1021/ac050752h. [CrossRef] [PubMed]
4.	X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta 620, 8–26 (2008). URL http://dx.doi.org/10.1016/j.aca.2008.05.022. [CrossRef] [PubMed]
5.	A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised Formulation for the Refractive Index of Water and Steam as a Function of Wavelength, Temperature and Density,” Journal of Physical and Chemical Reference Data 27, 761–774 (1998). URL http://dx.doi.org/10.1063/1.556029. [CrossRef]
6.	H. Takashashi, “Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,” Appl. Opt. 34, 667+ (1995). URL http://www.opticsinfobase.org/abstract.cfm?id=45986. [CrossRef] [PubMed]
7.	L. Eldada, “Advances in telecom and datacom optical components,” Opt. Eng. 40, 1165–1178 (2001). URL http://dx.doi.org/10.1117/1.1372703. [CrossRef]
8.	Y. Kokubun, N. Funato, and M. Takizawa, “Athermal waveguides for temperature-independent lightwave devices,” IEEE Photon. Technol. Lett. 5, 1297–1300 (1993). URL http://ieeexplore.ieee.org/xpls/abs all.jsp?arnumber=250049. [CrossRef]
9.	J. D. Suter, I. M. White, H. Zhu, and X. Fan, “Thermal characterization of liquid core optical ring resonator sensors,” Appl. Opt. 46, 389–396 (2007). URL http://dx.doi.org/10.1364/AO.46.000389. [CrossRef] [PubMed]
10.	V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Optics Letters 29, 1209–1211 (2004). URL http://dx.doi.org/10.1364/OL.29.001209. [CrossRef] [PubMed]
11.	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, 1645–1652 (2008). URL http://dx.doi.org/10.1364/OE.16.001645. [CrossRef] [PubMed]
12.	G. Maire, L. Vivien, G. Sattler, A. Kaźmierczak, B. Sanchez, K. B. Gylfason, A. Griol, D. Marris-Morini, E. Cas-san, D. Giannone, H. Sohlström, and D. Hill, “High efficiency silicon nitride surface grating couplers,” Opt. Express 16, 328–333 (2008). URL http://dx.doi.org/10.1364/OE.16.000328. [CrossRef] [PubMed]
13.	J. Blasco and C. A. Barrios, “Compact slot-waveguide/channel-waveguide mode-converter,” in Conference on Lasers and Electro-Optics Europe 2005 , p. 607 (2005). URL http://dx.doi.org/10.1109/CLEOE.2005.1568383. [CrossRef]
14.	P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202 (2006). URL http://www.opticsinfobase.org/abstract.cfm?id=114595. [CrossRef] [PubMed]
15.	C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Optics Letters 32, 3080–3082 (2007). URL http://www.opticsinfobase.org/abstract.cfm?id=144251. [CrossRef] [PubMed]
16.	A. Kaźmierczak, F. Dortu, O. Schrevens, D. Giannone, L. Vivien, D. M. Morini, D. Bouville, E. Cas-san, K. B. Gylfason, H. Sohlströom, B. Sanchez, A. Griol, and D. Hill, “Light coupling and distribution for Si₃N₄/SiO₂ integrated multichannel single-mode sensing system,” Opt. Eng. 48, 14, 401+ (2009). URL http://dx.doi.org/10.1117/1.3067875.
17.	C. F. Carlborg, K. B. Gylfason, A. Kaźmierczak, F. Dortu, M. J. Bañuls, A. M. Catala, G. M. Kresbach, H. Sohlström, T. Moh, L. Vivien, J. Popplewell, G. Ronan, C. A. Barrios, G. Stemme, and W. van der Wijngaart, “A packaged optical slot-waveguide ring resonator sensor array for multiplex label-free assays in labs-on-chips,” Lab on a Chip 10, 281–290 (2010). URL http://dx.doi.org/10.1039/b914183a. [CrossRef] [PubMed]
18.	P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luys-saert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography,” IEEE Photon. Technol. Lett. 16, 1328–1330 (2004). URL http://dx.doi.org/10.1109/LPT.2004.826025. [CrossRef]
19.	Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, “Efficient coupling of a semiconductor laser to an optical fiber by means of a tapered waveguide on silicon,” Appl. Phys. Lett. 55, 2389–2391 (1989). URL http://dx.doi.org/10.1063/1.102290. [CrossRef]
20.	D. R. Lide, ed., CRC handbook of chemistry and physics . (CRC ; Taylor & Francis [distributor], 2008). URL http://www.worldcat.org/oclc/219996604.
21.	H. Sohlström and M. Öberg, “Refractive index measurement using integrated ring resonators,” in The 8th European Conference on Integrated Optics , pp. 322–325 (1997).
22.	C. A. Barrios, B. Sánchez, K. B. Gylfason, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Demonstration of slot-waveguide structures on silicon nitride / silicon oxide platform,” Opt. Express 15, 6846–6856 (2007). URL http://www.opticsinfobase.org/abstract.cfm?id=134979. [CrossRef] [PubMed]
23.	J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16, 4296–4301 (2008). URL http://dx.doi.org/10.1364/OE.16.004296. [CrossRef] [PubMed]
24.	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 Photonics Journal 1, 197–204 (2009). URL http://dx.doi.org/10.1109/JPHOT.2009.2031596. [CrossRef]
25.	C. A. Barrios, “Analysis and modeling of a silicon nitride slot-waveguide microring resonator biochemical sensor,” in Optical Sensors 2009, F. Baldini, J. Homola, and R. A. Lieberman, eds., vol. 7356, pp. 735,605+ (SPIE, 2009). URL http://dx.doi.org/10.1117/12.820172.
26.	M.-S. Kwon and W. H. Steier, “Microring-resonator-based sensor measuring both the concentration and temperature of a solution,” Opt. Express 16, 9372–9377 (2008). URL http://dx.doi.org/10.1364/OE.16.009372. [CrossRef] [PubMed]
27.	J. N. Lee, C. Park, and G. M. Whitesides, “Solvent Compatibility of Poly(dimethylsiloxane)-Based Microfluidic Devices,” Anal. Chem. 75, 6544–6554 (2003). URL http://dx.doi.org/10.1021/ac0346712. [CrossRef] [PubMed]
28.	I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16, 1020–1028 (2008). URL http://www.opticsinfobase.org/abstract.cfm?id=148904. [CrossRef] [PubMed]
29.	F. Dell’Olio and V. M. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15, 4977–4993 (2007). URL http://dx.doi.org/10.1364/OE.15.004977. [CrossRef] [PubMed]
30.	T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081,101+ (2005). URL http://dx.doi.org/10.1063/1.1871360. [CrossRef]

OCIS Codes
(120.6810) Instrumentation, measurement, and metrology : Thermal effects
(130.6010) Integrated optics : Sensors
(230.5750) Optical devices : Resonators

ToC Category:
Integrated Optics

History
Original Manuscript: October 20, 2009
Revised Manuscript: January 20, 2010
Manuscript Accepted: January 29, 2010
Published: February 1, 2010

Virtual Issues
Vol. 5, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Kristinn B. Gylfason, Carl F. Carlborg, Andrzej Kazmierczak, Fabian Dortu, Hans Sohlström, Laurent Vivien, Carlos A. Barrios, Wouter van der Wijngaart, and Göran Stemme, "On-chip temperature compensation in an integrated slot-waveguide ring resonator refractive index sensor array," Opt. Express 18, 3226-3237 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-4-3226

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References

D. Markov, D. Begari, and D. J. Bornhop, "Breaking the 10−7 Barrier for RI Measurements in Nanoliter Volumes," Anal. Chem. 74, 5438-5441 (2002), http://dx.doi.org/10.1021/ac020403c. [CrossRef] [PubMed]
R. Karlsson, A. Michaelsson, and L. Mattsson, "Kinetic analysis of monoclonal antibody-antigen interactions with a new biosensor based analytical system," J. Immunol. Methods 145, 229-240 (1991), http://dx.doi.org/10.1016/0022-1759(91)90331-9. [CrossRef] [PubMed]
Z. Wang and D. J. Bornhop, "Dual-Capillary Backscatter Interferometry for High-Sensitivity Nanoliter-Volume Refractive Index Detection with Density Gradient Compensation," Anal. Chem. 77, 7872-7877 (2005), http://dx.doi.org/10.1021/ac050752h. [CrossRef] [PubMed]
X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, "Sensitive optical biosensors for unlabeled targets: A review," Analytica Chimica Acta 620, 8-26 (2008), http://dx.doi.org/10.1016/j.aca.2008.05.022. [CrossRef] [PubMed]
A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, "Revised Formulation for the Refractive Index of Water and Steam as a Function of Wavelength, Temperature and Density," Journal of Physical and Chemical Reference Data 27, 761-774 (1998), http://dx.doi.org/10.1063/1.556029. [CrossRef]
H. Takashashi, "Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition," Appl. Opt. 34, 667+ (1995), http://www.opticsinfobase.org/abstract.cfm?id=45986. [CrossRef] [PubMed]
L. Eldada, "Advances in telecom and datacom optical components," Opt. Eng. 40, 1165-1178 (2001), http://dx.doi.org/10.1117/1.1372703. [CrossRef]
Y. Kokubun, N. Funato, and M. Takizawa, "Athermal waveguides for temperatureindependent lightwave devices," IEEE Photon. Technol. Lett. 5, 1297-1300 (1993), http://ieeexplore.ieee.org/xpls/abs all.jsp?arnumber=250049. [CrossRef]
J. D. Suter, I. M. White, H. Zhu, and X. Fan, "Thermal characterization of liquid core optical ring resonator sensors," Appl. Opt. 46, 389-396 (2007), http://dx.doi.org/10.1364/AO.46.000389. [CrossRef] [PubMed]
V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and confining light in void nanostructure," Optics Letters 29, 1209-1211 (2004), http://dx.doi.org/10.1364/OL.29.001209. [CrossRef] [PubMed]
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, 1645-1652 (2008), http://dx.doi.org/10.1364/OE.16.001645. [CrossRef] [PubMed]
G. Maire, L. Vivien, G. Sattler, A. Kázmierczak, B. Sanchez, K. B. Gylfason, A. Griol, D. Marris-Morini, E. Cassan, D. Giannone, H. Sohlström, and D. Hill, "High efficiency silicon nitride surface grating couplers," Opt. Express 16, 328-333 (2008). URL http://dx.doi.org/10.1364/OE.16.000328. [CrossRef] [PubMed]
J. Blasco and C. A. Barrios, "Compact slot-waveguide/channel-waveguide mode-converter," in Conference on Lasers and Electro-Optics Europe 2005, p. 607 (2005), http://dx.doi.org/10.1109/CLEOE.2005.1568383. [CrossRef]
P. A. Anderson, B. S. Schmidt, and M. Lipson, "High confinement in silicon slot waveguides with sharp bends," Opt. Express 14, 9197-9202 (2006), http://www.opticsinfobase.org/abstract.cfm?id=114595. [CrossRef] [PubMed]
C. A. Barrios, K. B. Gylfason, B. S’anchez, A. Griol, H. Sohlstr¨om, M. Holgado, and R. Casquel, "Slot-waveguide biochemical sensor," Optics Letters 32, 3080-3082 (2007), http://www.opticsinfobase.org/abstract.cfm?id=144251. [CrossRef] [PubMed]
A. Kázmierczak, F. Dortu, O. Schrevens, D. Giannone, L. Vivien, D. M. Morini, D. Bouville, E. Cassan, K. B. Gylfason, H. Sohlstr¨om, B. Sanchez, A. Griol, and D. Hill, "Light coupling and distribution for Si3N4/SiO2 integrated multichannel single-mode sensing system," Opt. Eng. 48, 14,401+ (2009), http://dx.doi.org/10.1117/1.3067875.
C. F. Carlborg, K. B. Gylfason, A. Ka’zmierczak, F. Dortu, M. J. Ba˜nuls, A. M. Catala, G. M. Kresbach, H. Sohlstr¨om, T. Moh, L. Vivien, J. Popplewell, G. Ronan, C. A. Barrios, G. Stemme, and W. van der Wijngaart, "A packaged optical slot-waveguide ring resonator sensor array for multiplex label-free assays in labs-on-chips," Lab on a Chip 10, 281-290 (2010), http://dx.doi.org/10.1039/b914183a. [CrossRef] [PubMed]
P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, "Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography," IEEE Photon. Technol. Lett. 16, 1328-1330 (2004), http://dx.doi.org/10.1109/LPT.2004.826025. [CrossRef]
Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, and D. A. Ackerman, "Efficient coupling of a semiconductor laser to an optical fiber by means of a tapered waveguide on silicon," Appl. Phys. Lett. 55, 2389-2391 (1989), http://dx.doi.org/10.1063/1.102290. [CrossRef]
D. R. Lide, ed., CRC handbook of chemistry and physics. (CRC; Taylor & Francis [distributor], 2008), http://www.worldcat.org/oclc/219996604.
H. Sohlström and M. Öberg, "Refractive index measurement using integrated ring resonators," in The 8th EuropeanConference on Integrated Optics, pp. 322-325 (1997).
C. A. Barrios, B. Sánchez, K. B. Gylfason, A. Griol, H. Sohlstr¨om, M. Holgado, and R. Casquel, "Demonstration of slot-waveguide structures on silicon nitride / silicon oxide platform," Opt. Express 15, 6846-6856 (2007), http://www.opticsinfobase.org/abstract.cfm?id=134979. [CrossRef] [PubMed]
J. T. Robinson, L. Chen, and M. Lipson, "On-chip gas detection in silicon optical microcavities," Opt. Express 16, 4296-4301 (2008), http://dx.doi.org/10.1364/OE.16.004296. [CrossRef] [PubMed]
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 Photonics Journal 1, 197-204 (2009), http://dx.doi.org/10.1109/JPHOT.2009.2031596. [CrossRef]
C. A. Barrios, "Analysis and modeling of a silicon nitride slot-waveguide microring resonator biochemical sensor," in Optical Sensors 2009, F. Baldini, J. Homola, and R. A. Lieberman, eds., vol. 7356, pp. 735,605+ (SPIE, 2009), http://dx.doi.org/10.1117/12.820172.
M.-S. Kwon and W. H. Steier, "Microring-resonator-based sensor measuring both the concentration and temperature of a solution," Opt. Express 16, 9372-9377 (2008), http://dx.doi.org/10.1364/OE.16.009372. [CrossRef] [PubMed]
J. N. Lee, C. Park, and G. M. Whitesides, "Solvent Compatibility of Poly(dimethylsiloxane)-Based Microfluidic Devices," Anal. Chem. 75, 6544-6554 (2003), http://dx.doi.org/10.1021/ac0346712. [CrossRef] [PubMed]
I. M. White and X. Fan, "On the performance quantification of resonant refractive index sensors," Opt. Express 16, 1020-1028 (2008), http://www.opticsinfobase.org/abstract.cfm?id=148904. [CrossRef] [PubMed]
F. Dell’Olio and V. M. Passaro, "Optical sensing by optimized silicon slot waveguides," Opt. Express 15, 4977-4993 (2007), http://dx.doi.org/10.1364/OE.15.004977. [CrossRef] [PubMed]
T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, "High-Q optical resonators in silicon-on-insulatorbased slot waveguides," Appl. Phys. Lett. 86, 081,101+ (2005), http://dx.doi.org/10.1063/1.1871360. [CrossRef]

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