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We demonstrate experimentally an optical sensor based on a monolithically integrated Mach-Zehnder interferometer comprising a liquid-core waveguide in one of the optical paths. The device is fabricated with a technique for self-forming microchannels in silica-on-silicon using standard photolithography and deposition processes. Refractometry with a resolution of better than 4×10-6 is demonstrated using the thermo-optic effect of the liquid medium to vary its refractive index. The polarization dependence of the device response is analyzed.
©2008 Optical Society of America
1. Introduction
Integrated optofluidic devices have great potential for robust biochemical sensors that can be implemented in arrays [1]. Small changes in refractive index due to temperature, concentration, chemical modification, or other changes in the system can provide a key to effectuate sensing in liquid media. Integrated refractometers have been implemented in different material systems using an evanescent-wave approach, where the test liquid is in contact with unclad waveguide sections in integrated Mach-Zehnder interferometers (MZI) [2–4]. Integrated liquid-core waveguides can allow direct optical probing of a liquid sample, with maximum overlap with the waveguide optical mode, in addition to the minimal loss for long path lengths afforded by waveguides in general. Single-mode propagation is preferred, in order to eliminate additional interference signals. Low-loss single-mode waveguides have been demonstrated using antiresonant reflecting optical waveguide structures [5]. These structures allow the inclusion of low-index liquids as the core medium such as aqueous solutions. Recently, the fabrication of Mach-Zehnder devices has been demonstrated using these structures [6], although with high loss. We have previously demonstrated a fabrication technique allowing the seamless integration of solid-core and liquid-core waveguides [7]. The technique allows single-mode liquid-core waveguides to be realized, with lengths limited only by wafer size. However, since the structures are index-guided, currently only liquids with a refractive index larger than 1.45 can serve as a core medium. We have fabricated a number of liquid-core devices, including MZIs, for integrated refractometry [8]. In Ref. 8 we presented the monochromatic response of a liquid-core MZI. We have also recently presented the spectral response of a similar device [9]. In this paper we demonstrate that an absolute-value reading of the device used as a refractometer can be made with a resolution better than 4×10-6 in refractive index. In order to effectuate controllable small-scale changes in refractive index of the liquid medium, we rely on the thermo-optic effect of the liquid medium while controlling the chip temperature.
2. Device description
Fig. 1. Top views of the Mach-Zehnder device: (a) Schematic mask layout for silica ridges, (b) optical micrographs of the fully fabricated liquid-core input and output junctions, (c) a representative micrograph of the device cross-section showing both microchannel and solid-core waveguide mesas. In the actual device, the two mesas are 50 µm apart. The position and size of the solid-core waveguide is outlined with a drawn square.
The MZI with a liquid-core waveguide is represented schematically in Fig. 1(a). The device is fabricated from doped silica layers deposited on silicon wafers using plasma enhanced chemical vapor deposition (PECVD). Conventional photolithography and reactive ion etching (RIE) were employed to define the device template. The template, etched from a Ge-doped silica layer deposited on the oxidized silicon substrate, consists of the silica waveguide core regions with additional ridges that allow the subsequent formation of microchannels. In this case, the latter consists of a single ridge pair with flaring endpoints, aligned with the solid-core waveguide ridges, as can be seen on the top of Fig. 1(a). The MZI structure is created using two 1×2 multimode interference (MMI) couplers. When the top cladding, a 12-µm-thick borophosphosilicate glass layer, is deposited, voids are formed between the closely spaced ridges. During a high temperature anneal, the top layer undergoes a partial reflow during which the voids are reshaped into quasi-circular channels that are aligned with the solid-core waveguides. Mesa structures on the top surface are formed above every indented feature of the template. Although the reflow is partial, the silica layers are fully annealed and stable in refractive index. The mesas, microchannels, and solid-core waveguides are illustrated in Fig. 1(c). The flaring of the microchannel endpoints leads to the formation of topside openings that allow the introduction of fluids from the surface of the chip [7]. This type of opening is illustrated in Fig. 1(b). It is worthy of note that the fabrication process for the devices comprising these embedded microchannels is strictly the same as that for silica waveguide devices without microchannels. The formation of microchannels is obtained through the mask layout (template), the concentrations of B and P dopants in the top silica layer, and the anneal temperature and duration. The cross-wafer uniformity of the microchannel dimensions is better than ±0.2 µm in diameter, limited to the measurement error. Batch-to-batch uniformity is dependent mainly on the deposition and annealing conditions for the top cladding layer. The limited number of devices produced to date have shown excellent reproducibility; long-term reproducibility will continue to be monitored and optimized.
The Ge-doped layer is 3.5 µm thick with a refractive index of 1.470. The ridges defining the solid-core waveguides are 3.5 µm wide, while the microchannel-forming ridges have a nominal width of 2 µm. The dimensions of the MMI couplers are 335×24 µm2 in the wafer plane. The distance between the MMI outputs is 13.4 µm center to center. The dimensions of the microchannels are 2.8±0.2 (width)×3.2±0.2 (height) µm2. These dimensions were estimated from an optical micrograph of devices fabricated on the same device chip. The length of the microchannel section is 20 mm. The length of the device chip is 30 mm. The top cladding layer has a refractive index of 1.4447±8×10-4, a close match to the oxidized silicon substrate. The microchannel was filled with a refractive index matching oil having a refractive index of nliq=1.478 at 1500 nm wavelength (Cargille Laboratories series A index fluid nD=1.49). The calculated propagation losses for the fundamental mode of the microchannel structure is 0.5 dB/cm, while the overlap with the mode of the solid-core waveguide is calculated to be 0.94. The thermo-optic coefficient of the liquid is -3.98×10-4/°C. The calculated thermal dependence of the effective index of the liquid-core waveguide mode is approximately -2×10-4/°C at room temperature.
Each of the interferometer arms will have a respective phase of 2πneffL/λ, where neff is the effective index of either the solid-core or the liquid-core waveguide, L is the relevant path length, and λ the wavelength. The phase difference between the MZI arms can be expressed in the frequency domain by
where Δφ0 is an initial phase imbalance resulting from fabrication-related size variations in the device structure, Δneff(ν) is the optical frequency-dependent difference in effective index between the solid-core and liquid-core waveguides, LLC is the length of the liquid-core waveguide, ν the optical frequency, and c0 the speed of light in vacuum. Note that the two optical paths of the MZI are the same physical length.
The monochromatic fringe period of the MZI corresponds to a variation of Δneff that yields a phase shift of 2π. In the spectral domain, a nonzero Δneff produces a fringe pattern, the period of which can be expressed as a frequency spacing, in the absence of dispersion, by Δν=c0/LΔneff. This fringe spacing is, however, dependent on the waveguide dispersion, or rather, on the difference in the solid-core and liquid-core waveguide dispersions. If we assume a linear dispersion function on the effective index difference, expressed by
we can write the 2π phase shift corresponding to one fringe using the relation
Introducing the group index difference
into Eq. (3), assuming Δν≪ν, and neglecting the term in Δν 2, the fringe spacing can be written simply as:
Since this quantity is frequency-dependent, we can expect the fringe spacing to be uneven across a given spectral range.
3. Experiments and results
The device chip was set on a thermo-electric cooler (TEC) itself resting on a heat sink connected to a circulating chiller unit. The chip was partially insulated from the laboratory environment by an enclosure. Light from a superluminescent diode emitting in the 1490–1590 nm range was coupled to the device using a single-mode fiber. The polarization state of the input light was not controlled. The output light was collimated with an aspherical lens of 2.8 mm focal length and 0.65 numerical aperture. This collimated beam was then coupled to another single-mode fiber using another aspherical lens. This fiber was connected to an optical spectrum analyzer. Between the two lenses, a Glan laser polarizer was inserted to select the output polarization (either vertical or horizontal). The spectral response for each of the polarizations was measured successively as a function of temperature, which was measured using a calibrated thermistor set on the TEC. The temperature was controlled over 1 °C spans using the TEC controller, while the chiller unit was used to vary the temperature in 1° C steps. As mentioned earlier, the variation of temperature is used as a means of changing the effective index of the liquid-core waveguide through the thermo-optic effect. The input and output fibers were realigned after each adjustment of the chiller temperature. A series of data was acquired over a period of several days for temperatures ranging from 20 to 40 °C for both polarizations. The device output is shown in Fig. 2 for both polarizations, for temperatures of 25.0 and 35.0 °C. The vertical (out of the wafer plane) and horizontal (in the wafer plane) polarizations are noted TM and TE respectively, for convenience. The envelope of the fringe pattern, which can be best seen in Fig. 2(b), corresponds to the spectral distribution of the source.
Fig. 2. Output spectra of the LCMZI for both polarization states at temperatures of (a) 25.0 °C and (b) 35.0 °C.
As the device temperature is increased, the spectral fringe patterns scroll along the wavelength axis at a rate of approximately 1 fringe per 0.4 °C, or per 1.6×10-4 in the liquid medium’s refractive index. Meanwhile, the fringe spacing progressively shrinks as the temperature increases. The evolution of the fringe spacing as a function of temperature, is shown in Fig. 3(a), for a central wavelength of 1540 nm. The central wavelengths are defined as the average wavelength of two consecutive transmission minima from which the fringe spacings, expressed as a frequency difference, are measured. On the top scale of Fig. 3(a) is shown the refractive index of the liquid medium, corresponding to the temperature scale, as calculated from the manufacturer data. The value of Δng corresponding to the fringe spacing, calculated from Eq. (5), is given in Fig. 3(b). The slope for Δng, is approximately 3×10-4/°C for both polarizations.
Fig. 3. (a) Frequency spacing as a function of temperature and the refractive index of the medium (top scale), for a fixed central frequency (1540 nm wavelength), and (b) the corresponding difference in group indexes between the liquid-core and solid-core waveguides, as calculated from Eq. (5).
In contrast to fringe counting, which allows only variations of the liquid refractive index to be measured, a single reading of the fringe spacing yields an absolute estimate of the optical path difference, expressed in terms of a group index difference. This difference is dependent on the dispersion of the liquid medium in addition to its mean value, which both influence the liquid-core waveguide dispersion. Thus, in order to measure the mean index of the liquid medium using the fringe spacing, the dispersion of the liquid medium must be known. Ultimately, the precision of the fringe spacing measurement method depends on the wavelength resolution of the transmission minima. For a 4 THz spacing (found near 30 °C in Fig. 3(a)), a typical 0.1 nm wavelength resolution leads to a resolution of 5×10-3 for the group index difference.
A more precise measurement method consists in measuring the wavelength of a transmission minimum. Like fringe counting, in itself, this method is inherently ambiguous. However, we can use the fringe spacing to disambiguate the transmission minimum data, in order to obtain a measurement of the liquid refractive index that is both absolute and precise. Figures 4 (a) and (b) show the relationship between fringe spacing, fringe central wavelength, temperature, and liquid refractive index, for a set of 190 spectra measured while the temperature is varied from 34.3 °C to 35.5 °C. The data set forms five bands in Fig. 4(a) and 4(b), each corresponding to a specific fringe or transmission minimum pairs. Figure 4(a) shows the center wavelengths as a function of temperature. It can be seen that the center wavelengths follow a linear dependence on the temperature or mean refractive index. The slope for the trace labeled “5” to “6” in Fig. 4(a) is 52.3 nm/°C, or 1.31×105 nm/refractive index units (nm/RIU). This is several orders of magnitude larger than grating-based devices [10]. For a 0.1 nm wavelength resolution, this would correspond to a potential resolution of 8×10-7 on the refractive index. The slope is dependent on the base refractive index or temperature. In Ref. 9 we show that higher slope values, from 250 to 100 nm/°C, are obtained for temperatures between 20 to 30 °C. However, higher resolutions do not necessarily follow, as the device baseline noise increases with the slope.
On Fig. 4(b) is shown the evolution of the fringe spacings as a function of center wavelength. These data can be used to disambiguate the center wavelength value, i. e. an absolute value reading can be done on Fig. 4(a) if it is known to which of the bands (i. e. 1–2, 3–4, 5–6, 7–8, or 9–10) the center wavelength corresponds. Figure 4(b) allows this correspondence to be made, as long as the bands do not overlap. The spacing between the bands yields the group index difference variation corresponding to one fringe count. The shape of these traces is determined by the dispersion of the group index difference. In the absence of differential group dispersion (i. e. both waveguides have the same dispersion and thus Δng(ν) in Eq. (5) is constant), the different traces in Fig. 4(b) would be linear. The dispersion-free slope of these traces can be determined by multiplying the relevant slope in Fig. 4(a) (52.3 nm/C) by the fringe period (0.4 C), divided by the spacing between the traces in Fig. 4(b) (50 GHz). For the trace labeled “5–6”, a slope of 2.4 GHz/nm is obtained. As we have mentioned, the liquid-core waveguide dispersion is dependent on the mean index of the liquid medium. Consequently, the shape of the traces seen on Fig. 4(b) varies (slowly) as a function of temperature or refractive index, despite that the material dispersions of all media remain virtually unchanged. Therefore, to obtain a reading for an arbitrary state of the device, an expanded data set such as the one shown in Fig. 4 is required, covering the anticipated range of operation. The precise wavelength dependence of the differential group index is not required, since one only needs to distinguish between the different traces, such as the ones in Fig. 4(b), in order to use the traces such as those in Fig. 4(a). The thickness of these traces is the result the 0.1 nm wavelength resolution of the transmission spectra. With this resolution, we project that the frequency spacing traces overlap for an effective index mismatch of 0.03 between the liquid-core and solid-core waveguides. This corresponds to a working range of 1.450–1.493 in terms of the refractive index of the liquid medium, for the present device. Although 1.450 represents a hard limit corresponding to the cutoff of the liquid-core waveguide’s fundamental mode, an increase of the upper limit could be engineered with a mismatch of the interferometer path lengths. However, the 0.03 effective index range can only be increased with an improvement of the wavelength resolution.
To evaluate the precision of this measurement method, the following procedure was used. First, the chiller unit was turned off to eliminate the temperature fluctuations due to its cycling. Then, the TEC current was set to 100 mA and a small heat source (a light bulb) was introduced in the enclosure. The system was allowed to stabilize for a few hours, after which the temperature was increasing at a slow rate of approximately 0.1 °C/hr. The wavelength of a transmission minimum near 1540 nm was tracked during half an hour, along with the temperature reading from the thermistor. To eliminate numerical noise from the temperature data, a linear fit of the temperature evolution is used as the x-axis on Fig. 5. The wavelength resolution is also apparent in Fig. 5, where the 500 individual data points merge into straight 0.1 nm bands. On Fig. 5 we demonstrate an experimental resolution of better than 10-2 °C for the MZI used as a temperature sensor near 28.7 °C. This corresponds to a resolution of better than 4×10-6 in refractive index. With this resolution, the detection of transparent liquid impurities could be performed with a volume proportion as low as 0.004 % approximately, for an index difference of 0.1 between the impurities and liquid, and assuming the liquid refractive index varies linearly with composition.
Fig. 4. Synthesis of the measured spectral response of the device for 190 temperature points between 34.3 °C and 35.5 °C, TM polarization. The circled numbers label the trace endpoints to establish the correspondence between (a) and (b). (a) Center wavelengths (i. e. the average wavelength of two consecutive minima) as a function of temperature. Top scale: calculated refractive index of the liquid medium at 1540 nm wavelength, from manufacturer data. (b) Fringe spacings as a function of center wavelength, for the same data set.
Fig. 5. Wavelength of one of the transmission minima as a function of temperature, showing the device resolution near 28.7 °C.
4. Polarization dependence
The solid-core and liquid-core waveguides have distinct birefringences that determine the polarization-dependent response of the device. Let us define the waveguide birefringence
Where X stands for either LC (liquid-core) or SC (solid-core). The birefringence difference between the two waveguides can be written
The cross-section of these waveguides is represented in Fig. 6. Using a commercial semi-vectorial mode solver (C2V Olympios), we calculate an effective group index birefringence on the order of 10-5 and 10-4 for the solid-core and liquid-core waveguides, respectively. These values stem from the stress-free form birefringence. The stress of the upper cladding layer has a determinant effect on waveguide birefringence [11]. It has been demonstrated from previous experiments that the reflow of the upper cladding influences the birefringence [12]. Since the liquid-core microchannel is shaped by the reflow of the upper cladding, we may expect a different stress distribution than that of the solid-core waveguide, which is formed by a static ridge around which the cladding reflow is effectuated.
The results shown in Fig. 3(b) indicate that the difference in group index birefringence (around 3×10-4 at the higher temperatures) is higher than the calculated value in the stress-free case (around 10-4 from the numbers above). This observation is in agreement with the hypothesis of different initial stress fields within the respective waveguide claddings. Using the measured values of the group index differences and the calculated dispersions for the respective waveguides, we estimate the initial birefringence difference to be on the order of 2×10-4.
Fig. 6. Schematized cross-sections of the two waveguides in the MZI (silicon substrate not shown). (a) solid-core waveguide (b) liquid-core waveguide. The liquid core is represented by a black ellipse.
The measurement of the birefringence difference as a function of temperature yields some information on the differential temperature-dependent stress distribution within the waveguides. Using a fixed wavelength of 1540 nm, we have performed a fringe counting experiment as a function of temperature. Starting at a temperature of approximately 17 °C, 43 fringes were counted for an increase of 16.53 °C for the TE polarization, while the same fringe count was achieved for an increase of 16.98 °C for the TM polarization. From these data we calculate that the temperature difference represents 1.17 TE fringes. From Eq. (1) we can calculate the corresponding effective index difference, which, divided by the temperature variation of 16.53 °C, allows us to deduce that ΔB (Eq. (7)) changes by 5.5×10-6/°C. This indicates that the stress distribution varies differently, for each of the waveguides illustrated in Fig. 6, as a function of temperature. However, it is not clear whether the double-ridge structure or microchannel itself is the principal source of this difference. In any case, this effect represents a 3% polarization dependence of the monochromatic device response.
The data in Fig. 3(b) show that the temperature dependence of group index birefringence difference, i. e. the slope difference between the two curves shown in Fig. 3(b), is 2×10-5/°C. This still represents only a perturbation on the device response, albeit a larger one (7%) than in the monochromatic case.
The polarization dependence of the device makes the fringe visibility dependent on the input polarization state, although there are limited regions (for example, in Fig. 2(b)) where the device is somewhat polarization insensitive. Unless the operation can be restricted to such a region, a single input polarization (either TE or TM) will be preferable. In addition, some care needs to be exercised if temperature ramps are used to calibrate the device, as some polarization differentials follow. On the other hand, a liquid-core waveguide-referenced device should be polarization insensitive, as the birefringence in both interferometer arms should be similar. Similarly, a temperature-ramp calibration of such of a device should result in polarization-insensitive values, as the thermal-dependent stress would be similar in both interferometer arms. However, this operation requires the use of two liquids of similar index with a different thermo-optic coefficient.
5. Conclusion
An optical sensor consisting of a liquid-core waveguide integrated in a silica-on-silicon Mach-Zehnder interferometer is demonstrated experimentally at wavelengths near 1550 nm. With a static liquid core medium, refractometry is demonstrated through the thermo-optic effect of the liquid, which dominates the thermal device response. A resolution better than 4×10-6 in refractive index is obtained. This resolution is achieved through a simple measurement of a wavelength of a transmission minimum. A measurement of the spectral fringe spacing can be used to disambiguate the reading based on the minimum transmission wavelength to obtain a high precision, absolute-value measurement of the refractive index of the liquid medium. The calibration and operation of the refractometer requires fluid motion within the microchannel that constitute the liquid-core waveguide. Since the microchannel endpoints are connected to the surface of the device chip, we can envision fluid motion being implemented through a “microfluidic layer” deposited on the chip. The device calibration could be done with a series of discrete reference liquids, combined with short-scale temperature ramping to provide the slopes of transmission minima and wavelength dependence of the fringe spacing. Since the measurements are done through the transmission spectrum, no power calibration of the device is required. An athermal version of the device could be obtained by adding a reference liquid-core waveguide in the solid-core arm of the interferometer. As interferometers represent the most sensitive device to measure refractive index changes [8], this type of device, combining a centimeter-scale path lengths, picoliter sampling volumes, and a good single-mode overlap with the liquid medium, constitutes a prime candidate for on-chip microfluidic characterization that can complement absorption spectroscopy methods.
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