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Abstract
The refractive index of phosphate-buffered saline (PBS) solutions, for concentrations ranging from 0 mol/L to 1.516 mol/L, was experimentally determined in the telecom C + L infrared bands, ranging from 1510 to 1620 nm, which is commonly used for silicon photonics biochemical sensors. The infrared measurements were performed with a silicon photonics arrayed waveguide sensor and compared with the optical visible range values measured with a handheld refractometer. An equation for the refractive index of PBS solutions as a function of wavelength and PBS concentration is presented. Moreover, the conductivity of the test solutions was determined and the relation between conductivity and refractive index was established, allowing for a fast, easy, cost-effective, indirect method of refractive index determination of PBS solutions. The data presented will enable more realistic simulation of optical biosensors and their precise experimental calibration.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Phosphate-buffered saline is a water-based buffer solution containing a phosphate buffer, sodium chloride, and in some formulations potassium chloride [1]. The buffer maintains the solution pH constant, while the salt contents cater for ion concentrations and osmotic pressure similar to those found in the human body. Due to this isotonicity between PBS solutions and most human cells, PBS is a buffer solution of wide spread use in cell biology, from cell culture applications such as washing, transporting and dilution of cells [2], preparation and maintenance of live tissue [3] and bacteria [4], DNA sensing [5], and packaging of contact lenses [6]. Moreover, PBS is extensively used in testing procedures for benchmarking of optical biosensors, as part of the surface functionalization and washing, as well as transport media [7–16].
Most bio-optical sensors aim at label-free detection mechanisms, usually monitoring changes in optical properties on the surroundings of the sensor, either through bulk or surface detection. The sensor surroundings are typically constituted by buffer solutions, or cell culture media, and the analyte of interest. The optical properties of such liquids influence the behavior of the sensors and their performance indicators like sensitivity and limit of detection. As such, the optical properties of these elements, including their refractive index, are crucial at all stages of any optical biosensing related measurement and application, from the sensor design phase to planning of experiments and data interpretation. And yet, despite its widespread deploy, the refractive index (RI) of PBS in the telecom wavelength range, namely in S (1460-1530 nm), C (1530-1565 nm), and L (1565-1625 nm) bands, the most important to silicon photonics, is to the best of the authors knowledge missing from the literature. The refractive index of PBS in the interval between 1510 to 1620 nm is all the more relevant in the context of the expanding interest of silicon-based integrated photonic sensors [17]. Responding to the mentioned deficiency on PBS refractive index information this work determines it, along its dependence on concentration, both in the near-infrared and visible ranges. As the refractive index of PBS depends on its basic formulation, the study presented here focus on the most common PBS formulation, described in detail in the section 2.1.2.
Furthermore, by establishing the relation between the refractive index and the conductivity, this work seeks to provide a fast, cost effective and, attending to the wide profusion of handheld conductivity meters in worldwide biochemistry laboratories, a convenient method to determine the RI of PBS solution.
2. Experimental methodology
2.1 Measurement of the real part of PBS refractive index by spectral response analysis of a silicon photonics refractometer
2.1.1 Arrayed waveguide refractometer
The real part of RI of different concentrations of PBS was determined using a silicon photonics waveguide array sensor [18]. The sensor was fabricated on silicon-on-insulator (SOI) wafer stack composed by a 220 nm-thick silicon (Si) device layer and a 3 µm-thick SiO2 buried layer on a 675 µm Si handle layer (Fig. 1(a)). Based on parallel waveguide coupling, the sensing device consists of a set of four, 450 nm-wide and 220 nm-thick Si strip parallel waveguides, evanescently coupled. The Si waveguide cores seat on top of the buried SiO2 layer. Over the parallel waveguide region, a sensing window was opened in the SiO2 top cladding through which changes in the refractive index of the sensor surroundings influence the light propagating in the device, effectively enabling its detection and quantification. The total effective sensing area of the sensor is 426 µm2.
Fig. 1. (a) Diagram of the photonic sensor composed by a set of parallel Si waveguides on a SiO2 layer and covered by PDMS. Red arrows represent the light travel through the device with multiple lateral coupling events; (b) Scanning electron microscope images of the fabricated array waveguide sensor; (c) Experimental setup for photonic chip testing and sensing.
In short, the sensor is based on parallel waveguide coupling, explained by coupled mode theory through supermode propagation and interference: waveguides in close proximity become coupled, and exchange power along the direction of light propagation (Fig. 1(b)). The power exchange is mediated by the coupling coefficients between waveguides and the propagation constants of each supermode. Both parameters depend on the refractive indices of the materials constituting the sensor: the waveguide core (Si), the bottom cladding (SiO2) and the top cladding. In the case of this device, the typical top cladding material of most silicon photonics chips, a thick SiO2 layer, was removed over the sensing region (parallel waveguide region). As the device is placed in contact with different solutions, the top cladding over the sensing region changes, and so does the characteristic optical modal field distribution over the entire structure and its spectral output.
The device features were patterned through electron-beam lithography and transferred to the Si layer through fluorine-based reactive ion etch. A 20 nm thick layer of Si3N4 followed by 1 µm thick SiO2 top cladding were deposited by Plasma-Enhanced Chemical Vapor Deposition (PECVD). Due to its slower etch rate when compared to SiO2, a silicon nitride layer was deposited to act as an etch-stopper layer for the buffered oxide etch (5:1) [19]. Despite the index difference between the cladding materials, owing to the small thickness of the Si3N4 layer, its modal influence is negligible.
The limit of detection (LOD) is the minimum detectable variation of the environmental refractive index, which depends on both the sensitivity of the device (463.54 nm/RIU in the refractive index range of interest [18]) and the minimum spectral shift unequivocally attributed to index variations. Considering the minimum unequivocal detectable shift (0.077647 nm) to be three times the standard deviation of a set of measured shifts (obtained from an ensemble of sequential wavelength scans), the LOD of the sensor was determined to be 5.0 × 10−4 RIU [18]. This LOD is the refractive index resolution of the system defined above and takes into account both the measured experimental results and the data treatment. This value represents the uncertainty associated with any given refractive index measurement produced through this method.
2.1.2 Experimental setup and procedure for refractive index measurement in the infrared range
The sensing device was spectrally interrogated in a typical photonic chip testing setup constituted by an infrared C + L-band tunable laser source (Agilent 81600B Tunable Laser Source), an optical power sensor (InGaAs Agilent 81636B detector), both housed in an Agilent 8164B mainframe, a manual fiber polarization controller (Thorlabs FPC-2), and two lensed fibers used to couple to light the photonic chip and to collect light from it Fig. 1(c). Both the chip and the lensed fibers were mounted on a set of xyz translation stages for the required chip-to-fiber alignment. Optical measurements on the photonic chip were performed under TM polarized light in the wavelength range from 1500 nm to 1640 nm. The PBS solutions were dispensed on top of the chip by a micro-volumetric pipet. Droplets of 5 µL sufficed to fully cover the sensing window in the top cladding. The measurements were conducted at a room temperature of 22 °C and relative humidity of 50%, which are standard laboratory conditions.
To determine the refractive index of PBS solutions of different concentrations and its dispersion in the wavelength range of 1510 to 1620 nm, the spectral output of the sensor was recorded when in contact with deionized (DI) water, seven solutions of diverse concentrations of aqueous PBS, and in contact with a set of refractive index calibration liquids (Cargille).
The used buffer was a 10x solution (P32060, RPI) with the following composition: 1.37 M sodium chloride, 27 mM potassium chloride, 101.4 mM sodium phosphate dibasic and 17.6 mM potassium phosphate monobasic, where M stands for molar, a concentration unit defined as mol/L. The standard stock 10x PBS (1.516 M) was diluted with DI water to achieve the 1x, 2x, 3x, 4x, 5x, and 7x PBS solutions. The concentration of the solutions was defined in molarity as the sum of concentration of each constituent, ranging from 0 M, for DI water, and 1.516 M, for the 10x solution.
As for the Cargille refractive index liquids, the sensor was tested with five different liquids. The dispersion of the Cargille liquids follows the Cauchy equation:
where λ is the wavelength in nanometer, and A, B, and C are the Cauchy coefficients. The Cauchy coefficients for each of the five refractive index liquids at a temperature of 25°C are shown in Table 1, as provided by the supplier [20]. These Cauchy coefficients are valid for the wavelength range from 225 nm to 3700 nm. In addition, Table 1 also lists the corresponding refractive index at 1550 nm at a temperature of 25°C, and the thermo-optic coefficient (TOC) for each liquid, valid in the range between 15 °C to 35 °C. The TOCs allow the determination of the refractive index of the Cargile liquids at T = 22 °C, the temperature at which the experiments were conducted.
Table 1. Optical coefficients of the Cargille refractive index liquids: Cauchy coefficients for T = 25°C, refractive indices at a wavelength of 1550 nm, and the thermo-optic coefficients [20].
2.2 Measurement of the imaginary part of PBS refractive index by optical transmittance
The transmittance spectrum of the PBS solutions was measured to determine the imaginary part of its refractive index. Measurements were done in a PerkinElmer LAMBDA 1050 UV/Vis/NIR spectrophotometer. Quartz cuvettes with 1 mm light path were used during the measurements. The absorption of the cuvette itself is accounted by the instrument, which simultaneously measures the transmittance through the sample of interest and an empty reference cuvette.
2.3 Conductivity measurements
The conductivity measurements were performed by a handheld conductivity meter (EZ-1 TDS&EC METER) with an accuracy of 2%. The measurements were carried out by dipping the meter in each of the test solutions. To avoid cross-contamination, the meter was thoroughly cleaned in between measurements with DI water heated up to 60 °C.
2.4 Real part refractive index measurement with handheld refractometer at visible wavelengths
The refractive index at visible wavelengths were measured with a traditional handheld refractometer (accuracy of 0.001), an inexpensive and readily available instrument, based on total internal reflection on a prism system, projecting a shadow on a reticle. The refractometer was calibrated with DI water by setting the scale origin at a refractive index of 1.000. Therefore, the measured refractive indices of the PBS solutions are differential, representing the RI increment over the base value: DI water’s refractive index. Standard office fluorescent white light was used as the illumination source. These measurements allow for a fast determination of the refractive index in the visible range, and for dilution control of PBS in a chemical lab environment.
2.5 pH measurement
The pH of the solutions was measured with an Oakton pH 110 handheld pH meter. This equipment yields a pH resolution and accuracy of ± 0.01. The probe was fully immersed in the solutions during the readings, and thoroughly cleaned between solutions. Dipped in several cleaning baths of DI water, the probe was considered clean when the pH reading of a control DI water was consistent with previous measurements.
3. Results and discussion
3.1 Refractive index in telecom C + L infrared range
Most silicon photonics biosensors operate in the telecom C + L range, where numerous light sources and components are readily available for spectral analysis. To determine the refractive index of the PBS solutions in the telecom C + L infrared range, the sensor’s spectral response had to be characterized with media of known refractive index in this wavelength region. Cargille refractive index liquids are very stable liquids, with known refractive index and dispersion coefficients, hence they were selected to characterize the sensor’s dependency on the refractive index of the top cladding. In addition, the sensor’s spectral response was acquired for a set of PBS solutions with varying concentration, as detailed in the Experimental Methodology section.
The spectral responses of the chip in contact with the Cargille liquids and the PBS solutions are shown in Figs. 2(a) and 2(b), respectively, and are characterized by the presence of four interference peaks. As the refractive index of the Cargille liquids increased, the spectra shifted towards shorter wavelengths. The spectra show the same shift direction when the concentration of the PBS solution increases, which is in agreement with the expected increase of refractive index when the concentration of the solutions increases.
Fig. 2. Normalized transmission spectra of the sensor for (a) Cargille liquids and (b) PBS solutions.
The linear dependency of each peak position as a function of RI, $ \lambda (n )$, and as a function of concentration of PBS, $\lambda (C )$, can be extracted from the data in Figs. 3(a) and 3(b), respectively, in which are plotted the resonant wavelengths for each peak as function of RI and PBS concentration.
Fig. 3. Resonant wavelength of each peak of the transmission spectrum as a function of (a) refractive index of each Cargille liquid; (b) concentration of PBS solutions.
The fitted linear equations are summarized in Table 2. Each equation is valid for the spectral region near the correspondent peak position. Matching equations $\lambda (n )$ to $\lambda (C )$, the relation between RI and concentration of PBS can be obtained in the vicinity of each peak spectral position, thus yielding the relation $ n(C )$, which is also reported in Table 2. Using the relation $ n(C )$, the different concentration values can then be converted into refractive index values for four spectral regions. The resulting refractive index values are presented in Table 3. The uncertainty associated to the reported index values is the above mentioned LOD of the measurement sensor, $5 \times {10^{ - 4}}$ RIU.
Table 2. Linear dependence of the spectral positions of each peak as function of RI and concentration.
Table 3. Data for the refractive index as a function of concentration and peak position.
The refractive index data were fitted to the empirical equation established by Quan and Fry [21] for the refractive index of water as a function of salinity and wavelength. The data were fitted in Origin, using Levenberg-Marquardt algorithm for implementation of a least-squares iterative fitting approach. The uncertainty of each data point is known (the mentioned LOD) and affects every point equally. The Levenberg-Marquardt algorithm supports data weighting (instrumental weighting, ${\omega_i=1/\sigma_i}$) to account for varying data errors (${\sigma _i}$) across a pool of points, which in turn accounts for the relative importance the mean value of observations with larger errors should bear. However, in this case such has no effect over the fitting parameters because the error of each RI data point is the same. Thus, it leads to the same set of fitting parameters obtained through an iterative process of minimization of the chi-squared test, ${\chi ^2}$, independently of the error of the data points
where ${\omega _i}$ is the weight of the ith observation, ${Y_i}$ is the value of the ith observation, f is the fitting model, ${x_i}$ is the independent variable, and $\beta $ is the fitting parameters vector.The standard error of the fitting parameters is likewise affected by the weight factor as defined before (${\omega_i=1/\sigma_i}$), which is the same for all points, as mentioned above. The standard error is roughly the typical magnitude of the estimation error, in this case the error of a given fitting parameter. The standard error provides a precision of the fitted values, and its magnitude should typically be lower than the fitted values. When the standard errors are considerably greater than the fitted values, this means the fitting model is overparametrized. In this case, the terms for which the standard deviation of the coefficient was larger than the coefficient itself were eliminated. The resulting terms were again fitted, resulting in the following equation for the refractive index of PBS aqueous solutions as a function of concentration and wavelength:
where C is the PBS concentration in molar (M), and λ is the wavelength in nanometer. The fitting coefficients are presented in Table 4. The validity of the model is confirmed by a deviation between data points and fitting function inferior to 0.16% over the entire data set, the relative low magnitude of the standard errors of the model parameters, and an adjusted R2 of 0.96018. Moreover, the chosen model, displayed in Eq. (3), accounts for the known absorption band of water in the 1450 nm region [22].Table 4. Fitting parameters of Eq. (2) for the refractive index of PBS.
The contour plot of the refractive index of PBS as a function of wavelength and the concentration given by the fitted model is presented in Fig. 4, for wavelengths ranging from 1510 nm to 1620 nm, and for concentrations ranging from 0 M to 1.516 M. As can be seen in Fig. 4, the refractive index exhibits a peak that shifts towards larger wavelengths as the concentration increases. For DI water (CPBS = 0 M), and in concordance with [23], only the normal dispersion is visible on the range of 1510 nm to 1620 nm. As the concentration of PBS increases, the peak spectral position red-shifts and becomes visible within the measurement window of 1510 nm to 1620 nm. After the resonance, the RI follows the normal dispersion, i.e., decreases for longer wavelengths. Raman scattering data show that the concentration of dissolved NaCl on water affects the OH-stretching vibration band of the water [24], which in turn affects the optical dispersion and the refractive indices of the solutions, hence corroborating the reported findings.
The imaginary part of the refractive index, k, of the PBS solutions was determined through the transmittance data using the following equation:
where d is the length of the light path in the quartz cuvette, and T is the transmittance. Figure 5(a) shows the k values of the PBS solutions on the wavelength range from 1000 nm to 1800 nm. The inset details the k values for the peak in the vicinity of 1450 nm. As can be seen, the position of the absorption peak blue-shifts with the increase of the PBS concentration. The contour plot of the k values in the spectral region of interest, ranging from 1500 nm to 1620 nm, is presented in Fig. 5(b).Fig. 5. (a) 2D plot of k of the PBS solutions as a function of wavelength in the range 1000 nm to 1800 nm. Inset: Detail of the maximum at the wavelength region of 1450 nm. Contour plot of k (b) and the standard deviation of k (c) in the spectral region ranging from 1500 nm to 1620 nm.
The standard deviation of the imaginary part of the refractive index, σk, can be determined through error propagation (or propagation of uncertainties). As per Eq. (4), the imaginary part of the refractive index depends on the variables d, λ, and T. The standard deviation of λ (0.02 nm) and T (<0.1%) are much smaller than the σd, the standard deviation of d (50 µm, as provided by the manufacturer, AirekaCells), hence σk is dominated by σd. The calculated σk is presented in Fig. 5(c).
3.2 Conductivity
The experimental results of the conductivity measurements are shown in Fig. 6. The data were fitted to Eq. (5), conductivity as a function of the concentration of the PBS solutions, yielding an R2 of 0.9999. The corresponding fitting parameters are presented in Table 5.
Inverting Eq. (5) and plugging $C(\sigma )$ into Eq. (3) yields the relation between RI and conductivity in Eq. (6), which is plotted in Fig. 7.Fig. 7. Surface plot of the refractive index of PBS solutions as a function of wavelength and conductivity.
Table 5. Fitting parameters of (Eq. 4) for the conductivity of PBS.
3.3 Refractive index at optical wavelength and pH
The measurements in the visible range of the spectrum are displayed in Fig. 8. The increasing refractive index of the test solution shows a linear relation with the concentration of PBS in water. The differential refractive index perturbation caused by the saline solution comparatively with pure DI water follows the equation
where C is the PBS concentration in M, with an adjusted R2 = 0.9972.Fig. 8. Relative refractive index of PBS as a function of concentration, measured by a portable refractometer under white light, using pure DI water as reference.
The pH of the solutions decreases with the increase of concentration of PBS in the mixture, becoming increasingly acidic, as can be seen in Fig. 9. The pH evolves according to the negative exponential equation reported below in Eq. (8), with an adjusted R2 = 0.99803. The DI water used as the solvent of the mixtures has a pH of 7.1.
Both relations are useful for purposes of control and verification, as they account for quick and easy experimental verification of the PBS concentration. Through the relations concentration-refractive index (in the visible range) and concentration-pH is possible to quickly interrogate a PBS solution of unknown concentration or validate the preparation of said solutions.Inverting Eq. (8) and inserting it into Eq. (7) and Eq. (3), a relation between n and pH can be established for the visible and infrared range, respectively.
Such as Eqs. (7) and 8, Eq. (9) use should be limited to applications which do not require high accuracy, but rather a reasonable approximation/estimation, whose usefulness is limited in scope to quick and coarse quality control of PBS solutions in a laboratory environment.
4. Conclusion
The refractive indices of aqueous PBS solutions of different concentrations were determined both at the telecom and visible wavelength ranges.
At the infrared wavelength, an empirical equation for the refractive index of PBS was obtained as a function of wavelength and PBS concentration, with applications in biological optical sensors. This equation is valid for concentrations of PBS ranging from 0 M to 1.5160 M and for wavelengths within the range 1510 nm to 1620 nm. In addition, the imaginary part of the refractive index was reported for the same wavelength range.
The relation between concentration and conductivity of the PBS solutions was also determined. Furthermore, relations between the refractive index, for both the visible and the infrared range, and the conductivity and pH of the solutions were established. The data presented will enable more realistic simulation of optical biosensors and their precise experimental calibration.
Funding
Khalifa University (CIRA-2018-110, CRPA-2020-019).
Acknowledgements
The authors wish to acknowledge the contribution of Khalifa University's high-performance and research computing facilities and micro/nanofabrication facility to the results of this research.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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