The Thermo-Optic Discrimination of an Aqueous Solution Composition Using a Multimodal Interference Fiber Optic Sensor ^†

Abstract

Fiber optics sensors based on multimodal interference (MMI) have proven effective for refractometry of liquid samples. Here, we extend these capabilities to demonstrate that aqueous solutions with a similar refractive index (RI), which at room temperature are indistinguishable at the same concentration, can be discriminated against based on their thermo-optical response. We used an MMI sensor with the standard singlemode–multimode–singlemode architecture, where a section of no-core multimode fiber provides environmental sensitivity to the fiber surroundings. The proposed idea has been tested on aqueous solutions of tris and fructose, whose RI has a similar dependence on concentration. Indeed, we verified that they produce indistinguishable wavelength shifts as a function of concentration, measuring 0.2179 nm/% for tris and 0.2264 nm/% for fructose. Then, by varying the temperature in a controlled manner, from 25 °C to 45 °C in 2.5 °C increments, the distinct thermo-optic response can be unveiled for the two samples, which now permits differentiating them. Thermal sensitivities of 0.14433 nm/°C for tris and 0.1852 nm/°C for fructose were observed. This optical sensor requires no specific preparation or specialized equipment because the temperature range needed to achieve thermo-optical discrimination is accessible. Therefore, the measurement protocol can be incorporated into commercial refractometers equipped with temperature control.

1. Introduction

Refractive index (RI) is a fundamental optical property that determines how light interacts with a material. In fiber optic sensors, RI has been employed for the identification and characterization of aqueous solutions of numerous materials, including formaldehyde [1], ethanol [2], and glycerol [3], just to name a few. Although compounds may differ chemically and functionally, some exhibit similar RI when dissolved in water, as in the case of several sugars and sweeteners [4]. Unfortunately, although it is desirable, distinguishing materials with a similar RI is not an easy task.

Like many other liquid samples, the RI of aqueous sugar solutions is measured with commercial-grade refractometers, where the mixture of interest and its environment have temperature stability, allowing for high-precision measurements. Importantly, at a single wavelength and fixed temperature, aqueous solutions of sugars cannot be discriminated against based on their concentration behavior, because their RI has close values within instrumental uncertainties [5,6]. At a fixed temperature and concentration, discrimination based on RI measurements is feasible by analyzing their dispersion properties over an extended wavelength range [7]. In this regard, it should be noted that most commercial refractometers operate at a single wavelength (589.3 nm standard), and measuring the dispersion curve requires custom implementations that allow for multi-wavelength measurements [7,8]. These measurements are much more sophisticated and, to help discrimination, the dispersion curve is preferably measured in the VIS range [7] to take advantage of its natural increase toward shorter wavelengths. Even so, sample distinction is not obvious due to the measured values of RI, and the dispersion curves are very close to each other at all wavelengths; sometimes, the curves even intercross [7].

Alternatively, we propose leveraging their thermo-optic response by using the distinct way in which their RI varies with temperature as the basis for discrimination. Proof-of-concept experiments were carried out on aqueous solutions of tris and fructose by using a fiber optics multimodal interference (MMI) sensor as a refractometer [9,10,11,12]. This fiber optics device does not intend to overcome the performance of commercial refractometers or more sophisticated analytical tools [4], but it provides advantageous features of fiber optic sensors, like its capability for remote sensing, multiplexing, and real-time operation [13,14], that could be useful for in situ monitoring [15]. First, we verified that the tested aqueous solutions have a similar RI dependence on the concentration at room temperature, producing indistinguishable wavelength shifts. Then, we increased the temperature at the same concentration and unveiled a distinct thermo-optic response for the samples, allowing them to be differentiated. Our methodology is simple and does not require preparing the samples in a special manner. The temperature range required to achieve thermo-optic discrimination is accessible, and the measurement protocol can be incorporated into commercial refractometers equipped with temperature control.

2. Materials and Methods

The configuration of the MMI fiber optic sensor corresponds to the standard singlemode-multimode-singlemode architecture, often referred to as SMS, described in Figure 1 (dotted box), which consists of a coreless multimode fiber segment (NC-MMF) spliced between two common single-mode fibers (SMF) [16,17,18]. When introducing a wideband optical field from SMF to an NC-MMF fiber, the excited optical modes interfere with each other, generating periodic self-images of the input field [19,20]. Therefore, the NC-MMF fiber must have a specific length to reconstruct the field at its output, and only a specific wavelength meets the condition of constructive interference, given approximately by the following [20]:

$$\lambda =p{\displaystyle \frac{n{W}^2}{L}}$$

(1)

where $p$ is the reimage coefficient; $n$, $W$, and $L$ are the effective RI, effective optical diameter, and effective length of the multimode section, respectively. In a homogeneous MMF, $L$ corresponds to the length of the MMF. If the diameter of the core of the MMF is much larger than the wavelength, $W$ can be taken as the geometrical diameter of the MMF, ignoring the extent of the evanescent field in the cladding, which is on the order of the wavelength [12]. In Equation (1), the thermal dependence of the wavelength shift, ${\displaystyle \frac{d\lambda }{dT}}$, can be calculated as

$${\displaystyle \frac{d\lambda }{dT}}={\displaystyle \frac{p}{L^2}}\left(L{W}^2{\displaystyle \frac{dn}{dT}}+2LWn{\displaystyle \frac{dW}{dT}}-n{W}^2{\displaystyle \frac{dL}{dT}}\right)$$

(2)

The first term in Equation (2) accounts for the thermo-optical response, i.e., ${\displaystyle \frac{dn}{dT}}$ is the effective thermo-optic coefficient, while the second and third terms describe the effects of the thermal expansion along the transverse direction, ${\displaystyle \frac{dW}{dT}}$, and the longitudinal direction, ${\displaystyle \frac{dL}{dT}}$, respectively. The effective RI of the multimode section depends on the propagation constant of the excited modes, integrating the contributions of the core and the cladding.

Although the effective RI is often expressed in terms of the normalized frequency and transverse wavenumbers [12], it implicitly accounts for the thermo-optic effects of silica, ${\displaystyle \frac{dn}{dT}}\approx +1\times {10}^{-5 }°C^{-1}$ [21], and the cladding. In our case, when using an NC-MMF surrounded by a liquid being tested, ${\displaystyle \frac{dn}{dT}}$ reflects the contribution from the thermo-optical response of the sample. By keeping the fiber parameters constant, variations in spectral shift as a function of temperature can only be attributed to differences in the thermo-optical response of each sample, which is determined by its composition. According to Equation (1), the segment of NC-MMF was cleaved at a length of $L=59.6 \mathrm{m}\mathrm{m}$ to achieve a peak wavelength centered at $\lambda =1514.2 \mathrm{n}\mathrm{m}$.

The optical setup used to test the SMS sensor is shown in Figure 1. A super-luminescent laser diode (SLD, Model SLD1550S-A1, @Thorlabs, Newton, NJ, USA) emits a broadband spectrum (1420–1650 nm) that is directed to the SMS device with an FC/PC patch cord. The signal then travels through the SMS device and is collected by a second patch cord, and the transmitted signal is measured with an Optical Spectrum Analyzer (OSA, Model MS9740A, @Anritsu, Atsugi-shi, Kanagawa, Japan). The sensor is placed in a container that sits on a hot plate (^®IKA hot plate, Model HS7, Wilmington, NC, USA) and is located inside a thermally isolated temperature control chamber (Figure 1, blue box). To evaluate the sensor’s performance, aqueous solutions of tris and fructose were prepared using analytical-grade reagents from Sigma-Aldrich (^®Sigma Aldrich, 99% pure, Burlington, MA, USA) and deionized water in the concentration range of 5% to 40% v/v in 5% increments. At a concentration of 30% wt/wt, the RI of these solutions is 1.3797 for tris and 1.3803 for fructose. These compounds were chosen purposely due to their indistinguishable RI dependence on concentration at room temperature [4,5], but also for their industrial and biological significance: tris is widely employed as a buffering agent in molecular biology for its ability to stabilize pH in biological systems [22], while fructose is a key sugar in the food industry, recognized for its high sweetness and solubility [23].

Importantly, to ensure that the changes observed are only due to the thermo-optic response of the samples, the same SMS sensor was used in all the experiments.

3. Results and Discussion

Initial experimental tests were conducted at room temperature to confirm that the media were optically indistinguishable. The procedure involved recording the transmission spectrum with the sensor fully immersed in each sample, starting from the lowest concentration. After each measurement, the sensor was thoroughly rinsed with deionized water and allowed to dry until its baseline condition at 1514.2 nm was restored. This process was repeated for all aqueous solutions tested. Figure 2 shows the transmission spectra as a function of concentration for the aqueous solutions of fructose (Figure 2a) and tris (Figure 2b).

The two sets of spectra in Figure 2 were compared by following the most prominent feature, the peak wavelength of each spectrum. The spectral shift (Δλ) was evaluated as a function of concentration, with respect to the baseline condition where the sensor is in air, as shown in Figure 3. At the largest concentration tested, the total spectral shift was 7.95 nm and 8.25 nm for tris and fructose, respectively. The shift displayed a positive trend with a slightly quadratic dependence on sample concentration (r² > 0.99), with the quadratic term being negligible compared to the linear one.

This result indicates that, at higher concentrations, the penetration of the evanescent field into the cladding begins to influence the spectral behavior, revealing a quadratic dependence related to the effective optical diameter (λ_peak∝W²). For lower concentrations (≤30%), the slope was approximately 0.19 nm/%wt, while for higher concentrations (>30%), the slope increased to around 0.35 nm/%wt. More importantly, despite these variations, these results confirm that the samples are indistinguishable at room temperature (Figure 3).

To evaluate the feasibility of using the thermo-optic response as a means for sample discrimination, the samples at 30% concentration were purposely used because they showed the largest overlap in the previous experiment (see Figure 3). We used 30 mL of solution placed on a hot plate, with the sensor submerged in it (Figure 1, blue box). Measurements were taken at temperatures ranging from 25 °C to 45 °C in increments of 2.5 °C (Figure 4), revealing a positive spectral shift with a nonlinear dependence on temperature.

Figure 4 clearly shows that at room temperature, the samples cannot be differentiated; however, if larger thermo-optic changes are induced, they become distinguishable, even at the same concentration. In other words, the results in Figure 4 indicate the minimum temperature change that needs to be induced. In the case of these samples, the temperature needs to be increased to at least 45 °C to observe clear differences among them.

A higher-order polynomial was used to model data based on the thermo-optical behavior of the effective optical diameter. This behavior, represented by $d\left(\delta W\right)/dT$, is influenced by the thermo-optical response of the sample $d{n}_c/dT$. The spectral shifts were fitted to a temperature-dependent polynomial function of the form $\mathsf{\Delta }\mathsf{\lambda }=A+B{T}^1+C{T}^2+D{T}^3$, where A, B, C, and D are polynomial coefficients, similar to previous reports where similar trends have been observed [24]. The parameter A was kept fixed at 15.5 nm for all cases, while the others were free fitting parameters. The third-order polynomial accurately described the spectral changes across the entire temperature range ($r^2>0.97$ in all cases).

4. Conclusions

In summary, we demonstrated that aqueous solutions with a similar RI dependence on concentration at a fixed temperature can be distinguished based on their thermo-optical response. Using aqueous solutions of tris and fructose, we verified that they are optically indistinguishable at room temperature. Then, by controllably changing the temperature from 25 °C to 45 °C, we observed distinct thermo-optic behaviors that allowed for their differentiation.

From a procedural standpoint, the proposed strategy is simple and entails inducing temperature changes sufficiently large to demonstrate the sample’s thermal response that makes it differentiable from others. In this regard, we note that most commercial refractometers operate at a single wavelength and are equipped with temperature controls, which are typically used to keep the temperature constant during the measurements. Therefore, our thermo-optic methodology for sample discrimination, in principle, could be implemented in commercial refractometers simply by incorporating protocols for temperature sweeping.

Finally, although the results of our proof-of-concept experiments are encouraging, we acknowledge that the applicability of the proposed strategy under broader conditions requires further validation. In future work, we will include other sugars to extend our study to other families of substances with similar challenges and further explore the concentration requirements for achieving their RI-based discrimination.