Spectral Optical Readout of Rectangular-Miniature Hollow Glass Tubing for Refractive Index Sensing.

For answering the growing demand of innovative micro-fluidic devices able to measure the refractive index of samples in extremely low volumes, this paper presents an overview of the performances of a micro-opto-fluidic sensing platform that employs rectangular, miniature hollow glass tubings. The operating principle is described by showing the analytical model of the tubing, obtained as superposition of different optical cavities, and the optical readout method based on spectral reflectivity detection. We have analyzed, in particular, the theoretical and experimental optical features of rectangular tubings with asymmetrical geometry, thus with channel depth larger than the thickness of the glass walls, though all of them in the range of a few tens of micrometers. The origins of the complex line-shape of the spectral response in reflection, due to the different cavities formed by the tubing flat walls and channel, have been investigated using a Fourier transform analysis. The implemented instrumental configuration, based on standard telecom fiberoptic components and a semiconductor broadband optical source emitting in the near infrared wavelength region centered at 1.55 µm, has allowed acquisition of reflectivity spectra for experimental verification of the expected theoretical behavior. We have achieved detection of refractive index variations related to the change of concentration of glucose-water solutions flowing through the tubing by monitoring the spectral shift of the optical resonances.


Introduction
In recent years, increasing attention has been given to the realization of label-free optical sensors able to measure the refractive index (RI) of samples [1][2][3][4]. Label-free sensing has become of great interest, since, with respect to techniques that make use of exogenous markers, it is safer, usually cheaper and it does not contaminate the sample under test. Furthermore, optical readout allows remote sensing of the investigated parameters, being thus minimally invasive, an issue that must be carefully taken into account when dealing with biological and biomedical analyses.
Several types of sensors that fulfil the mentioned requirements have been investigated, such as resonant micro-cavities [2,[5][6][7][8], photonic crystals [9][10][11][12][13][14], ring resonators [15][16][17] and fiber-optic sensors, such as Fiber Bragg Gratings (FBG) and Long Period Gratings (LPG) [4,[18][19][20], in general combined with optical spectral readout. Many architectures have been developed and tested: in [21], for instance, Li et al. proposed a fiber-optic Fabry-Perot interferometer (FPI) based on a single-mode fiber ending with an open microcavity with the inner surfaces covered with gold films. With this design, they obtained a minimum detectable RI step of the order of 10 −6 RIU. Wang et al., in [22], proposed a RI sensor based on a 2D photonic quasicrystal structure composed of silicon rods, obtaining a sensing accuracy of 10 −4 RIU. 3D structures have been as well extensively investigated: Wu et al., for example, previously exploited optical readout method based on spectral reflectivity measurements. In particular, a Fourier transform analysis is conducted for a better understanding of the contribution of each cavity formed by the tubing flat walls and channel. Moreover, we investigate the impact on the RI sensitivity of a tubing structure with walls thinner than the channel. Given the same channel depth, tubings with asymmetrical geometry characterized by thinner walls, with respect to standard symmetrical devices, allow to achieve higher sensitivity values. This result, theoretically demonstrated and experimentally verified, may be intuitively explained as a consequence of the lower contribution of the thinner glass walls, clearly insensitive to RI fluid variations, on the total optical thickness crossed by the readout radiation.
In this work, an instrumental configuration, based on standard telecom fiberoptic components and a semiconductor broadband optical source emitting in the near infrared wavelength region centered at 1.55 µm, is then used for the acquisition of reflectivity spectra and experimental verification of the expected theoretical behavior. We demonstrate the effect of refractive index variations, induced by changes of concentration of glucose-water solutions flowing through the tubing, on the wavelength position of the optical resonances observed on the detected spectra.

Structure and Theoretical Optical Features of Rectangular-Miniature Hollow Glass Tubings
Rectangular-miniature hollow glass tubings (Vitrotubes™, VitroCom, Mountain Lakes, NJ, USA) with channel depth (d) and glass wall thicknesses (t f and t b ) of a few tens of micrometers can be modeled as a sequence of three layers of different materials limited by four, flat dielectric interfaces: air-glass, glass-channel, channel-glass and glass-air, respectively numbered from 1 to 4 in Figure 1. When they are illuminated by broadband electromagnetic radiation perpendicularly to the channel axis and to the surface of the wider flat side (Figure 1), back-reflected radiation shows a wavelength spectrum with a complex line-shape due to interference effects among the fields reflected at the refractive index (RI) discontinuities. The field reflection coefficient of each interface can be easily calculated by means of Fresnel equations [33] and the overall reflectance can be obtained by cascading the effects of various Fabry-Perot etalons, thus keeping into account multiple reflections.
Sensors 2018, 18, 603 3 of 13 particular, a Fourier transform analysis is conducted for a better understanding of the contribution of each cavity formed by the tubing flat walls and channel. Moreover, we investigate the impact on the RI sensitivity of a tubing structure with walls thinner than the channel. Given the same channel depth, tubings with asymmetrical geometry characterized by thinner walls, with respect to standard symmetrical devices, allow to achieve higher sensitivity values. This result, theoretically demonstrated and experimentally verified, may be intuitively explained as a consequence of the lower contribution of the thinner glass walls, clearly insensitive to RI fluid variations, on the total optical thickness crossed by the readout radiation. In this work, an instrumental configuration, based on standard telecom fiberoptic components and a semiconductor broadband optical source emitting in the near infrared wavelength region centered at 1.55 µm, is then used for the acquisition of reflectivity spectra and experimental verification of the expected theoretical behavior. We demonstrate the effect of refractive index variations, induced by changes of concentration of glucose-water solutions flowing through the tubing, on the wavelength position of the optical resonances observed on the detected spectra.

Structure and Theoretical Optical Features of Rectangular-Miniature Hollow Glass Tubings
Rectangular-miniature hollow glass tubings (Vitrotubes™, VitroCom, Mountain Lakes, NJ, USA) with channel depth (d) and glass wall thicknesses (tf and tb) of a few tens of micrometers can be modeled as a sequence of three layers of different materials limited by four, flat dielectric interfaces: air-glass, glass-channel, channel-glass and glass-air, respectively numbered from 1 to 4 in Figure 1. When they are illuminated by broadband electromagnetic radiation perpendicularly to the channel axis and to the surface of the wider flat side (Figure 1), back-reflected radiation shows a wavelength spectrum with a complex line-shape due to interference effects among the fields reflected at the refractive index (RI) discontinuities. The field reflection coefficient of each interface can be easily calculated by means of Fresnel equations [33] and the overall reflectance can be obtained by cascading the effects of various Fabry-Perot etalons, thus keeping into account multiple reflections. Thus, the device reflectance strongly depends on the refractive index of the channel filling. Using this simple model, we have carried out numerical simulations to calculate the spectral reflectivity of a tubing with channel depth d = 30 µm, side width w = 300 µm, and tf = tb = 21 µm (nominal dimensions of Part#5003 by VitroCom) and of a tubing with d=50 µm, w = 500 µm, and tf = tb = 35 µm (nominal dimensions of Part#5005 by VitroCom) in the wavelength range 1.45-1.65 µm. The calculated reflectivity spectra R(λ) = Pr(λ)/Pin(λ), where Pr is the reflected and Pin the incident optical power density, are reported in Figures 2 and 3, for the smaller and larger tubing, respectively. While Figure 1. Schematic structure of the rectangular-miniature hollow glass tubing, with input illuminating beam P in and back reflected beam P r . d: channel depth, w: side width, t f : thickness of front wall; t b : thickness of back wall. The inset shows a schema of a capillary longitudinal cross-section, where the four capillary interfaces are highlighted.
Thus, the device reflectance strongly depends on the refractive index of the channel filling. Using this simple model, we have carried out numerical simulations to calculate the spectral reflectivity of a tubing with channel depth d = 30 µm, side width w = 300 µm, and t f = t b = 21 µm (nominal dimensions of Part#5003 by VitroCom) and of a tubing with d=50 µm, w = 500 µm, and t f = t b = 35 µm (nominal dimensions of Part#5005 by VitroCom) in the wavelength range 1.45-1.65 µm. The calculated reflectivity spectra R(λ) = P r (λ)/P in (λ), where P r is the reflected and P in the incident optical power density, are reported in Figures 2 and 3   Although all spectra show peaks and valleys, corresponding to resonance wavelengths of the device, they exhibit very different line-shapes. Peaks with higher amplitude are observed, for both   Although all spectra show peaks and valleys, corresponding to resonance wavelengths of the device, they exhibit very different line-shapes. Peaks with higher amplitude are observed, for both Although all spectra show peaks and valleys, corresponding to resonance wavelengths of the device, they exhibit very different line-shapes. Peaks with higher amplitude are observed, for both tubing dimensions, in the spectra relative to the empty device, due to the higher refractive index step at the interfaces between wall and air-filled channel. More peaks are counted in the same wavelength interval on the spectrum relative to the water-filled tubing compared to what is observed for an empty tubing with the same channel depth. Comparing the results attained for tubings of different sizes, more peaks are counted in the same wavelength interval in the spectrum relative to a tubing with larger dimensions, but same filling.
The origins of the complex line-shape of the spectral response due to the different cavities formed by the tubing flat walls and channel have been investigated using a Fast Fourier Transform (FFT) analysis, to identify the main Fourier components of the signal. Broad peaks are expected at different locations on the 1/λ horizontal (abscissa) axis, or wavenumber, corresponding to the inverse of the wavelength separation ∆λ of each resonance, given by the relationship ∆λ = λ 2 /(2 · OT) where OT is the optical path length of the considered cavity and λ is the wavelength position of the resonance (for example, a reflectivity minima). For the cavity corresponding to the channel (between interfaces 2-3, see Figure 1), ∆λ channel is therefore estimated by placing OT= OT channel = n f · d, where n f is the filling fluid RI. For the cavity corresponding to the whole device (between interfaces 1-4), ∆λ device is calculated using OT = OT device = n f · d + n glass · (t f + t b ). Analogously, for the cavity corresponding to a single wall (interfaces 1-2 and 3-4), we have to consider OT wall = n glass · t f and for the cavity formed by a wall plus the channel OT w+c = n glass · t f + n f · d. For increasing values of 1/λ, the first peak is expected at 1/λ 1 = 1/ ∆λ wall , a second one at 1/λ 2 = 1/∆λ channel , then the third at 1/λ 3 = 1/∆λ w+c and another around 1/λ 4 = 1/∆λ device . The FFTs of the reflectivity spectra previously reported in Figures 2 and 3 are shown in Figures 4 and 5, respectively. By concentrating our attention on Figure 4a, relative to an empty tubing with channel depth d = 30 µm, we can actually distinguish only three peaks, since 1/∆λ channel ≈ 1/∆λ wall ≈ 25 µm −1 , and thus 1/λ 1 ≈ 1/λ 2 . Moving our attention to the graph in Figure 4b, four peaks become now evident since 1/λ 2 = 1/∆λ channel > 1/∆λ wall = 1/λ 1 , due to the contribution of the water refractive index that increases OT channel . Similarly, in Figure 5a, relative to an empty tubing with d = 50 µm, we can distinguish three peaks, since 1/∆λ channel ≈ 1/∆λ wall ≈ 42 µm −1 , and thus 1/λ 1 ≈ 1/λ 2 whereas in Figure 5b we can separate the contribution at 1/λ 1 from that at 1/λ 2 , since 1/λ 2 = 1/∆λ channel is slightly higher than 1/λ 1 = 1/∆λ wall due to the contribution of the water refractive index. tubing dimensions, in the spectra relative to the empty device, due to the higher refractive index step at the interfaces between wall and air-filled channel. More peaks are counted in the same wavelength interval on the spectrum relative to the water-filled tubing compared to what is observed for an empty tubing with the same channel depth. Comparing the results attained for tubings of different sizes, more peaks are counted in the same wavelength interval in the spectrum relative to a tubing with larger dimensions, but same filling. The origins of the complex line-shape of the spectral response due to the different cavities formed by the tubing flat walls and channel have been investigated using a Fast Fourier Transform (FFT) analysis, to identify the main Fourier components of the signal. Broad peaks are expected at different locations on the 1/λ horizontal (abscissa) axis, or wavenumber, corresponding to the inverse of the wavelength separation Δλ of each resonance, given by the relationship Δλ = λ 2 /(2 · OT) where OT is the optical path length of the considered cavity and λ is the wavelength position of the resonance (for example, a reflectivity minima). For the cavity corresponding to the channel (between interfaces 2-3, see Figure 1), Δλchannel is therefore estimated by placing OT= OTchannel = nf · d, where nf is the filling fluid RI. For the cavity corresponding to the whole device (between interfaces 1-4), Δλdevice is calculated using OT = OTdevice = nf · d + nglass · (tf + tb). Analogously, for the cavity corresponding to a single wall (interfaces 1-2 and 3-4), we have to consider OTwall = nglass · tf and for the cavity formed by a wall plus the channel OTw+c = nglass · tf + nf · d. For increasing values of 1/λ, the first peak is expected at 1/λ1 = 1/ Δλwall, a second one at 1/λ2 = 1/Δλchannel, then the third at 1/λ3 = 1/Δλw+c and another around 1/λ4 = 1/Δλdevice. The FFTs of the reflectivity spectra previously reported in Figures 2 and 3 are shown in Figures 4 and 5, respectively. By concentrating our attention on Figure 4a, relative to an empty tubing with channel depth d = 30 µm, we can actually distinguish only three peaks, since 1/Δλchannel ≈ 1/Δλwall ≈ 25 µm −1 , and thus 1/λ1 ≈ 1/λ2. Moving our attention to the graph in Figure 4b, four peaks become now evident since 1/λ2 = 1/Δλchannel> 1/Δλwall = 1/λ1, due to the contribution of the water refractive index that increases OTchannel. Similarly, in Figure 5a, relative to an empty tubing with d = 50 µm, we can distinguish three peaks, since 1/Δλchannel ≈ 1/Δλwall ≈ 42 µm −1 , and thus 1/λ1 ≈ 1/λ2 whereas in Figure 5b we can separate the contribution at 1/λ1 from that at 1/λ2, since 1/λ2 = 1/Δλchannel is slightly higher than 1/λ1 = 1/Δλwall due to the contribution of the water refractive index.  1/λ 1 1/λ 3 1/λ 4 1/λ 2 1/λ 1 1/λ 2 1/λ 3 1/λ 4   As already mentioned, when comparing Figure 2a with Figure 2b, as well as Figure 3a with Figure 3b, it becomes evident that the profile of the spectral reflectivity does severely change when a fluid flows through the capillary. To investigate the potentiality of these devices as fluid RI sensors, we have carried out numerical simulations to calculate the spectral reflectivity of the tubing filled by fluids with increasing values of refractive index, with respect to water, considered as the reference fluid. As an example, Figure 6 illustrates reflectivity spectra, calculated for the tubing with d = 30 µm, considering three different values of refractive index for the filling fluid. In Figure 6a, data are reported for the wavelength range 1.45-1.65 µm as in Figures 2 and 3 whereas Figure 6b is the zoom in the narrower range 1.51-1.57 µm, that corresponds to the bandwidth of the optical source employed in the experimental tests. It can be noticed that the wavelength position of the minima shifts towards longer wavelength when the refractive index of the fluid increases. In principle, if the channel depth were much smaller than the wall thickness so that OTchannel would remain substantially different from OTwall even with fluid filling, as in [34], the shift could be recovered from the Fourier transform after identification of the channel mode. In the case of the rectangular hollow tubing employed in this work, with OTwall of the same order of magnitude of OTchannel, the reflectivity spectrum is the result of the superposition of all resonance modes and the shift as a function of the fluid refractive index is better detected directly in the wavelength domain.  As already mentioned, when comparing Figure 2a with Figure 2b, as well as Figure 3a with Figure 3b, it becomes evident that the profile of the spectral reflectivity does severely change when a fluid flows through the capillary. To investigate the potentiality of these devices as fluid RI sensors, we have carried out numerical simulations to calculate the spectral reflectivity of the tubing filled by fluids with increasing values of refractive index, with respect to water, considered as the reference fluid. As an example, Figure 6 illustrates reflectivity spectra, calculated for the tubing with d = 30 µm, considering three different values of refractive index for the filling fluid. In Figure 6a, data are reported for the wavelength range 1.45-1.65 µm as in Figures 2 and 3 whereas Figure 6b is the zoom in the narrower range 1.51-1.57 µm, that corresponds to the bandwidth of the optical source employed in the experimental tests. It can be noticed that the wavelength position of the minima shifts towards longer wavelength when the refractive index of the fluid increases. In principle, if the channel depth were much smaller than the wall thickness so that OT channel would remain substantially different from OT wall even with fluid filling, as in [34], the shift could be recovered from the Fourier transform after identification of the channel mode. In the case of the rectangular hollow tubing employed in this work, with OT wall of the same order of magnitude of OT channel , the reflectivity spectrum is the result of the superposition of all resonance modes and the shift as a function of the fluid refractive index is better detected directly in the wavelength domain. In order to investigate the theoretically expected performances of the employed devices as fluid RI sensors, we further performed numerical simulations in the wavelength range of 1.51-1.57 µm for a wider interval of RI values. In particular, we considered RIs in the range from 1.3154 up to 1.3386 RIU, corresponding to glucose concentrations in water between 0 and 16% (separated by a step of 1%) filling the tubing with d = 30 µm, and RI values in the range of 1.3154-1.3299 RIU, corresponding to glucose concentrations from 0 to 10%, for the tubing with d = 50 µm. The RI interval was chosen in order to investigate the widest exploitable RI interval, depending on the distance between two consecutive minima (or maxima) of the same spectrum, that limits the maximum RI variation detectable without ambiguity. By reporting the detected position in terms of wavelength of the spectral minima as a function of the relative considered RI value, we obtained the theoretical response curves for both formats of glass tubings. Defining the sensitivity as S = dλmin/dn, the theoretical sensitivities were retrieved as the slope of the device response curves. Comparable values were found for both devices. In particular, the numerical evaluation of the device performances led to a maximum sensitivity value Smax = 500.03 nm/RIU for the tubing with d = 30 µm, and to Smax = 507.5 nm/RIU for the tubing with d = 50 µm. As mentioned before, the reflected spectra result from the superimposition of contributes coming from different cavities, but where just the cavities incorporating the channel are affected by the fluid RI. A device is expected to be more sensitive as the weight of the channel on its overall thickness is higher. For the nominal devices we considered, i.e. the one characterized by tf = tb= 35 µm and d = 50 µm and the one with tf = tb = 21 µm and d = 30 µm, the impact of the channel depth on the total optical thickness is the same, thus similar RI sensing performances should be achieved. In order to investigate the theoretically expected performances of the employed devices as fluid RI sensors, we further performed numerical simulations in the wavelength range of 1.51-1.57 µm for a wider interval of RI values. In particular, we considered RIs in the range from 1.3154 up to 1.3386 RIU, corresponding to glucose concentrations in water between 0 and 16% (separated by a step of 1%) filling the tubing with d = 30 µm, and RI values in the range of 1.3154-1.3299 RIU, corresponding to glucose concentrations from 0 to 10%, for the tubing with d = 50 µm. The RI interval was chosen in order to investigate the widest exploitable RI interval, depending on the distance between two consecutive minima (or maxima) of the same spectrum, that limits the maximum RI variation detectable without ambiguity. By reporting the detected position in terms of wavelength of the spectral minima as a function of the relative considered RI value, we obtained the theoretical response curves for both formats of glass tubings. Defining the sensitivity as S = dλ min /dn, the theoretical sensitivities were retrieved as the slope of the device response curves. Comparable values were found for both devices. In particular, the numerical evaluation of the device performances led to a maximum sensitivity value S max = 500.03 nm/RIU for the tubing with d = 30 µm, and to S max = 507.5 nm/RIU for the tubing with d = 50 µm. As mentioned before, the reflected spectra result from the superimposition of contributes coming from different cavities, but where just the cavities incorporating the channel are affected by the fluid RI. A device is expected to be more sensitive as the weight of the channel on its overall thickness is higher. For the nominal devices we considered, i.e. the one characterized by t f = t b = 35 µm and d = 50 µm and the one with t f = t b = 21 µm and d = 30 µm, the impact of the channel depth on the total optical thickness is the same, thus similar RI sensing performances should be achieved.

Instrumental Configuration
Experimental verification of the expected theoretical behavior has been carried out thanks to an all-fiber setup shown in Figure 7. A fiber-pigtailed Superluminescent Light Emitting Diode (SLED, Exalos EXS1510-2111) with Gaussian emission profile centered at λ = 1.549 µm has been employed for illuminating the tubing. The optical power coupled in standard single-mode optical fibers is approximately 1.8 mW, when the SLED is driven by a pumping current I = 180 mA, at a temperature of 20 • C.

Instrumental Configuration
Experimental verification of the expected theoretical behavior has been carried out thanks to an all-fiber setup shown in Figure 7. A fiber-pigtailed Superluminescent Light Emitting Diode (SLED, Exalos EXS1510-2111) with Gaussian emission profile centered at λ = 1.549 µm has been employed for illuminating the tubing. The optical power coupled in standard single-mode optical fibers is approximately 1.8 mW, when the SLED is driven by a pumping current I = 180 mA, at a temperature of 20 °C. The fiber-coupled emitted radiation is guided through an optical isolator, to avoid undesired back reflections into the SLED, and then through a 2 × 2, 50:50 fiber-coupler. One of the output ports of the coupler ends with a micro-lens that shines the beam orthogonally onto the flat side of the rectangular tubing. The other output port is terminated with an angled connector to eliminate its contribution in reflection. Back reflected light is coupled back in the optical fiber and redirected to an Optical Spectrum Analyzer (OSA, Agilent 86142B, Agilent Technologies, Santa Clara, CA, USA) that allows to visualize the power density spectrum of the reflected light as a function of the wavelength. The spectrum analyzer is connected to a computer for data acquisition. The tubing is mounted on a manual micro-positioner that can be moved in the x, y and z direction, in order to maintain it in a stable and fixed position that optimizes back coupling. The liquid samples, stored in conic micro-tubes, flow into the channel by capillarity, without any external aids and exit by turning on a peristaltic pump.

Experimental Spectra
To confirm the expected theoretical results, we proceeded with the experimental testing of one kind of asymmetrical rectangular glass tubing as RI sensor. Given the same expected behavior in terms of sensitivity for both kind of devices, we choose to test the tubing with the narrower channel, i.e. the one with d = 30 µm, thus allowing to work with smaller quantities of sample. Figure 8 reports the reflected power spectra collected on a tubing with channel depth d = 30 µm, side width w = 300 µm, and tf = tb = 21 µm (nominal dimensions of Part#5003) by flowing glucosewater solutions at increasing concentrations (and thus RI). The wavelength range 1.51-1.57 µm corresponds to the emission bandwidth of the SLED. The spectral shift of minima or maxima is, as expected, toward longer wavelength for increasing values of RI. The behavior is quite similar to what was found theoretically, in particular with regard to the number of peaks and valley in the same The fiber-coupled emitted radiation is guided through an optical isolator, to avoid undesired back reflections into the SLED, and then through a 2 × 2, 50:50 fiber-coupler. One of the output ports of the coupler ends with a micro-lens that shines the beam orthogonally onto the flat side of the rectangular tubing. The other output port is terminated with an angled connector to eliminate its contribution in reflection. Back reflected light is coupled back in the optical fiber and redirected to an Optical Spectrum Analyzer (OSA, Agilent 86142B, Agilent Technologies, Santa Clara, CA, USA) that allows to visualize the power density spectrum of the reflected light as a function of the wavelength. The spectrum analyzer is connected to a computer for data acquisition. The tubing is mounted on a manual micro-positioner that can be moved in the x, y and z direction, in order to maintain it in a stable and fixed position that optimizes back coupling. The liquid samples, stored in conic micro-tubes, flow into the channel by capillarity, without any external aids and exit by turning on a peristaltic pump.

Experimental Spectra
To confirm the expected theoretical results, we proceeded with the experimental testing of one kind of asymmetrical rectangular glass tubing as RI sensor. Given the same expected behavior in terms of sensitivity for both kind of devices, we choose to test the tubing with the narrower channel, i.e. the one with d = 30 µm, thus allowing to work with smaller quantities of sample. Figure 8 reports the reflected power spectra collected on a tubing with channel depth d = 30 µm, side width w = 300 µm, and t f = t b = 21 µm (nominal dimensions of Part#5003) by flowing glucose-water solutions at increasing concentrations (and thus RI). The wavelength range 1.51-1.57 µm corresponds to the emission bandwidth of the SLED. The spectral shift of minima or maxima is, as expected, toward longer wavelength for increasing values of RI. The behavior is quite similar to what was found theoretically, in particular with regard to the number of peaks and valley in the same wavelength range and the shift magnitude. The differences in the line shape between the experimental results in Figure 8 and the numerical results in Figure 6b can be attributed to the tolerances in the real tubing dimensions (10% channel depth and 20% wall thickness), which affects the absolute position of maxima and minima, and to coupling losses due to material diffusion, which affects the amplitude.
wavelength range and the shift magnitude. The differences in the line shape between the experimental results in Figure 8 and the numerical results in Figure 6b can be attributed to the tolerances in the real tubing dimensions (10% channel depth and 20% wall thickness), which affects the absolute position of maxima and minima, and to coupling losses due to material diffusion, which affects the amplitude.  [35,36]).
Data have been actually collected on the same tubing using glucose-water solutions at 13 different concentrations and the results are reported in Figure 9 as 2D view of a 3D reconstruction of the sequence of spectra. Amplitude values are represented using false colours, indicated on the right side of the graph. Data have been actually collected on the same tubing using glucose-water solutions at 13 different concentrations and the results are reported in Figure 9 as 2D view of a 3D reconstruction of the sequence of spectra. Amplitude values are represented using false colours, indicated on the right side of the graph. wavelength range and the shift magnitude. The differences in the line shape between the experimental results in Figure 8 and the numerical results in Figure 6b can be attributed to the tolerances in the real tubing dimensions (10% channel depth and 20% wall thickness), which affects the absolute position of maxima and minima, and to coupling losses due to material diffusion, which affects the amplitude. Data have been actually collected on the same tubing using glucose-water solutions at 13 different concentrations and the results are reported in Figure 9 as 2D view of a 3D reconstruction of the sequence of spectra. Amplitude values are represented using false colours, indicated on the right side of the graph. Monitoring the spectral response allows estimation of RI variations of solutions flowing into the tubing channel with respect to a reference fluid, due for example to a change of concentration of the solute. Toward this aim, the response curves reported in Figure 10 have been obtained by fitting the wavelength position of the four minima of the spectra in the range 1.51-1.57 µm as a function of the refractive index. Defining the sensitivity as S = dλ min /dn (that is the slope of the response curves), values in the range of 290.1−484.5 nm/RIU have been found. These values are in good accordance with the numerical ones and higher than those experimentally obtained previously on symmetrical tubings [26]. Moreover, they are comparable with sensitivity values found in literature, but often obtained with devices fabricated or custom modified by means of sophisticated micromachining techniques. Considering the experimentally obtained standard deviations and sensitivities, we estimated a resolution, or, as indicated by other authors, LoD, in the range of 10 −4 -10 −5 RIU, through the equation 3 solute. Toward this aim, the response curves reported in Figure 10 have been obtained by fitting the wavelength position of the four minima of the spectra in the range 1.51-1.57 µm as a function of the refractive index. Defining the sensitivity as S = dλmin/dn (that is the slope of the response curves), values in the range of 290.1−484.5 nm/RIU have been found. These values are in good accordance with the numerical ones and higher than those experimentally obtained previously on symmetrical tubings [26]. Moreover, they are comparable with sensitivity values found in literature, but often obtained with devices fabricated or custom modified by means of sophisticated micromachining techniques. Considering the experimentally obtained standard deviations and sensitivities, we estimated a resolution, or, as indicated by other authors, LoD, in the range of 10 −4 -10 −5 RIU, through the equation 3Ϭ/S, where Ϭ is the experimental standard deviation. Eventually, retrieving the RI of solutions with known solute and solvent allows estimating the concentration. The best sensitivity value found in the experimental verification was slightly lower than that expected theoretically: probably, this result can be explained by a mismatch between the nominal and effective geometrical dimensions of the device. To estimate the actual dimensions, we characterized the tubing employed for refractometric detection through low-coherence interferometric measurements, that give the optical thickness as OTg = ng · x, where ng is the group refractive index of the material and x its geometrical thickness, as explained in [37,38]. We thus found the device geometrical dimensions by placing ng,glass = 1.4752 RIU [39] and ng,air = 1 RIU, obtaining tf = 22.40 µm td = 22.30 µm and d = 29.84 µm. The difference between the nominal values and the actual ones, though compatible with the given tolerances, may explain the minor discrepancy between the experimental and theoretical highest sensitivities.

Conclusion
The operating principle of the micro-opto-fluidic sensing platform that employs rectangularminiature hollow glass tubings and an optical readout method based on spectral reflectivity detection has been described by defining an analytical model of the tubing that allows calculation of the output signal as superposition of the effects of different optical cavities. The Fourier transform analysis has demonstrated that the components of the complex line-shape of the spectral response are related to the different cavities formed by the tubing flat walls and channel.
This effective and low-cost system provides performances comparable to those obtained with more expensive and more complex devices at the state of the art. The obtained results have been found in agreement with the theoretically expected values calculated through numerical simulations. In addition, the proposed sensor is suitable for the detection of a wide range of different biological fluids and samples. The use of read-out sources emitting in the near-infrared offers a double advantage, allowing to work in a wavelength region of minimum invasiveness for biological samples solute. Toward this aim, the response curves reported in Figure 10 have been obtained by fitting the wavelength position of the four minima of the spectra in the range 1.51-1.57 µm as a function of the refractive index. Defining the sensitivity as S = dλmin/dn (that is the slope of the response curves), values in the range of 290.1−484.5 nm/RIU have been found. These values are in good accordance with the numerical ones and higher than those experimentally obtained previously on symmetrical tubings [26]. Moreover, they are comparable with sensitivity values found in literature, but often obtained with devices fabricated or custom modified by means of sophisticated micromachining techniques. Considering the experimentally obtained standard deviations and sensitivities, we estimated a resolution, or, as indicated by other authors, LoD, in the range of 10 −4 -10 −5 RIU, through the equation 3Ϭ/S, where Ϭ is the experimental standard deviation. Eventually, retrieving the RI of solutions with known solute and solvent allows estimating the concentration. The best sensitivity value found in the experimental verification was slightly lower than that expected theoretically: probably, this result can be explained by a mismatch between the nominal and effective geometrical dimensions of the device. To estimate the actual dimensions, we characterized the tubing employed for refractometric detection through low-coherence interferometric measurements, that give the optical thickness as OTg = ng · x, where ng is the group refractive index of the material and x its geometrical thickness, as explained in [37,38]. We thus found the device geometrical dimensions by placing ng,glass = 1.4752 RIU [39] and ng,air = 1 RIU, obtaining tf = 22.40 µm td = 22.30 µm and d = 29.84 µm. The difference between the nominal values and the actual ones, though compatible with the given tolerances, may explain the minor discrepancy between the experimental and theoretical highest sensitivities.

Conclusion
The operating principle of the micro-opto-fluidic sensing platform that employs rectangularminiature hollow glass tubings and an optical readout method based on spectral reflectivity detection has been described by defining an analytical model of the tubing that allows calculation of the output signal as superposition of the effects of different optical cavities. The Fourier transform analysis has demonstrated that the components of the complex line-shape of the spectral response are related to the different cavities formed by the tubing flat walls and channel.
This effective and low-cost system provides performances comparable to those obtained with more expensive and more complex devices at the state of the art. The obtained results have been found in agreement with the theoretically expected values calculated through numerical simulations. In addition, the proposed sensor is suitable for the detection of a wide range of different biological fluids and samples. The use of read-out sources emitting in the near-infrared offers a double advantage, allowing to work in a wavelength region of minimum invasiveness for biological samples is the experimental standard deviation. Eventually, retrieving the RI of solutions with known solute and solvent allows estimating the concentration. The best sensitivity value found in the experimental verification was slightly lower than that expected theoretically: probably, this result can be explained by a mismatch between the nominal and effective geometrical dimensions of the device. To estimate the actual dimensions, we characterized the tubing employed for refractometric detection through low-coherence interferometric measurements, that give the optical thickness as OT g = n g · x, where n g is the group refractive index of the material and x its geometrical thickness, as explained in [37,38]. We thus found the device geometrical dimensions by placing n g,glass = 1.4752 RIU [39] and n g,air = 1 RIU, obtaining t f = 22.40 µm t d = 22.30 µm and d = 29.84 µm. The difference between the nominal values and the actual ones, though compatible with the given tolerances, may explain the minor discrepancy between the experimental and theoretical highest sensitivities. solute. Toward this aim, the response curves reported in Figure 10 have been obtained by fitting the wavelength position of the four minima of the spectra in the range 1.51-1.57 µm as a function of the refractive index. Defining the sensitivity as S = dλmin/dn (that is the slope of the response curves), values in the range of 290.1−484.5 nm/RIU have been found. These values are in good accordance with the numerical ones and higher than those experimentally obtained previously on symmetrical tubings [26]. Moreover, they are comparable with sensitivity values found in literature, but often obtained with devices fabricated or custom modified by means of sophisticated micromachining techniques. Considering the experimentally obtained standard deviations and sensitivities, we estimated a resolution, or, as indicated by other authors, LoD, in the range of 10 −4 -10 −5 RIU, through the equation 3Ϭ/S, where Ϭ is the experimental standard deviation. Eventually, retrieving the RI of solutions with known solute and solvent allows estimating the concentration. The best sensitivity value found in the experimental verification was slightly lower than that expected theoretically: probably, this result can be explained by a mismatch between the nominal and effective geometrical dimensions of the device. To estimate the actual dimensions, we characterized the tubing employed for refractometric detection through low-coherence interferometric measurements, that give the optical thickness as OTg = ng · x, where ng is the group refractive index of the material and x its geometrical thickness, as explained in [37,38]. We thus found the device geometrical dimensions by placing ng,glass = 1.4752 RIU [39] and ng,air = 1 RIU, obtaining tf = 22.40 µm td = 22.30 µm and d = 29.84 µm. The difference between the nominal values and the actual ones, though compatible with the given tolerances, may explain the minor discrepancy between the experimental and theoretical highest sensitivities.

Conclusion
The operating principle of the micro-opto-fluidic sensing platform that employs rectangularminiature hollow glass tubings and an optical readout method based on spectral reflectivity detection has been described by defining an analytical model of the tubing that allows calculation of the output signal as superposition of the effects of different optical cavities. The Fourier transform analysis has demonstrated that the components of the complex line-shape of the spectral response are related to the different cavities formed by the tubing flat walls and channel.
This effective and low-cost system provides performances comparable to those obtained with more expensive and more complex devices at the state of the art. The obtained results have been found in agreement with the theoretically expected values calculated through numerical simulations. In addition, the proposed sensor is suitable for the detection of a wide range of different biological fluids and samples. The use of read-out sources emitting in the near-infrared offers a double advantage, allowing to work in a wavelength region of minimum invasiveness for biological samples

Conclusions
The operating principle of the micro-opto-fluidic sensing platform that employs rectangularminiature hollow glass tubings and an optical readout method based on spectral reflectivity detection has been described by defining an analytical model of the tubing that allows calculation of the output signal as superposition of the effects of different optical cavities. The Fourier transform analysis has demonstrated that the components of the complex line-shape of the spectral response are related to the different cavities formed by the tubing flat walls and channel.
This effective and low-cost system provides performances comparable to those obtained with more expensive and more complex devices at the state of the art. The obtained results have been found in agreement with the theoretically expected values calculated through numerical simulations.
In addition, the proposed sensor is suitable for the detection of a wide range of different biological fluids and samples. The use of read-out sources emitting in the near-infrared offers a double advantage, allowing to work in a wavelength region of minimum invasiveness for biological samples and to make use of standard optical components already commercially available as they have been developed for optical communications.
As future perspective, it would become very interesting to translate the spectral shift in amplitude variations at a single wavelength [40], for example using a laser and a photodiode for the detection of the reflected optical power, thus obtaining a compact, cheaper and potentially portable system.