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Abstract
In this work we discuss the effect of infiltration of different antiresonant fibers with low-refractive-index liquids, such as water and ethanol, on their optical properties. The fibers with single- and double-ring capillaries have been designed to show broad transmission bands in visible and near infrared range as it is required for optofluidics, in particular spectrophotometric applications. We show experimentally that their transmission windows shift toward shorter wavelengths and only modestly reduce their width. The transmission bands are located in the wavelength ranges of 533-670 nm and 707-925 nm, for the fibers when infiltrated with water. The two types of analyzed antiresonant fibers infiltrated with the liquids show similar light guidance properties when they are straight, but significantly lower bending loss can be achieved for the double-ring than for the single-ring antiresonant fiber. For this reason, the double-ring antiresonant fibers are more suitable as a compact solution for optofluidic applications, although transmission windows are reduced due to broader resonance peaks.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Interactions between light and liquids are investigated in the majority of biological and chemical laboratories. These spectrophotometric investigations make it possible to identify absorption bands or photoluminescent phenomena that are originated by a composition of the liquids, including particles suspended in them. For these measurements, the magnitude of the light-liquid interactions corresponds to the interaction length which is typically limited to 1 cm-long liquid-containing glass or polymer cuvettes used in spectrophotometric setups.
Optical fibers, especially those based on capillaries, come as a perfect solution to extend the interaction length and enhance the sensitivity of the approach. However, due to total internal reflection (TIR) phenomenon, the light-guiding inside standard capillaries is limited to liquids showing higher refractive index (RI) than that of the capillary fiber glass [1–2]. Therefore liquid core step-index fiber composed of capillary infiltrated with high RI liquids have found applications mainly in nonlinear optics, where highly nonlinear liquids and suspension of nanoparticles are used [3–7].
For biological or chemical applications, liquids showing low RI are mainly of interest. The RI of water-based organic solutions is slightly higher than the one of water (nD = 1.3330) [8], while that of silica is around 1.47 over the same wavelength range. Buffers and cell culture media used in biological experiments, which are required to keep microorganisms alive, also show RI similar to that of water in the visible and near-infrared (NIR) spectral range [9]. In the case of these low-RI liquids, in order to maintain TIR as the light-guiding mechanism, liquid core fibers with cladding made from low-index materials such as amorphous fluoropolymers [10,11], or sub-unitary index chalcogenide semiconductors [12], may be used. However, such waveguides are usually characterized by poor mechanical properties, or large core size [10,11]. Sub-unitary index chalcogenide semiconductors have been used to design fibers with small core diameter (around 10 µm), however, this material has low refractive index only in ultra-violet wavelength range (around 220-400 nm) [12], thus it is not suitable to guide the light in visible and near-infrared. Other route for TIR liquid core fiber is to use a sophisticated hollow-core fiber design with a high fraction of air-filled region (larger than 70%) in the microstructured cladding [13,14]. Such a fiber structure has been considered for application in e.g., biosensors and optofluidic biolasers [15–17]. However, this approach requires selective infiltration of the core with liquid and simultaneous preservation of air-filled photonic cladding to fulfill the requirements for TIR. Thus technically advanced fiber postprocessing is required to collapse all air holes in the photonic cladding and leave only the hollow core open to enable its selective infiltration [18].
As an alternative, the photonic bandgap (PBG) mechanism can be used, where light guiding in optical fibers with the low-RI core is possible [19]. In this case, photonic crystal structure created in a periodic air-glass fiber cladding limits the guiding to the core area. Some wavelengths are reflected by the photonic crystal and trapped in the low RI photonic crystal defect which plays the role of a core. This mechanism is also possible to be obtained in all-glass PBG fibers, when air holes are replaced by glass with low refractive index [20]. However, due to low contrast in photonic cladding, the transmission bandgaps in these fibers are very limited [21–25]. For example, in the case of all-glass PBG fiber made of a pair of soft glasses with refractive index contrast of Δn = 0.09, a photonic bandgap limited to 70 nm spectral width in the NIR has been reported [25]. In turn, when air-glass silica-based PBG filled with liquids are considered, the infiltration results in a significant reduction of transmission band widths and in their shifting towards shorter wavelengths [21–24]. A heavy water filling of PBG fiber with a cladding pitch of 3 µm, a core diameter of 8.2 µm and the fiber length of 40 cm caused a shift of transmission band centered at 1050 nm to around 600 nm [21]. Moreover, the initial bandwidth of 300 nm was narrowed to 170 nm (reduction by ∼43%). For some other fiber with 3.75 µm and 10 µm of cladding pitch and core diameter, respectively, and length of 70 cm, the shift was from 1600 to 905 nm with a bandwidth decrease from 400 to 230 nm (reduction by ∼42.5%) [21]. Other work reported 10 cm-long water-filled PBG fiber of 2.75 µm pitch and 10 µm core diameter [23]. In this case, as a result of infiltration, the transmission band centered at 1060 nm shifted to around 595 nm and its bandwidth decreased from 280 nm to 170 nm (by 39%). Water-filled large-core polymer microstructured fiber with 68 µm core diameter, 3 rings of air holes around the core, and a length of 49.5 cm has also been reported [22]. The measured central wavelength of transmission windows for air-filled fiber were 1430 nm and 1140 nm, where after filling with water they were shifted to 875 and 700 nm center wavelengths, respectively. The reduction in bandwidth was from 120 to 85 nm (by 29%) and from 200 to 100 nm (by 50%). Due to such narrow width of the transmission bands in the visible and NIR range, the ability of using liquid-core PBG fiber for optofluidic applications is rather limited. Moreover, since the PBG fiber core size reaches a couple of micrometers, its infiltration with a liquid is very time-consuming and a flow-rate of a liquid inside the fiber is hardly controllable. Among other disadvantages of PBG fiber for optofluidic applications, can be pointed out an increase in confinement and bending losses when the difference between RI of glass and the liquid decreases [21].
In contrast to PBG fibers, anti-resonant hollow-core fibers (ARFs) offer wider transmission bands and can readily be designed to have significantly larger cores [26]. They are considered for low latency transmission since the effective RI is close to 1 [27,28]. They are also used for ultrashort pulse delivery since in their broadband transmission window they have near-zero chromatic dispersion and weak nonlinear response [29,30]. Silica-based ARFs are also considered for gas sensing, since they offer transmission in the mid-infrared beyond 4 µm which overlaps spectral fingerprints of various gases [31].
Up to now only a few works considered infiltration of ARF fibers with liquids and studied their properties [24,32–38]. Preliminary results have shown that reduction of RI contrast between core and cladding does not dramatically decrease the width of transmission windows, as was in the case of the PBG fibers [32]. Liquid-filled ARFs have already been considered for various sensors [33,35–36] and chemical nanoreactors [34,38]. Liu et al. have applied ARF for sensing when one or more of the side capillaries is filled with ethanol [35]. Nissen et al. have shown using UV absorption spectroscopy and a single ring kagome lattice ARF that it is possible to detect some selected pharmaceuticals, such as sodium salicylate and sulfamethoxazole at concentration of 0.1 µM [33]. Wei et al. have numerically studied application of ARF for temperature sensing and found a sensitivity of 2.48 nm/°C when shift of transmission bands with temperature was considered [36]. Unterkofler et al. have demonstrated the use of an ARF with kagome lattice for online analysis of photochemical reaction [38]. With the use of the ARF it was possible to form a nanoreactor with a continuous flow of liquid and this configuration allowed to measure in real-time products of the reactions in volumes as small as few nL per cm of the fiber. Recently, Cubillas et al. have shown a high-RI glass single-ring ARF used as an optofluidic chemical nanoreactor for photolysis reaction in toluene [34]. Individual capillaries of ARF fibers were also used as an optofluidic ring resonator laser. However, in this case ARF was used only as mechanical support to excite whispering gallery modes in an individual capillary with submicron thickness [37].
In this work, we discuss application of ARFs with single- and double-ring tubular capillaries and similar geometrical parameters for low-RI optofluidics. Change in optical properties, specifically in the width and spectral position of their transmission bands, for the two fibers infiltrated with water and ethanol are analyzed numerically and verified experimentally. Origins of losses in these fibers, i.e. surface scattering, confinement, and material loss, as well as bending properties are identified. The influence of ARF internal structure on bending losses is also discussed.
2. Experimental details
2.1 Fabrication of the antiresonant fibers
We have fabricated the ARFs in-house using the conventional stack-and-draw method. Figure 1 contains scanning electron microscope (SEM) images of the investigated single-ring and double-ring ARF. Both fibers have a cladding consisting of 7 cladding capillaries with an average gap between cladding capillaries to thickness of the capillaries ratio (g/t) reaching 8. For such conditions, the confinement losses in the NIR range are reduced as was previously shown by Wei et al. [26]. A 7-capillary fiber design allows reducing both the confinement loss and the number of guided higher-order modes [30]. Moreover it allows for achieving a large core of the fiber without large increase of the outer diameter of the fiber. Recent results showed 5- and 6-capillary ARF with extremely low loss and excellent higher-order-mode extinction ratio [39,40]. In our case the use of lower number of capillaries would require either larger distances between the capillaries (when keeping the same outer and core diameter) or further scaling of the whole size of the fiber. Thus, the 7 capillary design was assumed as the optimal one. The inner diameter of the jacket tube and the core diameter (Dcore) of the single-ring ARF is 114.15 µm and 63.2 µm, respectively. The cladding capillaries have average outer diameter (d1) and wall thickness (t1) of 25.24 and 1.81 µm, respectively. In contrast to single-ring ARF, the double-ring ARF has additional capillaries nested at the same azimuthal angle inside in the tube lattice. In this fiber, two anti-resonant reflections are created due to the double negative curvatures at the inner and outer glass tubes. This structure offers significant advantages over single-ring configuration, such as reduced confinement loss [26] and lower bending loss [41]. The inner diameter of the jacket tube, the Dcore, d1 and t1 geometric parameters of the double-ring ARF are 116.1 µm, 64.9 µm, 25.86 µm, and, 1.802 µm, respectively. The nested capillaries have average outer core diameter (d2) and thickness (t2) are 14.8 µm and 0.909 µm, respectively. The nested capillary of the double-ring ARF is of a smaller thickness than the larger one due to the technological process conditions. The fibers also have relatively large gap separation between the capillaries. It has to be noted that these two factors contribute to the increase of confinement losses [41]. However material losses of the considered liquids are the dominant contribution to attenuation of the liquid core fibers in the considered case of liquid core ARFs. In this work, the relatively large gaps between the cladding capillaries allowed obtaining large hollow core diameters in the developed fibers, which facilitated efficient and fast infiltration of the core with liquids in sensing applications. Parameters of our developed ARFs investigated in this work are summarized in Table 1.
Fig. 1. SEM images of the investigated fibers, where (a) shows single-ring and (b) double-ring ARF. Geometrical parameters labelled in these images are explained in Table 1.
Table 1. Geometrical parameters of the investigated ARFs.
2.2. Optical properties of the investigated materials
In this work water and ethanol were chosen as liquids for infiltration of the ARFs. These liquids can be considered as a good reference to media often used in biological and chemical experiments [42]. RI of the liquids considered later in numerical simulations was assumed following the work of Kedenburg et al. [8]. Figure 2(a) shows real part of RI (n). Based on the imaginary part of RI (κ) reported in [8], we calculated attenuation for water and ethanol as shown in Fig. 2(b).
Fig. 2. (a) Real part of RI for silica glass, water and ethanol, and (b) calculated attenuation of water and ethanol.
2.3 Numerical investigations
Modal properties of the investigated fibers were analyzed numerically with the finite element method (FEM), implemented in COMSOL. The geometric parameters of the fibers’ structures, shown in Fig. 3 and summarized in Table 1, were extracted from the SEM images. The images obtained from SEM are preprocessed using mathematical morphology algorithms (a series of opening and closing operations) to smooth fine features of the structures. Next, the bitmap images are converted into idealized vector models of the fiber structures using in-house developed software in Matlab environment. We assumed mesh elements as triangles with maximum and minimum sizes of 0.4/0.015, 0.6/0.06, and 6.37/0.036 µm for capillary walls, the hollow core area, and the capillary interior, respectively. The boundary conditions were set as a cylindrical, perfectly matched layer (PML). It was a single layer with thickness of 3 µm. We performed tests of convergence for various thicknesses of the PML layer for the considered antiresonant fibers. The accepted thickness was sufficient for the antiresonant fibers, because the guided mode was well located in the core. Conditions for infiltration of the fiber with the liquids were assumed as replacing the air by a medium with properties of water and ethanol in the whole hollow area of the fiber. The results obtained for liquid-filled fibers were compared to these without any infiltration (air-filled fiber, further referred as unfilled).
Fig. 3. Schematic representation of the modeled ARF, where (a) shows single-ring and (b) double-ring ARF. Intensity distribution for the fundamental mode is shown in (c) and (d) for single-ring and double-ring ARF, respectively.
The supported mode structure of the fibers was assessed based on numerical simulations and with the criterion of CL equal to 10 dB/m as the mode cut-off. The air-filled fibers support 5 modes, namely LP01, LP11, LP21, LP02 and LP31 at a wavelength of 1500 nm. The water- and ethanol-filled fibers support 6 modes: LP01, LP11, LP21, LP02, LP31 and LP12 at a wavelength of 800 nm.
2.4 Experimental setup
The setup as shown in Fig. 4 was used to measure the transmission of the ARFs. A Koheras SuperK supercontinuum source emitting in the wavelength range of 450-2400 nm was used as a broadband light source. The light was coupled into the investigated fibers using a microscope objective MO1 through a glass window into a custom-made metal reservoir, as it is shown in Fig. 4(a). During the experiments, the reservoir was entirely filled with liquids and constantly pumped using a microfluidic pressure controller (Fluigent, MFCS-EZ) with a pressure of 10 kPa. The fiber sample was around 20 cm in length and the infiltration time was about 20 seconds. The whole hollow area of the fiber, including the interior space of the capillaries, was filled during this time with one of the liquids. The output beam was collimated by a microscope objective MO2 and then delivered to a spectrometer through a commercial multimode fiber patchcord. For single- and double-ring ARFs, with air in the core, the following spectrometers were used to record the output spectrum: Thorlabs CCS 175 (visible and NIR) in a range 500-1100 nm and a NIR spectrometer (Avantes, AvaSpec-NIR256-1.7) in a range 900-1700 nm. Due to high absorption of water and ethanol in the NIR, only the first spectrometer was used for ARFs infiltrated with liquids.
Fig. 4. (a) Schematic representation of a setup used for investigating transmission of ARF and (b) its experimental implementation.
3. Results and discussion
3.1 Numerical analysis
Changes in optical properties of the hollow area of the ARF affect the resonance conditions of the fiber, resulting in the shifting of the transmission bands. The resonant wavelengths of the investigated fibers can be calculated following Eq. (1), where t is the thickness of the capillary, n, and nl are RI of fused silica glass and liquid, respectively [26].
According to Eq. (1) the resonance corresponding to m=1 is located at longer wavelengths and transmission is between resonances corresponding to higher values of m at shorter wavelength range.
In order to identify the total attenuation of liquid-infiltrated ARFs, material losses (ML), surface scattering loss (SSL) and microbend loss (MBL) should be taken into account. The ML corresponds to the liquid characteristics shown in Fig. 2(b). SSL is related to surface roughness of the glass cladding capillaries and following [41] can be described with Eq. (2):
where F is the power fraction of the guided mode in fiber glass, η is a surface roughness coefficient and λ0 is a calibration wavelength. The values of the coefficients were estimated following [43] and [44] as equal to η = 97.243 and λ0 = 0.75 µm, respectively. The reduced refractive index contrast of the liquid-glass structure should cause a decrease of SSL level, thus the assumed parameters for scattering loss calculation performed for the unfilled fiber determined the upper limit of the SSL in the hollow core fibers used in this work.Fig. 5. Calculated and measured losses of single-ring ARF when it is (a) unfilled, (b) water-filled, and (c) ethanol-filled. The blue solid line in (a) marks CL from simulation and red line marks the measured attenuation of the unfilled fiber. The dashed line in (b) and (c) marks CL, dotted line – SSL, and solid line – total losses, including ML and MBL. Thick solid line in (b) marks the measured attenuation of the water-filled fiber. Numbers denote order of transmission windows.
Power fraction F was calculated as a ratio between power transmitted in the glass and total transmitted power, estimated as the z-component of the Poynting vector. SSL is a significant source of loss in the short-wavelength range due to the αSC ∼ λ−3 relationship [41]. MBL was calculated according to model proposed earlier [45]. Since power coupling from LP01 to LP11 mode was the dominating source of microbend loss, MBL estimation was limited to power coupling losses between these two modes. All the contributing losses for single- and double-ring ARFs are presented in Fig. 5 and in Fig. 6, respectively. In the visible range, both the liquid-infiltrated fibers show their losses below 10 dB/m, and typically at the level of 0.1-1 dB/m. Confinement loss (CL) and SSL were calculated for the fundamental mode of the fibers. The considered wavelength range for the case of liquid-infiltrated ARFs (500-1100 nm) was selected as a typical one required for biomedical measurements [46,47]. In the investigated spectral range for the liquid-filled cases, resonances corresponding to m=3 and 4 are observed. It can be found that the minimal estimated values of SSL reach the level of 10−3 dB/m for all of the investigated cases and it decreases with increasing wavelength. CL shows an opposite trend and for the transmission band at a lower wavelength, they are comparable to the SSL.
Fig. 6. Calculated and measured losses of double-ring ARF when it is (a) unfilled, (b) water-filled, and (c) ethanol-filled. The blue solid line in (a) marks CL from simulation and red line marks the measured attenuation of the unfilled fiber. The dashed line in (b) and (c) marks CL, dotted line – SSL, and solid line – total losses, including ML and MBL. Thick solid line in (b) marks the measured attenuation of the water-filled fiber. Numbers denote order of transmission window
It can be noted that for the whole investigated transmission bands both CL and SSL are relatively low when compared to MBL and ML of the liquids. The total loss of the investigated fibers is dominated by MBL in the shortest wavelength range and ML of the liquid for the longer wavelengths, while the CL and SSL can be neglected within the transmission bands, since both the MBL and ML are few orders of magnitude higher. Both the CL and SSL contribute increasingly to the total attenuation in the vicinity of the resonance wavelengths only. This observation is in agreement with results reported previously [32].
Attenuation of the unfilled and water-filled fibers was measured using the cut-back method, results are included in Figs. 5(a), 5(b), 6(a), and 6(b). Attenuation measured for the unfilled single-ring fiber was around 0.7 dB/m at 1100 nm and 1500 nm. After filling with water, measured attenuation in the transmission windows of the corresponding order was around 11 dB/m at the wavelength of 600 nm and around 13 dB/m at 800 nm. Attenuation measured for the unfilled double-ring fiber was 0.2-0.3 dB/m at 1100 nm and 1500 nm wavelengths. After water infiltration, it was ∼16 dB/m at 600 nm and ∼15 dB/m at 800 nm. The measurement for the ethanol-filled fibers was not possible in scope of this work due to strong bubbling of the liquid. The discrepancy between the measured attenuation of the fiber and calculated confinement loss is attributed to an influence of higher-order modes excited in the fiber during the experiment.
The fundamental advantage of an antiresonant fiber is that the transmission bands do not disappear when it is filled with liquids. It must be noted that as a result of infiltration, the RI contrast between core and fiber microstructure is dramatically reduced from around 0.45 down to 0.09. Moreover, width of transmission windows is only moderately reduced and their high transmittance is maintained (if ML stemming for the liquid properties is neglected). The width of the transmission window between the 2nd and the 3rd resonance peaks (3rd transmission window) is 453 nm (1256-1709nm) for air-filled single-ring ARF, when defining the width of transmission window as the distance between points with losses of 10 dB/m less than the maximum loss in the resonance peak. It is reduced to 328 nm (712-1040 nm) and 277 nm (632-909 nm) for the case of core filled with water and ethanol, respectively. This behavior is radically different than for PBG fibers where reduction of the RI contrast between core and cladding is followed by significant decrease of transmission band and width of transmission windows is significantly reduced [21–23]. Infiltration of the fibers with liquids also resulted in significant shift of their transmission bands towards shorter wavelengths. Therefore ARF is much better suited for any applications related to the use of fiber with low RI liquids in the core.
When losses of the two fibers are compared, CL of the double-ring ARF is slightly lower than that of single-ring ARF. This result is in agreement with the results reported in [41]. The total losses of both types of infiltrated ARFs are similar. As indicated above, the similarity is an effect of the dominating influence of the ML. The double-resonance peaks observed for the double-ring ARF at around 1000 and 900 nm for water and ethanol infiltration, respectively, are caused by different thicknesses of the larger and the nested capillaries as shown in Figs. 6(b) and 6(c). Due to nearly two times thinner nested capillary wall, the separation of the resonance peaks is small and observable only in the NIR range, where it contributes to spectral narrowing of the transmission bands.
The effect of RI of the liquid on the transmission spectrum has been analyzed next. We have analyzed the evolution of the position and size of the 4th transmission window located between two resonance peaks corresponding to m=3 and m=4 as shown in Fig. 7. Here the width of the transmission window is defined simply as a whole distance between the resonance wavelengths. The analysis was performed for a material with RI varying between 1 and 1.4 to ensure the condition of low RI core in ARF. In the considered RI range, the center of the transmission window shifted by 715 nm, which corresponds to the average sensitivity of ∼1790 nm/RIU. At the same time, the width of transmission window is reduced by 80%. However dramatic reduction of width of transmission window is observed, if refractive index of the liquid is close to the RI of silica glass, especially beyond the value of 1.37. The dashed lines in Fig. 7 are the appropriate function fits, resulting from Eq. (1). When assuming m=3 and m=4 the function takes the form $\frac{{7t}}{{12}}\sqrt {n{{(\lambda )}^2} - n_l^2} $ and $\frac{t}{6}\sqrt {n{{(\lambda )}^2} - n_l^2} $, for the center and width of the transmission window, respectively. The best fit was achieved for parameter t equal to 1.778 µm. Notably, for the lowest RI contrast (RI of the filling material equal to 1.4) Eq. (1) is no longer an accurate approximation of the position of the resonances. This explains why the fitted function does not match the value obtained in simulation.
Fig. 7. Evolution of transmission band central wavelength (a) and width of transmission band (b) placed between two resonance peaks corresponding to m=3 and 4 in single-ring ARF when RI of the core increases from 1 to 1.4.
Next, we analyzed the evolution of the resonance peak wavelengths on small changes in the RI of the infiltrated liquid, assuming different water-ethanol mixtures. The RI values of these liquid mixtures were calculated as weighted averages of the RIs of ethanol and water, based on weight fraction of ethanol in water. As a result, we were also able to observe a shift of resonance peaks toward shorter wavelengths with the RI, which corresponds to an increase of ethanol fraction in the water-ethanol mixture, as shown in Fig. 8. In the considered spectral range, an evolution of the resonance wavelength for two resonance peaks corresponding to m=2 and m=3 was investigated. The RI sensitivity of the approach reaches 4088 nm/RIU and 2623 nm/RIU for the resonance peaks m=2 and m=3, respectively. This high sensitivity allows to consider ARFs as very accurate sensors for measurement of low refractive index of liquids and for determination of the percentage composition of two-component liquid mixtures. We note however, that the RI sensitivity herein is lower when compared to other results reported earlier [48–50]. The increase of capillaries thickness in the ARF cladding can improve RI sensitivity, however, this comes at a cost of narrowing of the transmission windows.
Fig. 8. CL (dashed line) and CL, SSL and ML (solid line) calculated for the single-ring ARF infiltrated with a different mixture of water and ethanol.
3.2 Results of the measurement
The properties of liquid-filled ARFs analyzed numerically above, are in this section verified experimentally. Figs. 9 and 10 show the transmission spectra of both the ARFs when the fibers were used without introducing any liquid into the core. One can note the appearance of some additional peaks resulting from multimode guidance in the investigated fiber and interference between the modes, including the fundamental mode and high-order modes. The transmission bands of the fibers are denoted by their order and additionally indicated by order of resonance peaks that limits their width. As the 1st and 2nd transmission windows were beyond the wavelength range of the experiment, they are not presented. A blue-shift of the resonances for the order predicted theoretically is confirmed experimentally and the corresponding resonances are indicated graphically by the arrows. The calculated CL, indicating transmission windows of the single-ring and double-ring ARFs, shown in Fig. 9(a) and in Fig. 10(a), respectively, were added for a direct comparison between experimental and numerical results.
Fig. 9. Calculated attenuation spectra (considering CL) of unfilled (blue line), water-filled (red line), and ethanol-filled (green line) single-ring ARF (a). Experimentally determined transmission spectra of the single-ring ARF (b).
Fig. 10. Calculated attenuation spectra (considering CL) of unfilled (blue line), water-filled (red line), and ethanol-filled (green line) double-ring ARF (a). Experimentally determined transmission spectra of double-ring ARF (b).
When comparing the spectral locations of resonances a very good agreement between numerical and measurement results can be noticed. There is a small discrepancy in the positions of resonances for the unfilled fibers, which is assigned to the uncertainty in the readout of fiber geometric parameters in the SEM imaging. This impacts the capillary wall thicknesses of the physical fibers taken in the simulations.
For the unfilled single-ring ARF the 3rd and 4th transmission windows have widths of 365 nm and 276 nm with central wavelengths at 1513 nm and 1156 nm, respectively, as shown in Fig. 9. After infiltrating with water, the central wavelengths shift to 816 nm and 602 nm, while the width of transmission bands reached 218 nm and 137 nm (reduction by 40.3% and 50.4%), respectively. In the case of the infiltration with ethanol, the shift progresses and the bands are centered at 746 nm and 547 nm, while their spectral widths reduce by 34.5% and 65.9% respectively.
A similar effect can be observed for the double-ring ARF, as shown in Fig. 10. Here the transmission bands for the unfilled fiber are 372 nm and 166 nm-wide and are located around 1489 nm and 1078 nm, respectively. A strongly reduced width of the 4th transmission window is caused by multiple capillary in the structure, i.e. both large and nested capillaries, which seemingly widens the resonance regions. In the case of infiltration with water, the centers of 3rd and 4th transmission windows are shifted to 837 nm and 629 nm with the widths reduced to 191 nm and 136 nm (reduced by 48.7% and 18.1%), respectively. For ethanol-filled fiber, the 3rd transmission window was shifted to 776 nm central wavelength and its width reached 247 nm (reduced by 33.6%).
3.3 Discussion
Experimentally achieved transmission parameters (central wavelengths and spectral width of transmission bands) for the unfilled fibers and infiltrated with both the liquids are summarized in Table 2. We showed numerically and experimentally that both fibers infiltrated with low RI liquids offer broader transmission bands than the unfilled ones in the same wavelength range. For both water- and ethanol-filled fibers the 3rd transmission band which is located between resonance peaks m=2 and m=3 is broader than 190 nm. Except for a relatively narrow resonance band (37 nm in width for infiltration with water), almost 400 nm-wide transmission band in the visible and NIR spectral range can be obtained for the single-ring ARF. Such a broadband operation of the liquid-filled fiber opens a wide range of opportunities for a number of spectrophotometric applications when changes in absorption characteristics are monitored, or sensor for measurement of liquid mixtures concentrations when the shift of resonance peaks are considered. Comparing to single-ring ARF, double-ring ARF offers a narrower transmission band when infiltrated with liquids, but this fact can be attributed to non-optimized geometrical parameters of the fiber, i.e., thicknesses of the capillaries, and can be further tuned at the stage of fiber fabrication process. Based on both numerical and experimental results, the double-ring ARF features very similar properties in terms of propagation loss and widths of transmission bands.
Table 2. Measured central wavelengths and spectral widths of transmission bands of unfilled and liquid-infiltrated ARFs investigated in this work.
Another significant property of the fiber for optofluidic applications, which should be considered, is its bending loss. Bending of the fiber allows for reducing size of the device. The losses in the bending radius (RB) range of 25 - 40 cm for ARFs with liquid infiltration were numerically calculated at λ = 600 nm and are shown in Fig. 11. The analyzed wavelength is chosen due to relatively low total loss - around 1 dB/m as shown in Figs. 5(b) and 5(c) and in Figs. 6(b) and 6(c) - resulting from considerably low material attenuation of both liquids in the vicinity of this wavelength, Fig. 2(b).
Fig. 11. Numerically simulated bend loss at a wavelength of 600 nm for fundamental mode and ARF with (a) water and (b) ethanol infiltration. The insets show the electric field distribution of the fundamental mode profiles at the bend radius of 25 cm and 40 cm.
The obtained high values of bend loss correspond to the general property of ARF, i.e., bend losses decrease with wavelength [35]. Infiltration with liquid increases the bend loss even more. As no literature reports of bend loss of liquid-filled hollow-core fibers are available, the achieved results cannot be compared to any previous result and the critical bend radius was calculated according to [51]. The obtained values at 600 nm wavelength are ∼28 cm for water-infiltrated single ring fiber and ∼29 cm for ethanol-infiltrated single-ring fiber, and ∼31 cm and ∼32 cm for the water- and ethanol-filled double-ring fiber, respectively. The critical bend radii obtained for the double-ring fiber are 2-4 cm larger due to slightly different geometrical parameters of the fiber. For this reason at the tightest investigated bend radius of 25 cm for water-filled fibers, the bend loss is higher for the double-ring fiber, as shown in Fig. 11(a). The critical bend radius calculation is in agreement with the simulation results showing the fundamental mode profile for a bend radius of around 25 cm becoming highly deformed. With further decrease of the bend radius, the fundamental mode profile splits into 2 parts (double-ring fiber) or locates in the capillary (single-ring fiber). Double-ring ARF allows for lower bending loss in both the cases i.e., infiltration with water and ethanol. Large differences between the results for both liquids correspond to the fact, that for the case of ethanol, the 600 nm wavelength was close to the long-wavelength edge of the transmission window. In such a case, the role of nested capillaries of the structure is even more beneficial. Despite the high loss values obtained, the improvement may be significant, as a number of optofluidic applications require a short section of the fiber, significantly shorter than 1 meter.
4. Conclusions
We have numerically and experimentally analyzed the feasibility of antiresonant fibers as basic elements for optofluidic applications. As it was previously shown, antiresonant fibers filled with liquid maintain their guiding properties and can be used as low index cores, similarly to air-core fibers [32]. In contrast to photonic bandgap fibers, a reduction of contrast does not degrade dramatically the spectral width of transmission bands. Transmission bands are only moderately reduced by 35% in the most cases of near-infrared and visible ranges. Moreover, we observe that transmission bands are significantly shifted toward shorter wavelengths. In the case of ARF filled with water or ethanol, the most interesting windows in the near-infrared and visible ranges are blue-shifted by more than 700 nm. This is very beneficial for spectroscopic and sensing applications. Transmission windows in the visible and near-infrared range 300-1100 nm are broader for the liquid-filled core than air-core ARF. This finding has an important practical implementation, because typically transmission windows of ARFs narrow down with decreasing wavelengths [27,41].
We have compared the properties of liquid core single and double ring ARFs. Both types of ARFs have similar optical properties. Double ring ARF has broader resonance peaks due to existence of double resonances and therefore transmission windows are reduced. On the other had double ring ARFs offer lower bending losses, similarly as was reported previously for an air-core ARF [52]. Therefore single ring ARFs are better suited for applications where short unbend sample of fiber is used, while double ring ARFs can be used in systems where fiber requires bending and very long fiber can be used.
ARFs are interesting for further application in optofluidics. A large core allows easy infiltration with liquids. There is full overlap between an electromagnetic field with guided liquids which ensures strong interaction. These features allow to obtain a long and efficient 1D system for interaction between the light beam and the liquid medium.
Various mechanisms of sensing can be used in parallel with such a platform. A shift of resonance peaks allows to detect changes of the refractive index with a sensitivity beyond 4000 nm/RIU. Attenuation of liquid or scattering can be measured simultaneously in broadband optical windows that corresponds to large transmission bands related to the antiresonant guiding mechanism. This allows to measure even very low concentration of particles in liquid and simultaneously measure their size distribution. This feature can be used for measurements of nanoparticle mixtures and identify their composition and concentrations. Finally, we can also use ARF systems for measurement of absorption in liquids which allows to identify concentration of liquid mixtures.
Funding
Fundacja na rzecz Nauki Polskiej (TEAM NET POIR.04.04.00-00-1644/18); Narodowe Centrum Nauki (OPUS UMO-2016/21/B/ST7/02249); Ministry of Science and Technology (ĐTĐL.CN- 32/19).
Disclosures
The authors declare no conflicts of interest.
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