Self-assembled sub-picoliter liquid periodic structures in a hollow optical fiber

Firstly, we fusion spliced one facet of HOF with a cleaved SMF, leaving the other facet of HOF open. We structured the one side closed channel with HOF and SMF. Then, we filled the HOF with deionized (DI) water by the capillary force. According to Washburn’s equation²⁹, the length of the liquid-filled segment (L) by the capillary force is given by

where \(\:\theta\:\) is the contact angle and t is the time for a liquid of viscosity \(\:\eta\:\), and surface tension \(\:\gamma\:\) to a distance L into a capillary of radius r. In our experiments, we used a HOF with a hole diameter of 6.3 μm, L was approximately 1.8 cm for DI water and t ~ 1.0 s, which was consistent with the estimation given by Eq. (1).

After filling the HOF with water, the open-facet of HOF was fusion spliced to another SMF, as schematically shown in Fig. 1(a). A microscopic heat source (MHS) created a hot zone, and it brushed the DI water-filled HOF in the axial direction. We used two types of MHS: a C-type MOT, whose temperature was controlled by the flow rates of propane gas and O₂, and a RMH, whose temperature was controlled by the input electric power. MHS was mounted on a motorized stage, and we traversed the MHS along the axial direction of HOF. MHS parameters were temperature (T), traverse velocity (v), and heating area (A) over the HOF. T was varied in the range of 100 ~ 200 °C, which was measured near the outside surface of HOF using a thermocouple. v was maintained at ~ 1 mm/sec. The C-type MOT provides two hot spots, top and bottom, and each spot has a heating area of A ~ 4 mm². The RMH provided a uniform ring hot zone over the whole circumference of HOF, whose thickness was 1 ~ 2 mm. Here, we took only one unidirectional traverse of MHS. Due to the chaotic behavior of Zone 3 in Fig. 1(b), our systematic discussions focus only on Zone 1 and 2 in the following sections. Note that when we varied T, we repeated the experiments with new samples to take consistent measurements.

Zone 1 formed using a C-type oxyhydrogen torch MHS. (a) Variations in Λ and DC in Zone 1 as a function of MHS temperature. The insets are images taken from a fusion splicer at the given temperatures. In the center of HOF, water segments are shown bright, and dark regions represent the air segments. (b) High-resolution optical microscope images of Zone 1 at T = 212 °C. (MHS: micro heating source, Λ: average period of the water-air structure, Λ′: average thickness of the water segment. DC: Duty Cycle).

As the MHS completed its unidirectional single transverse over the water-filled HOF, self-assembled water-air structures formed along the axial direction, as shown schematically in the bottom of Fig. 1(b). In Zone 1, the water-air periodic structure inside the hole displayed a well-defined liquid droplet-air period (Λ) and a liquid droplet thickness (Λ′), both of which were nearly temperature-independent. The length of Zone 1 ranged from 400 to 500 𝜇m.

Within the temperature range of 106 to 212 °C, we captured microscopic images from a fusion splicer over Zone 1, some of which are shown in the inset of Fig. 2(a). Our periodic structures have pitches around 20 μm and droplet thicknesses of about 10 μm, as summarized in Table 1. To optically analyze these structures, we need a laser wavelength (λ) that matches the structure pitch (Λ)³⁰, which corresponds to a CO₂ laser. However, CO₂ lasers are strongly absorbed by both the silica cladding of the HOF and the water in the core, leaving little to no interferometric information. Additionally, the cylindrical surface of the HOF causes collimated incident light to focus, only to rapidly defocus upon exiting, resulting in secondary or even tertiary interference, which makes the analysis much more complex.

To address this, we used an advanced fiber optic fusion splicer, which has a feature that allows us to manually adjust the focus. This can either be aligned with the cladding surface for cladding splicing or centered on the core for core-aligned splicing³¹. By continuously controlling the focal point, we were able to capture optimal images for our experiments. In Fig. 2(a), average values of and the duty cycle (DC), Λ′/Λ, are plotted as a function of MHS temperature (T). The variation remained narrow to 22 to 25 𝜇m, and DC was between 0.45 and 0.50. This periodic structure was surprisingly regular despite the MHS temperature doubling. Figure 2(b) shows a high-resolution optical microscopic image of Zone 1 at T = 212 °C, with a clear distinction between water segments and air.

In Zone 2, we observed periodic water-air structures where both Λ and Λ′ consistently changed with T. The length of Zone 2 was similar to that of Zone 1. We captured microscopic images from a fusion splicer over Zone 2, and some of these images are shown in the inset of Fig. 3(a). More detailed measurement results are summarized in Table 2. In Fig. 3(a), the average values of Λ and DC are plotted against T. As T increased, both of them decreased monotonically. The Λ decreased from 182.8 to 38.7 𝜇m, which is about a five-fold reduction in the temperature range of 106 to 212 °C. DC decreased from 0.94 to 0.44, more than halving over the same temperature range. Notably, larger water droplets formed at the lower temperature range of about 100 to 130 °C, with a DC of 0.85 to 0.93. In this lower temperature range, the air segment length was significantly short, about one-tenth to one-ninth of the water droplet length. As T increased beyond 180 °C, the air segment length increased significantly, dropping the DC to 0.5 or less. Another noteworthy observation is that the periodic structures of Zone 1 and Zone 2 started to converge as T exceeded 180 °C. In Fig. 3(b), a high-resolution optical microscopic image of Zone 2 at T = 212 °C shows the regularity of the periodic water-air structure. The similarity between Fig. 2(b) and Fig. 3(b) confirms the convergence of the periodic structures in Zones 1 and 2 at higher temperatures.

For the measurements in Zone 2, we further estimated the volume of individual water droplets. Here, we approximated the water droplet as a circular plate whose diameter is the same as the hole diameter (D) of HOF, and its height is the average Λ′ of the given periodic structure to have the volume of \(\:V_droplet=\pi\:(D/2)^2\Lambda’\:\). Figure 4(a) illustrates the variation in the water droplet volume of water droplets within Zone 2 in response to MHS temperatures. It is noted that the water droplet volume monotonically decreased with increasing temperature. It is assumed that the liquid droplet broke into smaller volumes at a high temperature to accommodate the relative temperature difference between the preceding MHS and the cooled HOF segment following behind. Drawing upon the preceding findings, we demonstrate the capability to generate liquid droplets spanning from hundreds of femtoliters to a few picoliters in volume within the periodic structure in HOF.

Zone 2 formed using a C-type oxyhydrogen torch MHS. (a) Variations in Λ and DC in Zone 2 as a function of MHS temperature. The insets are images taken from a fusion splicer at the given temperatures. In the center of HOF, water segments are shown bright, and dark regions represent the air segments. (b) High-resolution optical microscope images of Zone 2 at MHS temperatures T = 212 °C. (MHS: micro heating source, Λ: average period of the water-air structure, Λ′: the average thickness of the water segment.).

(a) Volume of the water droplet with temperature varying from 212 °C to 106 °C in Zone 2. (b) Isopropyl alcohol (c) Ethanol.

In Fig. 4(b)~(c), we further investigate how the periodic structures changed with types of liquids. We chose isopropyl alcohol and ethanol such that their boiling temperatures T^B satisfied T^B_water (100℃) > T^B_{isopropyl alcohol} (82.3℃) > T^B_ethanol (78.4℃). For the lower boiling temperature liquids, we observed a notable increase in the air segment length Λ′ = 29.7 𝜇m in Fig. 4(b) and Λ′ = 5.8 𝜇m in Fig. 4(c). These changes subsequently reduced DC = 0.18 in Fig. 4(b) and DC = 0.08 in Fig. 4(c), which were not observable in water cases in Fig. 2, and Fig. 3. It is observed that the low T^B liquid provided larger air segments to reduce DC. which is related to boiling and recondensation process for the liquid in the experiments. These observations showed a high potential to flexibly vary the liquid-air periodic structures by proper choices of liquid’s physical characteristics, which is being further pursued by the authors.

To assess the optical properties of water-filled HOF, we conducted transmission measurements using a white light source (Yokogawa AQ4305) and an optical spectrum analyzer (Agilent 86142 A). In Fig. 5(a), a pristine HOF exhibits the LP11 mode cut-off wavelength, 𝜆_cutoff ~ 1290 nm before the water filling. When the water was filled, 𝜆_cutoff shifted toward a shorter wavelength near 850 nm. In a step-index fiber with the core refractive index n₁, cladding index n₂, and the core diameter D, 𝜆_cutoff is defined as below³².

HOF has a ring core with two asymmetric interfaces: the inner interface with the air at the central hole and the silica cladding. When the water replaces the air in the central hole, the difference in the refractive index between the ring core and the central hole significantly decreases to shift 𝜆_cutoff to a shorter wavelength.

After making a water-air periodic structure, we measured the transmission spectrum and subtracted it from that of HOF filled with water. Here, the structure had all Zone 1, Zone 2, and Zone 3. It was prepared at T = 212 °C so that the periodic structures in Zone 1 and Zone 2 converged to each other. The results are shown in Fig. 5(b). We observed two band-rejection filter characteristics, as shown in arrows 1 and 2. Band-1 has a broad bandwidth of ~ 150 nm with a maximum rejection efficiency of 2.5 dB, while band-2 has a full-width half maximum (FWHM) of ~ 30 nm and a maximum rejection of ~ 6 dB. The ring core surrounds the air-water periodic structure, and the periodic arrangement modulates the refractive index to form a long-period grating (LPG)³³. The phase matching condition between the core guided LP^core₀₁mode and the cladding modes LP^clad_lm is given below for a grating period of Λ_grating.

In conventional UV-induced LPGs, \(\:\varLambda\:\) _grating is typically between 200 ~ 500𝜇𝑚 and the index modulation 𝛥n ~ 10⁻⁴ to 10⁻³, to have band rejection of 10 ~ 25 dB in the optical communication window near 1550 nm. Note that in HOF, the light is guided in the ring core, and the periodic water-air droplet can provide a refractive index modulation. However, the refractive index modulation 𝛥n was not estimated since the net interaction between the light in the ring core and the water segments was not fully understood yet. Compared to conventional UV-induced LPGs, our water-air structure in HOF has a fraction of periodicity, where its high harmonics may satisfy the phase-matching condition with a lower band rejection efficiency. In further studies to characterize the band-rejection characteristics of the proposed device, it might be necessary to include multimode interference effects³⁴ among the cladding modes of HOF³⁵ excited at SMF-HOF splices. Non-ideal adiabatic mode transformation at SMF-HOF splices can excite cladding modes, which can interfere with one another to make the output transmission spectrum much more complex than the ideal phase-matching cases. The authors are pursuing the investigation of these band rejection characteristics to clarify their origin.

(a) Comparison of transmission spectra of HOF with water and without water. The water-filled HOF segment length was ~ 2 cm. (b) Relative transmission for a water-air periodic structure. Here, we subtracted the transmission of HOF with the water-air periodic structure from that of HOF filled with water. Two band rejection filter characteristics are indicated by arrows 1 and 2.

Furthermore, we have Zones 1, 2, and 3 in the prepared HOF, and non-uniform periodicity variations could affect the mode-coupling to reduce the band rejection efficiency. Even though the performance as a band rejection filter was not comparable to prior UV-induced LPGs, our experiments showed a potential to use the liquid-air periodic structure in optical applications. Notably, the liquid-air structure maintained its periodicity under vibration but showed a significantly high response to temperature changes (10 ~ 80 °C, a clinically important temperature range) and bending. Despite its liquid nature, the proposed structure showed significant resilience against external physical perturbations, such as temperature, humidity, and vibrations. It is noteworthy that the liquid structures were embedded inside HOF, which is made of silica. The outer diameter of HOF silica cladding was ~ 125 mm, while the central hole, where periodic liquid structures were present, had diameter of ~ 6 mm. This large ratio in both surface area and the volume imply that the responses to external thermo-mechanical perturbations would be mainly determined by the silica cladding. We have not observed any significant variations of the periodic structures during the experiments and after several days in the lab environment. While ambient temperature fluctuations potentially induce the instability through thermal expansion or contraction of both the HOF and the liquid droplets^36,37, conventional electronic temperature control with a suitable packaging can minimize such effects.

In this report, we used liquids without specific optical functionalities. By incorporating optically functional materials into the liquid, the proposed structure could have unique photonic applications. For example, dissolving an optical dye or quantum dots in a high refractive-index liquid could create an array of optical gain media, coupled through the circular ring core of the HOF. Each droplet could act as a micro-optical liquid cavity³⁸, with lasing characteristics mainly governed by whispering gallery modes³⁹. This structure offers a novel way to explore the laser dynamics of serially coupled laser cavities, pumped by the HOF’s ring core. Compared to solid grating structures embedded in optical fibers, the periodic liquid droplets in our design could be more sensitive to external factors like temperature, strain, and acceleration, opening up new possibilities for optical sensing applications. The authors are pursuing further sensor applications of the proposed liquid-air structure in HOF.