In recent years, tapered optical fibers [1–8], through which guided light can interact with micro/nanoscale systems, have found a wide range of applications, including nanophotonics [9–11], microfluidics [12,13], and micro/nanoscale sensing [14–17]. In these applications, free-space optical beams are limited in spatial resolution due to the diffraction limit. In addition, they suffer from the limited focal depth of objective lenses and from diffraction, especially for object features that are comparable with or smaller than the light wavelength. On-chip optical waveguides [18] provided a solution to these challenges, but they impose additional steps or difficulties on the fabrication process, and their positions cannot be adjusted after fabrication. Tapered optical fibers, however, with diameters in micrometers or submicrometers, can deliver guided light into and out of tightly spaced micro/nanoscale systems with readily adjustable positions and high spatial resolution.

Various geometries of tapered optical fibers have been developed and investigated. The most studied geometries include straight tapered fibers [12,19–22], dimpled tapered fibers [9,23], tapered fiber knots [5,6,16,17,24], tapered fiber coils [1,3,25,26], and tapered fiber loops [7,8,10]. Each of these geometries has its own unique advantages and, hence, has found various applications. For example, tapered optical fibers with circular geometries, such as loops [7,8], coils [1,3,25,26], and knots [4,6,16,17,24], are stand-alone optical resonators. Their high optical quality factors ($Q$, up to 97,260 [6]) allow them to find applications in sensing [16,17,25] and fiber-based lasers [27–29]. Optical trapping and sorting of particles have been mainly demonstrated with straight tapered fibers [12,13,20,22]. Tapered optical fibers have been particularly useful for nanophotonic device characterization. It is challenging for a straight tapered fiber to couple light to a monolithic in-plane device (See Supplement 1). The surrounding area of the device has to be etched down [19], which makes the fabrication process more complex. Dimpled fibers [9,23], which have a depression in the tapered region, and fiber loops [10] have been used to characterize tightly spaced in-plane devices.

Difficulty in the fiber taper fabrication varies. Straight fiber tapers are generally fabricated with the heat-and-stretch method [19,23], which is straightforward. The fabrication process of tapered fiber knots is relatively complex and requires delicate handling of the fiber tapers. In most of the demonstrated knots [4,16,17,24], one tapered fiber arm was broken during the fabrication process and reconnected to a separate straight tapered fiber after the knot was formed, resulting in poor mechanical stability. One recent work [6] demonstrated fiber knot fabrication without breaking the fiber. Tapered fiber coils were fabricated by wrapping a straight tapered optical fiber around a cylindrical rod, which limited their spatial flexibility and agility [1,26]. Dimpled fiber tapers [9,23] were fabricated by wrapping the fiber taper around a mold while heating the taper, a process that could be time consuming and that lacks controllability and repeatability. Tapered fiber loops have been fabricated by introducing internal torsional stress [8,10] or by bending [5,7] the straight tapers into a loop shape. Due to the residual torsional or bending stress in the loops, the two fiber arms may intersect with each other at an angle, resulting in low optical $Qs$ [30]. In most of the work, the shapes of the tapered fiber loops were not permanently fixed, but rather temporarily maintained by either the torsional stress or van der Waals and electrostatic forces, causing the loops to be mechanically unstable [6,10]. In order to make the loops stable and to achieve a high optical $Q$, the size of the loop was kept large (a few hundred micrometers to a few millimeters) [7,8], and sometimes the loop was fixed by glue [31] or by being embedded in a gel matrix [32].

In this Letter, we demonstrate a robust and repeatable method for fabricating tapered fiber loops and helices. The fiber loops and helices are mechanically stable without the need for any glue or gel matrix. Both the loop and helix geometries have a readily controllable diameter ranging from 15 to 500 μm. The tapered fiber probe can switch between the loop and helix by adjusting the axial tension along the fiber. Nanophotonic device characterization and microfluidic particle trapping have been experimentally demonstrated to showcase the applications of these fiber probes.

We started the fabrication process by making a straight fiber taper from a regular Corning SMF-28 fiber with a heat-and-stretch method [23], using an alcohol lamp as the heat source. The optical transmission was monitored in real time, and the tapering process was stopped right after the transmission became stable (see Supplement 1 for more details). All the fiber tapers in this work had a diameter ranging from 600 to 2 μm with tapered lengths of 35–40 mm and optical transmissions of 70%–95%. There was one rotational fiber holder (Thorlabs, RSP1 & SM1F1-250) on each side of the fiber taper, and each holder was fixed on a separate linear translation stage, as shown in Fig. 1(a). This setup allowed the control of both the separation and orientations of the two fiber arms. We relaxed the tension in the straight fiber taper by moving the two fiber arms closer by 1 mm to avoid breaking the fiber in the following steps. The two rotational fiber holders were rotated in opposite directions by 360° to introduce torsion in the fiber taper. We further moved the two fiber arms closer until the loop was formed in the center of the tapered region, as shown in Fig. 1(d). At this point, the diameter of the loop was around 300 to 500 μm. We shrunk the loop size by moving the two fiber arms apart. The final loop diameter could be continuously adjusted by the stage positions, and loop diameters as small as 15 μm were demonstrated experimentally.

 

Fig. 1. (a) Fabrication setup. The rotational fiber holders are on both sides of the fiber. (b), (c) SEM images and (d)–(f) optical microscope images of fabricated tapered fibers. (d) Fiber loop before annealing. (b)–(e) Fiber loop after annealing. (c), (f) Fiber helix. Scale bars: 15 μm.

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Similar to most of the previous work [5,7,8,10], loops at this stage had poor optical quality factors and were mechanically unstable. Even a small air current could cause considerable changes to loop geometry and optical transmission. Different from the previous work, we used a flame to anneal the loop for a few seconds. The diameter of the flame (a few millimeters) was much larger than the loop diameter ($<100\mathrm{\mu m}$), so the whole loop was heated and annealed without moving the flame. This post-annealing released the torsional stress in the fiber loop and hence “fixed” the loop shape, as shown in Figs. 1(b) and 1(e).

Fiber loops after post-annealing were mechanically stable. The annealed fiber loops could not be unwrapped by airflow. In fact, for all the fiber loops we fabricated and tested, the loops’ geometries were reserved even when they were broken by a strong airflow. According to the free spectral ranges of the transmission spectra, the change in loop size was around 1% over 43 h (See Supplement 1).

When we applied additional tension to an annealed fiber loop by moving the fiber arms apart, the loop was stretched into helical shapes, with the two fiber arms separated from each other, as shown in Figs. 1(c) and 1(f). Fiber helices were even more stable than loops, thanks to the additional tension. Because the loop geometry was fixed in the annealing process, the geometry of the fiber probe could be readily switched between a helix and a loop by controlling the tension. There was no additional optical loss for both annealed fiber loops and helices, when compared with the straight fiber tapers.

After the fiber loop was fabricated, we turned the two fiber arms into a U shape and mounted the fiber loop on a homemade fiber holder, which could adjust the tension along the fiber and hence could switch the geometry between a loop and a helix. This way of holding a fiber helix allowed it to serve as a probe that could easily reach out to devices for light coupling, similar to previous fiber dimples [9].

Swept-wavelength spectroscopy was used to characterize the optical properties of tapered fiber loops and helices. Light from a tunable laser source (Newport, New Focus 6700) was coupled into one end of the fiber, and the optical transmission was measured from the other end by a photodetector (Thorlabs, PDA50B). The transmission spectra of a loop before annealing, one after annealing, and a fiber helix are shown in Figs. 2(a), 2(b), and 2(c), respectively.

 

Fig. 2. Transmission spectra of (a) a fiber loop before annealing, (b) a loop after annealing, and (c) a fiber helix. No resonance was observed in the helix and the fiber loop without annealing. Multiple optical modes were observed in the annealed fiber loop. Left inset in (b) shows the zoomed-in transmission spectrum of one doublet. The doublet corresponds to two optical modes with the same mode number but different polarization states. An intrinsic optical quality factor of 32,500 is obtained from the curve fitting [blue solid line in the left inset in (b)]. Insets on the right in (a)–(c) are the optical microscopy images of the corresponding tapered optical fibers.

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Multiple optical modes were observed in the annealed fiber loop [Fig. 2(b)], with an intrinsic optical quality factor $Q=\mathrm{32,500}$ and a finesse of 137. The post-annealing created a smooth transition region at the intersection of the two fiber arms [Fig. 1(e)], which reduced the scattering loss and resulted in a high $Q$. Compared to on-chip silicon resonators [23,33], which can provide higher $Q$ and finesse, the tapered fiber loops are stand-alone optical resonators that do not require separate devices for optical input and output. No optical resonance was observed in the fiber loops without annealing [Fig. 2(a)] and the fiber helices [Fig. 2(c)]. The two arms of a loop without annealing intersected each other at a sharp angle [Fig. 1(d)], resulting in a high scattering loss and, hence, no observation of optical modes.

Thanks to the evanescent tail of the guided light that extends outside the fiber tapers, both the fiber loops and helices are useful tools for delivering light into and to interact with micro/nanoscale systems, with each having its unique advantages. The high $Q$ enables a high optical energy buildup in the annealed fiber loops, which helps increase the sensitivity in near-field sensing applications [16,17]. The resonances in fiber loops can also potentially be used for fiber-based laser applications [27–29]. By contrast, the fiber helices have high optical transmission, high mechanical stability, and no optical resonances, which made them ideal probes for characterizing the optical and mechanical performances of integrated photonic devices. In the rest of this Letter, we will focus on the experimental demonstration of two particular applications of the fiber helices—nanophotonic device characterization and microfluidic particle trapping.

A tapered fiber helix was used to characterize nanoscale ${\mathrm{Si}}_3{\mathrm{N}}_4$ tuning fork cavity optomechanical sensors. The fabrication and optomechanical coupling principles of these on-chip tuning fork devices have been published in our previous work [33]. Briefly, the sensor consists of a tuning fork nanomechanical resonator and a 15 μm diameter microdisk optical resonator. The device was fabricated on a 250 nm thick stoichiometric ${\mathrm{Si}}_3{\mathrm{N}}_4$ film. The prongs of the tuning fork are 150 nm in width and 20 μm in length. The tuning fork and microdisk are separated by a gap of 150 nm, enabling near-field optomechanical coupling. The mechanical displacement of the tuning fork modulates the optical whispering gallery modes of the microdisk, which in turn causes fluctuation of the optical transmission in a fiber probe coupled in the near field to the microdisk. In this paper, we used a fiber helix as the optical probe, and the experiment was carried out in air. The laser was input from one arm of the fiber helix and coupled from the lowest position of the helix to the microdisk, and the optical transmission of the fiber helix was read out by a photodetector.

The SEM and the optical spectrum of the tuning fork device are shown in Figs. 3(b) and 3(c), respectively. A $Q$ above a million was readily obtained. The output of the photodetector was sent to an electronic spectrum analyzer (ESA), and the mechanical spectrum of the thermal motion of the tuning fork was obtained and is shown in Fig. 3(d). Both the in-phase and out-of-phase mechanical modes were clearly observed, well above the noise ground. The mechanical quality factors in this work were lower than previously published results [33] due to higher damping in air compared with that in vacuum. The fiber helix is mechanically stable thanks to the additional tension, which allows precise control of the separation between the fiber and the microdisk, bestowing on the helix the capability of characterizing nanophotonic devices in air. Furthermore, similar with fiber dimples [9,23], the helical shape allows near-field light coupling between the fiber and the in-plane device, while preventing the two fiber arms from touching the substrate. This can be seen in Fig. 3(a), where the fiber helix curves away from the device plane on both sides (See Supplement 1). Compared to that of the fiber dimples, the fabrication process of the fiber helix is straightforward, controllable, and repeatable.

 

Fig. 3. (a) Computer-generated schematic of optical coupling between a tapered fiber helix and a microdisk resonator; the yellow arrows indicate the light propagation direction. (b) SEM image of the tuning fork cavity optomechanical device. Inset shows an optical microscopy image of the device being tested, and the fiber helix is coupled in the near field to the microdisk resonator. The scale bars are 10 μm. (c) Transmission spectrum of the tuning fork device. A $Q$ of $1.08\times {10}^6$ was readily obtained with the fiber helix probe. (d) Mechanical spectrum of the same tuning fork device. The two mechanical modes correspond to the in-phase and out-of-phase tuning fork modes, respectively. The device was tested in air, thanks to the mechanical stability of the fiber helix.

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In addition to characterizing nanophotonic devices, the fiber helix is also a useful tool in microfluidics for radiation-pressure-based particle trapping and manipulation. To demonstrate this capability, we used the fiber helix to optically trap and propel 4.64 μm diameter microscale silica beads in water. An illustration of the trapping is shown in Fig. 4(a). The evanescent field of the fiber helix applies two components of optical forces to the nearby beads: a gradient force that attracts beads towards the fiber and a scattering force that propels the beads along the fiber. The fiber helix can thus be used as a helical-shaped optical conveyor belt for particle transportation. The experimental setup is shown in Fig. 4(b). The U-shaped fiber helix was mounted onto a three-dimensional translation stage and a one-dimensional rotation stage for position and orientation control. A 500 mW continuous-wave laser at 1330 nm was used as the light source. The trapping experiment was monitored and recorded on an inverted microscope platform.

 

Fig. 4. (a) Schematic of a silica bead trapped and moved (shown as a green arrow) by a fiber helix, like a microscale roller coaster. The free beads move in random directions (shown as red arrows) because of Brownian motion. (b) Schematic of the microfluidic trapping setup. (c–h) Successive pictures showing the trapping results. The light guided in the fiber helix propagated from top to bottom. The red arrows indicate the position of the bead being trapped and propelled. The time interval between each adjacent frame is 3 s.

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The optical trapping experimental results are shown in Figs. 4(c)–4(h). A single silica bead with a diameter of 4.64 μm was trapped and subsequently propelled along the fiber helix, like a microfluidic roller coaster. We note that particle trapping in water can be influenced by the transmission of the fiber helix. The optical transmission of the fiber helix in water was around 20%. The transmission was considerably lower than that in air, which could make the trapping unstable. This reduced transmission in water might be caused by bending-induced optical loss [30] in the helix. Another possible reason is that the tapered fiber geometry is only adiabatic in air, and not in water. Work is underway to optimize the fiber tapering process in order to increase the transmission efficiency of the tapered fiber helix in water.

Compared with straight fiber tapers [12,13], the geometry of the fiber helices allowed optical transportation of microparticles along more complex, three-dimensional trajectories. In a stationary fluidic environment, the fiber helix can be used to selectively approach, trap, and propel a particular particle lying on the substrate from a group of particles, which is challenging for straight fiber tapers. In a microfluidic channel, the fiber helix can be used to prefocus particles to the center of the channel, as they pass through the channel. The geometry of the fiber helix allows for much more efficient particle focusing than straight fiber tapers. This prefocusing is important for effective subsequent optical detection or interrogation, such as flow cytometry [34] and cell stiffness measurements in optical stretchers [35].

In conclusion, we have demonstrated tapered fiber loops and helices with a straightforward and repeatable fabrication method. Due to a post-annealing process, the fiber loops and helices exhibited high mechanical stability. The measured optical quality factor ($Qo$) of the fiber loops was as high as 32,500. In addition, the fiber geometry could be readily switched between a loop and a helix by adjusting the mechanical tension. A fiber helix was used to characterize both optical and mechanical resonances of a monolithic nanophotonic device. In addition, we also used a fiber helix to optically trap and propel microscale silica beads in a fluidic environment. Thanks to their repeatable fabrication process, outstanding mechanical stability, and the ability to probe in-plane devices in the near field, fiber loops and helices can find a wide range of applications, including device characterization in nanophotonics, microfluidic particle manipulation, and optical sensing.