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Abstract
Liquid microdroplet resonators provide an excellent tool for optical studies due to their innate smoothness and high quality factors, but precise control over their geometries can be difficult. In contrast, three dimensional (3D) printed components are highly customizable but suffer from roughness and pixelation. We present 3D printed structures which leverage the versatility of 3D printing with the smoothness of microdroplets. Our devices enable the reliable creation of microdroplet resonators of varying shapes and sizes in an ambient environment, and our coupling scheme allows for high control over droplet position.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Microdroplet resonators provide a powerful tool in the fields of biology, optics, and physics. In biology, they are useful for sensing applications due to their biocompatibility and versatility [1,2]. They are used in optics to study lasing [3–6] and nonlinear effects [7,8]. In physics, they can be used to excite optomechanical effects [7,9] and for material analysis and sensing [10–12]. Among the benefits of microdroplet resonators is their innate smoothness and versatility.
Currently, common methods for creating and positioning liquid microdroplet resonators include suspending a droplet on a glass stem [9,13,14], placing a droplet on a hydrophobic surface [15], suspending a droplet in another liquid [3,7,16,17], and manipulating the droplet using optical tweezers [16,17]. These methods cover a wide range of complexity, control, and ease of use, with trade-offs among the three.
At the same time, three-dimensional (3D) printing has been used in many fields as a method for rapidly developing custom, inexpensive devices. In recent years, the precision of 3D printing has increased dramatically [18,19], making it an attractive alternative to other fabrication methods. In the field of optics, 3D printing has been used to create WGM resonators [20,21]; however, to date, no research combining the benefits of 3D printing with those of liquid microdroplet resonators has been demonstrated. In this paper, we demonstrate for the first time 3D printed mounts for microdroplet resonators. The flexibility of the design and rapid fabricate-test-redesign cycle allows us to engineer mounts that allow for both increased coupling stability and tailored features such as resonator shape, size, and type of liquid.
2. Methods
2.1 Device fabrication
To fabricate the devices, a custom digital light processor stereolithographic (DLP-SLA) printer with a 365 nm LED light source and a pixel pitch of 7.6 $\mu$m in the plane of the projected image was used [19]. A custom photopolymerizable resin was used that consists of poly(ethylene glycol)diacrylate (PEGDA, MW258) with a 1% (w/w) phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (Irgacure819) photoinitiator and a 2% (w/w) 2-nitrophenyl phenyl sulfide (NPS) UV absorber [18]. The 3D-printed devices were fabricated on diced and silanized glass slides. Each slide was prepared by cleaning with acetone and isopropyl alcohol (IPA), followed by immersion in 10% 3-(trimethoxysilyl)propyl methacrylate in toluene for 2 h. After silane deposition, the slides were kept in toluene until use. In a typical device, each build layer of the print is exposed to a measured optical irradiance of 21.2 mW/cm$^2$ in the image plane for 400 ms, with a layer thickness of 10 $\mu$m. Adjustments to the irradiance and exposure time were made as necessitated by device geometry. After printing, unpolymerized resin in interior regions is gently flushed with IPA, followed by device optical curing for 30 min in a custom curing station using a 430 nm LED having a measured irradiance of 11.3 mW/cm$^2$ in the curing plane.
In some cases, the devices were exposed to an oxygen plasma in a Technics PEII plasma etcher for two minutes at 200 W in order to make the device polymer more hydrophilic. The increased hydrophilicity is maintained while the device is coated in water; however, airborne contaminants cause the polymer to return to its nominal hydrophilicity after 8-10 hours of exposure to air.
2.2 Design considerations
This work builds upon our previous work, in which we combined the capabilities of advanced 3D printing techniques [18] and nano-water bridges [13], to create a device that was coated in a self-sustaining thin film of water [22] (referred to as thin-film devices hereafter), as shown in Figure (1). To make these devices suitable for sustaining high quality optical resonance, several modifications were introduced. The thin-film devices consist of a frustrum base and a rounded head, with a central capillary allowing water recirculation. Fig. (1(a)) shows a scanning electron microscope image of the thin-film device, which clearly exhibits the roughness and pixelation inherent in 3D printed devices. This roughness is eliminated, however when coated in a thin liquid film, as seen in Fig. (1(b)). The device is exposed to an oxygen plasma to make it highly hydrophilic. This allows a thin film to be formed and maintained passively through surface wetting and capillary action. The smoothing film of water can be maintained with high stability over an extended period of time, even in the presence of evaporation, provided there is a reservoir of water at the base of the device [22].
Fig. 1. (a) SEM image of the water recirculation device, which highlights the surface roughness of 3D printed devices. (b) The water recirculation device coated with a thin film of water. (c) The fundamental R Polarized mode of the thin film device with a film thickness of 5 $\mu$m. The 3D printed device is shown in tan, the water in light blue, and air in white. (d) Comparison of optical power inside and outside the 3D printed material as a function of water film thickness.
Nonetheless, the optical quality $Q$ of the device is reduced owing to penetration of the optical mode into the lossy 3D-printed resin. In order to create a 3D printed liquid microdroplet resonator with a high quality factor $Q$, the liquid film must be thick enough that the optical mode does not penetrate the 3D printed material. Figure (1(c)) shows the fundamental mode for light with the electric field primarily oriented in the radial direction (R polarized) for the thin film device with a film thickness of 5 $\mu$m. The 3D printed material is shown in tan, with the water film being shown in light blue, and air in white. To estimate the minimum required thickness, we simulated the mode profile for several film thicknesses and calculated the fraction of the optical power propagating inside the 3D printed material as shown in Fig. (1(d)). We compared this to the power propagating outside the 3D printed material (i.e., in the water and the air). As expected, devices with thicker films have less interaction with the lossy 3D printed material, and the simulation suggests that a minimum film thickness of 8-10 $\mu$m is required for a high Q resonator.
In order to create films of adequate thickness, careful balancing of liquid-liquid cohesive forces and liquid-solid adhesive forces were required, with many design-test cylces. As the liquid spreads across a solid, adhesive and cohesive forces interact, resulting in the liquid edge meeting the solid at a given angle, known as the contact angle, $\theta^{\ast}$, as seen in Fig. (2(a)). The more hydrophilic a material is, the smaller its contact angle will be. A result of the contact angle is corner pinning, a phenomenon in which an advancing liquid cannot proceed around a corner boundary at the native contact angle. Rather, the localized volume of the liquid will increase , with the solid-liquid interface increasing in angle until the critical angle $\theta ^c$ is reached, where $\theta ^c = (180-\phi )+\theta ^*$ and $\phi$ is the angle of the corner boundary relative to a flat surface.
Fig. 2. (a) Example of hydrophobic and hydrophilic innate contact angles $\theta$*. (b) Devices showing the effects of corner pinning. The liquid in (i) does not exhibit corner pinning, and thus the contact angle is $\theta$*. In (ii) the liquid is pinned at the bottom corner, and the angle formed is $\theta _p$ such that $\theta ^* < \theta ^p < \theta ^c$. (c) Our devices are sometimes treated by exposing them to oxygen plasma, which reduces the contact angle.
The surface roughness of the resin resulting from the 3D-printing process creates many corner boundaries. The native contact angle of the 3D printed material was measured to be 43$^{\circ }$, which is too high to overcome the corner boundaries and prevents the devices from wetting completely. By treating the devices with an oxygen plasma, the contact angle was reduced to 11$^{\circ }$, as seen in Fig. (2(c)), allowing the creation of of a stable film that overcomes the corner boundaries. However, owing to the the hydrophilicity of the resulting plasma treated material, the adhesive forces result in a film of water that is < 2 $\mu$m. [22].
To increase the film thickness, we sought a design that would create a larger contact angle while maintaining a droplet shape. Through over 30 design-test cycles we explored the design space of our 3D printed devices. We created designs that implemented microfluidic systems, hydrophobic microstructuring, and unique geometries, all of which were made practical by the rapid fabrication times and design flexibility of the 3D printing process which is not available using standard fabrication techniques. The best results were achieved by leveraging corner pinning at the lower boundary of the device head. To accomplish this, we adjusted our design to include a sharp undercut at the bottom of the device head, another geometry that can be difficult to fabricate using traditional stereolithography techniques. Pinning allows for a larger contact angle at the corner boundary. Figure (2(b)) shows this effect. As liquid is added to the device head, the solid-liquid boundary advances down the side of the head at the innate contact angle $\theta ^*$ as seen in Fig. (2(b(i))). Then, when sufficient liquid has been added, the liquid will pin at the bottom edge of the head as shown in Fig. (2(b(ii))). The resulting contact angle, $\theta ^p$ will obey $\theta ^* < \theta ^p<\theta ^c$, allowing a thicker film to be formed.
Figure (3) shows an example device utilizing our final design. Figure (3(a)) shows a profile view of the 3D printed mount. The device consists of a frustrum base with a chamfered cylindrical head. In an unsupported system, the surface tension of droplets forces them into a spherical shape. To mirror this, the heads of our devices are designed such that the diameter and the height are equal. Figure (3(b)) shows a microdroplet supported by our 3D printed mount. In Fig. (3), paraffin oil (Sigma Aldritch 76235) was used for the microdroplets, though our devices support the use of other fluids. Two constraints are observed in the creation of droplets that allow for control of droplet size. First, the corner boundary at the bottom of the head must not be overcome. When an excess of liquid is added to the droplet, the critical angle is overcome and the liquid flows down the entire device, resulting in a loss of curvature and thickness of the film. The second feature is the smoothness over the top corner boundary of the head. When an insufficient amount of liquid is placed on the head, there is not a smooth interface between liquid on the top of the head and liquid on the sides. This results in a corner at the top of the head. While the film formed in this manner can be thick enough to support the optical mode, the film is less stable than when a smooth interface is formed. These two features result in upper and lower bounds on the droplet size, and these bounds are determined by the size of the 3D printed head. In this way, we can constrain the droplet size to a specific range by scaling the 3D printed mount.
Fig. 3. (a) 3D printed device for supporting microdroplet resonators. (b) Paraffin oil droplet supported by the 3D printed device. (c) Fundamental Z Polarized mode of the droplet. Oil is shown in light blue, and air is shown in white. (d) Visualization of the experimental setup. After an optical fiber is tapered, a 3D printed device supporting a microdroplet is brought close enough to the fiber to enable evanescent coupling. The throughput is monitored to determine resonance qualities.
2.3 Experimental procedure
We create droplets on the device by dipping a bare optical fiber in liquid and then touching the fiber to the head of the device. Figure (3(c)) shows the calculated fundamental mode for light polarized in the vertical direction (Z polarized) for a spherical paraffin oil droplet with a radius of 243.5 $\mu$m, the measured radius of the droplet shown in Fig. (3(b)). Note that the mode size is consistent with that of the thin water film devices, and the droplets form a film approximately 50 $\mu$m thick.
Figure (3(d)) shows the optical coupling setup of our experiments, which used a tapered optical fiber and a tunable laser. The fiber is tapered using a heat-and-pull rig similar to those used in [14,23–25]. To determine the pull length, the optical throughput of the taper was monitored, and the pull is stopped when the fiber becomes single mode [14,25]. The droplets were then carefully brought into close proximity to the fiber to allow coupling into the resonant modes. The coupling efficiency was carefully monitored to ensure the microdroplet did not come into contact with the fiber. On occasions when there was a strong attraction between the fiber and the droplet, or when the two came into contact, the fiber required cleaning. The tapered fiber was rinsed with isopropyl alchohol, then deionized water, and, in some cases, the pulling stages were used to add tension to the fiber. Through this careful cleaning and tensioning of the fiber, we were able to maintain a stable coupling distance between the fiber and resonator, allowing us to control coupling efficiency, adjust polarization, and collect spectral data.
3. Results
Using this stable coupling, we were able to collect many data sets for varied resonator types. As these devices do not have a mechanism to overcome evaporation, non-evaporating liquids were used. Figure (4(a)) shows a profile view of a droplet formed from a water/glycerol mixture. The droplet has a measured radius of 257.9 $\mu$m. Figure (4(b)) shows a resonant peak of the droplet, having a central wavelength of 931.2133 nm and a quality factor of $Q = 1.7 \times 10^6$. The magnitude of the quality factor suggests that there was no penetration of the mode into the 3D printed material.
Fig. 4. (a) Profile view of a water/glycerol microdroplet of radius 257.9 $\mu$m supported by a 3D printed device. (b) Z polarized resonant peak of water/glycerol droplet, fitted with a Lorentzian.
Figure (5) shows resonant peaks of a paraffin oil microdroplet with a radius of 217.8 $\mu$m at both Z and R polarizations.
Boundary conditions from Maxwell’s equations do not allow the R polarized mode to have a continuous electric field across the edge of the droplet. As a result, the R polarized mode will have higher confinement to the resonator than the Z polarized mode. This leads to the R polarized mode having a smaller evanescent field, and thus a lower coupling efficiency, as seen when comparing the two plots of Fig. 5.
The peaks in these plots were fitted to a Lorentzian by using a rate equations model:
We can find the steady state of the rate equations, which is given in Eq. (2). Using this equation, we fit $\left |s_-\right |^2$ to the optical power at the photodetector.
After fitting the peaks, we found their quality factor (Q) using the the relation $Q = \omega _0/2(k_0+k_1)$, given that the linewidth of the peaks is $2(k_0 + k_1)$. The R polarized peak has a quality factor of $Q = 2.23 \times 10^5$ with the resonant wavelength being 1552.19589 nm. The Z polarized peak has a quality factor $Q = 4.55 \times 10^5$ with wavelength 1554.169066 nm. The Q of the resonances varies across the spectrum for each polarization. Throughout our experiments, both polarizations typically have peaks with Q ranging between $2 \times 10^5$ and $5 \times 10^5$.
In another experiment, we were able to observe coupling efficiency as a function of taper-droplet separation distance. Figure (6) shows a single resonant peak of a paraffin oil droplet with data collected at many different coupling distances (d) at the Z polarization. The R polarized data (not shown) is very similar. The spectral data was collected by first positioning the droplet at a distance outside the coupling regime (d $\approx \infty$). Then the droplet was carefully moved closer to the fiber until resonant peaks were observed. Spectral data was acquired for each polarization (Z and R), a process which took just under a minute to complete. Then the resonator was moved by increments $\Delta$d closer to the fiber, first with $\Delta$d = 150 nm, then with $\Delta$d = 30 nm. The process was repeated until the droplet came into contact with the fiber. Contact between the droplet and the fiber provided a reference for d = 0, which we then used to find all the coupling distances. After collection, the data was normalized to the non-coupled transmission spectrum and then fitted with a double-peaked Lorentzian. At a distance of 690 nm from the fiber, the coupling is only about 2% efficient, while at 30 nm the efficiency is near 50%. We note three other features visible in the data. First, there is a slight red shift in the resonant wavelength as the coupling distance decreases, with the peak at the greatest coupling distance being centered at 1554.42233 nm and the peak at the smallest coupling distance being centered at 1554.4402 nm. This effect is likely caused by the thermal dependence in the refractive index of the oil. Second, we see that the resonant peaks are split into doublets, which is due to coupling between modes with significant overlap. In smaller droplets, fewer doublet peaks were observed, since fewer modes are supported by the smaller droplet size. Finally, we observe off-resonance features in the data, which are strongly correlated with the coupling distance. We believe these features indicate coupling to higher-order modes in the droplet.
Fig. 6. Comparison of coupling distance and coupling efficiency using Z polarized light for a paraffin oil microdroplet resonator supported by a 3D printed base.
One of the benefits of using our 3D printed mounts to support the droplets is the mounts’ versatility. In conjunction with our precision coupling method, this versatility allows for various microdroplet resonators to be tested with no changes to the tapered fiber or any of the other optical components, ensuring that all changes are caused by the droplet. The mounts can be used with various liquids, and the size and shape of the mounts can easily be changed, resulting in corresponding changes to the microdroplet resonators. In our experiments, our mounts allowed us to create microdroplets of paraffin oil, silicone oil, and glycerol with diameters between $300 \mu$m and $600 \mu$m. Furthermore, we created mounts with racetrack-shaped cross sections, which supported ellipsoidal droplets of eccentricities as extreme as 0.58.
4. Conclusion
In conclusion, we present a unique 3D printed mount for optical microdroplet resonators. These mounts provide a robust and easy-to-use method for supporting microdroplet resonators while still allowing control over the droplet position, shape, and size. In our experiments, we found that the main deterrent to creating smaller droplets was the difficulty of placing the liquid on the mount by hand. We believe that with a more precise delivery method, the droplet size could be decreased dramatically.
In our future work, we hope to further explore the creation and implications of non-spherical microdroplet resonators, in addition to reducing the size of our mounts. We will also integrate 3D printed microfluidic systems that will allow us to deliver liquid to smaller devices and dynamically change the nature of the liquid used in the microdroplets by changing its volume or introducing analytes.
Funding
National Institutes of Health (R15GM123405-02).
Acknowledgments
We thank Mawla Boaks, Emma Frost, Elise Larson, and Devon Ward for their excellent help with 3D printing the devices. Partial funding was received from the National Institutes of Health.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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