Laser writing of parabolic micromirrors with a high numerical aperture for optical trapping and rotation

There has been a great interest^1,2 in developing optical lab-on-a-chip platforms in recent years as they are portable, robust, and scalable. Integrating multiple optical components has allowed great leaps in analyzing and sensing biological specimens.^3–5 One such powerful technique is optical trapping, which allows for the 3D manipulation of objects by using the transfer of momentum of light.⁶ As a well-established technique, it has found uses in single-molecule force spectroscopy,^7,8 particle sorting,^9,10 and sensing in both the far and near field.¹¹ An optical trap is characterized by the trap stiffness k, assuming that the trapped particle is in a harmonic motion.¹² Furthermore, it is possible to transfer the angular momentum of light to anisotropic particles through external or internal birefringence, inducing rotation when trapped by a circularly polarized beam.^13,14

The system must meet several requirements to allow for the confinement of the subject specimen in an optical potential in the far field: the particle must be of a higher refractive index than the surrounding medium and, for optimal performance, should be of a size comparable to that of the wavelength of the trapping beam.^15,16 In addition, a tightly focused beam is necessary to provide a large enough restoring force for trapping. A bulky, high numerical aperture (NA) and high magnification microscope objective is required, with multiple drawbacks. For one, the objective size makes the integration difficult, and the high magnification brings a small field of view, limiting the number of simultaneously manipulated samples. These and the high cost of high-NA objectives have resulted in the poor integration and scalability of the optical trapping platform.

Multiple schemes have been developed in the last two decades to address these issues to enable on-chip trapping.¹⁷ These include creating an optical lattice through interference,⁹ near and far field trapping enabled by fibers,¹⁸ as well as working to replace the microscope objective with a high numerical aperture but a much smaller optical lens equivalent, capable of similar focusing performance. The best performing have been metasurfaces,¹⁹ placed at the bottom of the microfluidic chamber for trapping in reflection,^19,20 grafted on top for trapping in transmission²¹ or placed on tips of optical fibers.²² With NA ranging from 0.56 to 1.2,^19,23 they can reach a performance almost matching that of high NA objectives, all while keeping a small footprint on the order of a square millimeter. Another option is the Fresnel diffractive elements.^24–26 However, for both systems, the fabrication process is time-consuming and expensive. Additionally, the small and delicate optical elements, which make up these lenses, can be easily damaged. Depending on the geometry, they will be wavelength-specific and polarization sensitive. Microlenses and micromirrors,^27,28 however, do not suffer from these problems. By imprinting pre-made lenses,^29,30 arrays of traps with relatively high NA have been fabricated. While convenient, this method is limited by the variety of lenses available to consumers. Chemical treatment can also be combined with other techniques to etch smooth mirrors into the substrate.^31–34 A method often combined with etching is silica CO₂ laser ablation, a well-established glass treatment process whereby a short (∼100 ns) pulse is used to form an approximately hemispherical mirror.³⁵ Silica is exceptionally absorbent for radiation above 4 μm,³⁶ meaning that a focused beam of CO₂ laser with a wavelength of 10.6 μm can evaporate the glass directly at the focus, melting the glass around it. The vapor pressure from the evaporation then creates a melt front, which travels away from the center until the glass re-solidifies, the entire process occurring in under a second.^37,38

Here, we present a significantly faster, more customizable technique for creating trapping arrays with high numerical aperture. Using a continuous wave (CW) CO₂ laser, we write micromirror structures through ablation. First, we expose the glass substrate for ∼100 ms to a focused TEM₀₀ mode of the laser, resulting in a nearly parabolic mirror profile.³⁹ The glass is then coated with a thin gold layer to achieve a smooth reflective surface. We show that by tuning the ablation parameters, the diameter and depth of the micromirrors can be controlled accurately based on the required application. To demonstrate the platform's viability, we use a high NA micromirror to trap 5 μm vaterite and 2 μm silica particles suspended in D₂O. As shown in Fig. 1, we use a hybrid optical setup that interchangeably allows trapping by a high NA objective or micromirrors. While not necessary to enable trapping, it is convenient for this demonstration, as trapping can be performed passively by illuminating using a collimated beam. We characterize the optical performance of the mirror and then proceed to use it to reverse the direction of rotation of a vaterite particle. Through this, we demonstrate the potential of micromirrors as a simple-to-fabricate and versatile lab-on-chip optical platform.

At the core of the setup for the fabrication of the micromirrors is the CO₂ ablation laser (Synrad 48-KA CW 25 W) [see Fig. 2(a)]. We controlled the duration of the ablation using a mechanical shutter (Thorlabs SC10) and set the average power through the duty cycle of the laser (∼8%, corresponding to ∼1.2 W at the sample plane). The glass sample was mounted vertically on a motorized 3D stage (Newport, Picomotor actuators). A visible diode laser (λ_D = 660 nm) with an adjustable divergence was used as a guide to precisely locate the x, y, and z positions of the focused CO₂ laser beam on the sample. For monitoring, we used a CMOS camera (Thorlabs DCC1545M) in conjunction with a collimated light-emitting diode. The shutter, CO₂ laser, and stage were synchronized and controlled using LabVIEW to rapidly fabricate customized arrays of micromirrors, as shown in Fig. S1. The automation also allowed for writing continuous channels in glass, as shown in Fig. S2. The beam profile of the CO₂ laser was spatially filtered using an aperture and finally focused onto the glass sample to a size of ∼100 μm using a ZnSe plano–convex lens (f = 15 mm), which also served as the imaging lens for the camera. After ablation, the sample was transferred to an electron beam evaporator (Edwards AUTO 306), where a 2 nm thick adhesion layer of NiCr was deposited, followed by 150 nm of gold. We characterized the micromirrors using optical microscopy and a surface profiler. We used optical microscopy to extract the mirror diameter and depth [Fig. 2(b)] and a contact mode profilometer (Veeco Dektak 150 with a 12 μm stylus) to accurately map the profile [Fig. 2(c)]. The figure shows the micromirror used for particle trapping with depth z = 7.3 μm and diameter D = 56.5 μm. The mirror profile resembles the Gaussian intensity profile of the CO₂ beam with deviations due to the long pulse durations used, meaning that a parabola more accurately describes the profile.³⁷ The exact scan geometry and alternative view of the profile are shown in Fig. S3. In total, 357 micromirrors with diameters of ∼40–120 μm were fabricated and characterized. We considered five parameters: the laser power, the position of the focus relative to the substrate, the duration and the number of exposures, and the size of the aperture [shown in Fig. 2(a)]. We found that the final profile of the micromirror was relatively insensitive to the duration and number of exposures, indicating that the shortest exposure created by the shutter (∼50 ms) was longer than the ablation timescale. In addition, the diameter of the micromirrors initially displayed a simple linear relationship with the laser power, which plateaued as the mirrors' diameter approached that of the focused beam. Finally, the depth of the micromirrors reached an upper bound at higher laser power (∼2 W), where the rapid change in temperature gradient resulted in cracks forming at the bottom of the mirrors. Furthermore, the diameter and the depth of the micromirrors had a nearly linear dependence on the aperture diameter. The exact position of the focus had the most substantial effect on the micromirror profile. If the mirror's center evaporated too quickly, it formed a secondary curvature inside the first, as the melt front would not move fast enough. Hence, the beginning of each fabrication included a calibration step where the exact z-plane was chosen based on the mirror shape observed through the CCD after ablation. For further information on mirror ablation, see the supplementary material Figs. S4–S7.

It is important to note that this comparison with lenses is only valid for mirrors where $θ ≤ π / 2$⁠, whereas for an infinitely extending parabolic mirror, θ approaches π.

The hybrid setup used for trapping and rotating the particles is shown in Fig. 4. The trapping laser (Omicron LuXx) had a total power of 230 mW at 830 nm and was linearly polarized (Thorlabs LPNIRB050), after which the beam was expanded by ten times using a telescope. The laser beam could then follow one of two paths depending on whether trapping by the objective (path 1) or micromirrors (path 2) was required. Path 1 (marked in blue in Fig. 4) uses a half-wave plate to match the beam's polarization to that of a spatial light modulator (SLM, Meadowlark 1920 × 1152) for moving the tweezers. The beam was, then, sent through a 4f system conjugating the plane of the SLM and the back focal plane of an inverted water immersion objective (Olympus UPLANSAPO, 60×, NA = 1.2). The use of the SLM was not necessary but allowed for the convenient alignment of the particle and mirror illumination when switching paths. For the rotation of particles, the beam was circularly polarized using a quarter-wave plate to allow for the transfer of angular momentum to birefringent particles. Path 2 (marked in red) could be switched using a pair of mirrors placed on a motorized linear stage (Thorlabs ELL20). The beam was then focused onto the back of the microscope objective (Fourier plane) using a lens (f₄ = 300 mm) and the quarter-wave plate for circular polarization. In this way, the incident beam onto the micromirrors would be collimated and circularly polarized. The illumination consisted of a fiber-coupled LED, and the imaging used a CCD camera (Basler acA640–750um) with an 800 nm short-pass filter in front of it.

The microfluidic chamber containing the mirrors and particles was prepared by placing a 100 μm thick vinyl spacer with a hole in the middle to create a well around the mirrors, then depositing the solution of particles, placing a coverslip on top and sealing the edges using nail varnish. The schematic is shown in Fig. S8. Particle loading on micromirrors consisted of first trapping a particle (either silica or vaterite) using the high-NA microscope objective (path 1), then delivering it ∼5 μm below the focal point of the micromirrors. Next, path 2 was switched, resulting in a collimated beam illuminating the entire micromirror, forming the optical trap (see the supplementary material video SV1). The handover from objective to micromirror would take <1 s.

To further show the potential of our platform as a versatile alternative to a microscope objective, we demonstrated its ability to reverse the preferred direction of rotation of a ∼5 μm piece of vaterite. While microvaterite has been shown to reach rotation speeds of up to 5 MHz in vacuum¹³ and up to 400 Hz in water,⁴⁶ the rate is highly dependent on the power at the sample plane and the particle size (typically in hundreds of nanometers). In our demonstration, we place a quarter-wave plate before the objective at 45° with respect to the direction of linear polarization to ensure circular polarization and verify the circularity using a polarimeter (Thorlabs PAX1000IR1) before and after the objective. We first trap the vaterite using objective-enabled optical tweezers and observe the clockwise rotation of the particle, as shown in the bottom panel of Fig. 5(b) and SV2. We then switch the optical path to trap using the micromirror and observe the particle change in the direction of rotation, as shown in the top panel of Fig. 5(b) and SV3. To simplify the trapping process, we used relatively large pieces of vaterite (∼5 μm diameter), which were quite asymmetric. These conditions, combined with the low power of our system (<30 mW vs typical W used⁴⁷), mean that we observed the particle exhibit a preferred axis of rotation. This is clearly seen in SV2 and SV3 and manifests through a non-uniform rotation rate. We have also considered the role of the angle of reflection on the circular polarization of the reflected beam, as while the effect of reflection from a plane is understood, the case is not as clear for a curved surface, such as a parabolic mirror.⁴⁸ While this would be a concern for extreme angles, as can be seen in Fig. S3(b) most of the reflections from the mirror happen for $θ < 45 °$⁠, where significant differences between s and p components of the polarization could become apparent.

In conclusion, we describe the rapid and versatile fabrication process of 357 high-NA parabolic micromirrors with diameters in the range of 80 μm using CW CO₂ laser ablation of silica, followed by gold coating. We show that the micromirrors can be used as a substitute for microscope objectives for optical trapping. We thoroughly analyze the trapping performance at multiple powers, yielding an average stiffness of $k ⊥$ = (52 ± 1) pN/μm/W for a mirror with an effective NA = 1.08 comparable with values in the literature.^16,49 Finally, we demonstrate the ability of the mirror to counter-rotate a vaterite particle. The mirror geometry is promising in creating integrated dual-beam trapping.⁵⁰ As closely spaced arrays of arbitrary size can be fabricated, this scheme is a promising technique for on-chip particle trapping and sorting and optical lattices for atoms.^51–53 Similar schemes have also shown great promise regarding the parametric cooling of particles in vacuum.⁵⁴ With an added laser writing capability, we envisage that guiding particles in arbitrary circuits by 2D trapping in channels would now be feasible in this platform.