Resonator nanophotonic standing-wave array trap for single-molecule manipulation and measurement

Nanophotonic tweezers represent emerging platforms with significant potential for parallel manipulation and measurements of single biological molecules on-chip. However, trapping force generation represents a substantial obstacle for their broader utility. Here, we present a resonator nanophotonic standing-wave array trap (resonator-nSWAT) that demonstrates significant force enhancement. This platform integrates a critically-coupled resonator design to the nSWAT and incorporates a novel trap reset scheme. The nSWAT can now perform standard single-molecule experiments, including stretching DNA molecules to measure their force-extension relations, unzipping DNA molecules, and disrupting and mapping protein-DNA interactions. These experiments have realized trapping forces on the order of 20 pN while demonstrating base-pair resolution with measurements performed on multiple molecules in parallel. Thus, the resonator-nSWAT platform now meets the benchmarks of a table-top precision optical trapping instrument in terms of force generation and resolution. This represents the first demonstration of a nanophotonic platform for such single-molecule experiments.


Device Parameters
In this section, we provide device parameters related to the nanophotonic aspect of the resonator-nSWAT. The trapping laser wavelength is = 1.064 μm. The Si 3 N 4 waveguide has a cross-section of 750 nm x 250 nm, embedded in SiO 2 . The fundamental TM-like mode is guided in the Si 3 N 4 waveguide to achieve higher manipulation forces to trapped beads 1 . The effective index of refraction ( ) and the group index of refraction ( ) of this TM-like mode at 1.064 μm is 1.57 and 1.91, respectively ( Supplementary Fig. 2). Group index is calculated using: . The total waveguide length of the resonator loop is = 8600 μm, including a 110 μm long fluid pool section where the top surface of the Si 3 N 4 waveguide is exposed to water. In the fluid pool region, two copies of the nSWAT device are brought close to each other to perform parallel single-molecule manipulations. The center-to-center separation between the two parallel waveguides in the fluid pool region is 2.6 μm, corresponding to an effective index of refraction difference ∆ = 0.000071 between the symmetric and anti-symmetric modes. The index of refraction of water at 1.064 μm is set as 1.3239 3 . For a 110 μm long fluid pool region ( ), the energy crosstalk between two copies of the nSWAT can be calculated to be: 1 ∆ = 0.05% ( Supplementary Fig. 3). This corresponds to minimal expected crosstalk between the two waveguides. We also did not observe any detectable crosstalk between the two copies of the nSWAT in our experiments.

Return laser power
In an nSWAT device, some of the light input to the device may be ultimately returned to the waveguide input by retracing the same path as that of the input light. This section describes a method for monitoring this return laser power.
Consider a single copy of resonator-nSWAT ( Supplementary Fig. 6). For a perfect 50/50 splitter, light will be eventually returned to the input port (port 1), without any light exiting port 2. In reality, the 50/50 splitter is often slightly imbalanced, and in that case, some light also exits port 2. Below, we show that the output light at port 2 is proportional to this return laser power and thus can be used for monitoring the return laser power.
Here, we denote the electrical fields of laser inputs (and outputs) of the 4 ports of the splitter as (and ), 1, 2, 3, 4, with port 1 being the incident waveguide of the nSWAT device. We also denote the loss coefficient and phase change of half the bus-waveguide loop where translocation microheaters are located as and respectively. Furthermore, we denote the input and output electrical fields of the resonator as and , and thus,

,
where is the transmission coefficient of the resonator coupler, is the loss coefficient of the resonator loop, is the phase change of the resonator loop.
We then have the relation between and , and between and : Under unit incident electric field from , we have the following relation: In general, for parallel waveguide couplers: where is the propagation constant in a single waveguide, ∆ is the difference between the symmetric and anti-symmetric modes in the two coupled waveguides, and is the length of the total coupling region.
Plug in 1, 0, and , we get: this section, we calculate the coupling coefficients of the optimized resonator nSWAT from measured resonance response curves.
Denote ( 1,2,3,4) as the complex electric field amplitudes of the 4 ports of the coupling region of the resonator loop ( Supplementary Fig. 5). We have the following relations: , , , where 1, : self-coupling coefficient.
: single-pass amplitude transmission coefficient of the resonator loop. We can derive the relation between the input and output laser intensities of the bus waveguide as: We can thus calculate the extinction ratio (ER) as: Since the return laser power is proportional to | | , ER can thus be obtained by the return power measurement: According to Bogaerts et al. 4 , Finesse can be expressed as: Thus, from the measured ER and Finesse, we can calculate values of and . Critical coupling occurs when . Under this condition, ER → ∞ and Finesse reaches a maximum.
Supplementary Fig. 7a shows an example of a measured resonance response curve of the laser power at the flood pool at 0.06 W input laser power, from which Finesse is measured to be: Finesse = 12.89. The bottom panel of Supplementary Fig. 5b shows the resonance curve of the return power for the same device at 0.06 W input laser power, from which ER is measured to be: ER = 30.92. We thus get: ( , ) = (0.91, 0.87), corresponding to slight under coupling condition; or ( , ) = (0.87, 0.91), corresponding to a slightly over coupling condition. Both scenarios are very close to the critical-coupling condition.
Another method to estimate and is to fit the resonance curves of the local laser intensity and the return power. The laser intensity at the fluid pool region is: Fitting this laser intensity by: with being a proportionality constant and the phase at the peak of resonance (top panel of Supplementary Fig. 5b), we obtain = 0.81. This agrees very well with the above calculation using ER and Finesse, which gives = 0.80.
We can also obtain values for and by fitting the return power resonance curve by: , with being a proportionality constant (bottom panel of Supplementary Fig. 5b). This fitting yields: ( , ) = (0.91, 0.86) or (0.86, 0.91), which is again consistent with the above results.
All of the above results consistently show that the resonator-nSWAT device under investigation is working at a condition very close to critical coupling.

Determination of the Q factor of the resonator
The quality ( ) factor of the resonator can be calculated using the measured local light intensity at the fluid pool region as we tune the resonator microheaters (Fig. 2a, middle section). At a low input laser power (0.06 W), the resonance curve is close to being symmetric, as shown in Supplementary Fig. 7 (see also Fig. 2a). From this measurement, we can calculate the finesse of the resonator Finesse , and then the factor using 4 : • Finesse. For 0.06 W input laser power, the measured finesse is 12.89, corresponding to a factor of 2.0 x 10 5 . At high input powers, the light induced thermo-optic effect leads to broadening of the resonance peak (enlarging FWHM) while keeping the FSR unchanged, thus reducing the finesse and the factor. This effect is discussed in more details in the reference 4 . Consequently, the measured finesse and factor indeed decrease as input laser power increases ( Supplementary Fig. 7).

Thermal drift reduction
To facilitate high-precision image tracking of the trapped beads, the image of the trapping region on an nSWAT chip must remain focused. However, during an experiment, heat is introduced to the chip during modulation of the microheaters, resulting in thermal expansion of the chip and therefore drift of the focused region. To minimize this drift, we have used the following method for heat dissipation. We have machined the sample stage out of a large aluminum block (27 mm x 58 mm x 80 mm) and suspended it from the instrument by two glass connections ( Supplementary Fig. 4a). The glass connections provide thermal insulation from the rest of the instrument, while the large aluminum block serves as a heat sink. An nSWAT chip is then placed onto the sample stage by a custom-made vacuum chuck.
To estimate the temperature rise due to the microheaters, we performed a COMSOL simulation ( Supplementary Fig. 4a). The simulation shows that the temperature rise at the fluid pool region is ~ 1.3 o C above the ambient temperature. The temperature across this flood pool region is highly uniform, with only 0.014 o C temperature difference across this region.
We then measured the vertical stage drift with and without the suspended stage ( Supplementary Fig. 4c). Our data show that the suspended sample stage efficiently reduces the focal drift of an nSWAT chip to less than 200 nm during microheater modulation.
In addition, during a typical stretching or unzipping measurement, the total power applied power to the two microheaters of each nSWAT remains constant, and the power applied to the microheaters of each nSWAT is also tuned to near the resonance and then kept constant. These settings further ensure the thermal stability of nSWAT devices during measurement.

Gravity flow cell
A gravity feed system is used to control the flow in the nSWAT flow cell. The gravity feed system consists of two reservoirs (each made by a 2 mL plastic vial) at an elevated height with two Tygon tubings connecting to the entry and exit ports of a resonator-nSWAT chip on the sample stage. One of the two reservoirs is mounted on a vertical translational stage controlled by a stepper motor. The stepper motor is controlled by a home-built control system to tune the relative height between the two reservoirs. This gravity flow cell control system enables accurate and responsive control of flow speed in the nSWAT trapping region, especially in the low-speed regime: -100 μm/s to 100 μm/s.

Test device for the reset speed of translocation microheaters
To detect the speed of the trap array relocation by translocation microheaters, a test device was fabricated (Fig. 2c). The test device consists of a Mach-Zehnder interferometer (MZI) controlled by two microheaters (Supplementary Fig. 9b) that were fabricated to have the same dimensions to those of the nSWAT translocation microheaters (Supplementary Fig. 9a). As the analysis below shows, the output from this test device can be used to assess the speed of the trap array relocation by translocation microheaters in a resonator-nSWAT device.
In this section, we use to denote the electrical field at an input and to denote the electrical field at an output. For a resonator-nSWAT device ( Supplementary Fig. 9a), under unit incident electric field ( =1 and =0), and a phase tuning difference ∆ between the two translocation microheaters, we have the following relation: where is the loss coefficient in one arm of the MZI, and is the phase change of that arm.
Using the relation between ( , ) and ( , ) for a 50/50 splitter: where is the coupling length of the resonator coupler, and ≡ ∆ , we have: Thus the time-averaged light intensity of the standing wave at position in the fluid pool is proportional to: where ≡ | | . For position located at an antinode before tuning, the light intensity is proportional to: 1 cos ∆ .
For the test device ( Supplementary Fig. 9b), the laser power output from port 1 or "output 1", is proportional to | | and is directly coupled to a tapered fiber connected to a balanced photodetector (Thorlabs PDB440C). When the same input power and phase tunings from translocation microheaters are present at the MZI, ( , ), ( , ), and ( , ) remain the same, while ( , ) depends on the length of the 50/50 coupling region : 1 .
Plugging in and , we get: The output laser power at port 1 is proportional to: Therefore, the dependence on phase tuning difference ∆ between translocation microheaters for the standing wave position of a resonator nSWAT and for the output of a MZI shares the same form ( Supplementary Figs. 9c and 9d). We can thus use the test device to measure the response time of translocation microheaters in a resonator-nSWAT.

Trap stiffness calibration and force determination
The trap stiffness along the waveguide ( axis) is calibrated by recording the Brownian motion of beads trapped on a resonator-nSWAT as a function of the trapping laser intensity. The two scatters of the light intensity samplers of the resonator measures the laser intensity traveling in the clockwise (grating 1) and counterclockwise (grating 2) directions (Supplementary Fig. 11a  and 11b). Thus, the standing wave intensity is estimated to be proportional to the average of these two scattering signals. The trajectories of the trapped beads are analyzed using the power spectrum method, including a correction for blurring and aliasing introduced by the camera 5 . Briefly, the resampled power spectrum is fitted by a modified Lorentzian function where is the thermal energy, is the corner frequency, is the sampling frequency, is the camera integration time, is the drag coefficient, and is the inherent position detection error. Fitting this modified Lorentzian function (truncating at 4) yields , , and ( Supplementary Fig. 11d). The trap stiffness, is then calculated by: 2 .
For each nSWAT device, the average trap stiffness for a mixture of the anti-dig and streptavidincoated 380 nm polystyrene beads is measured at several laser powers. The trap stiffness is plotted versus the average IR intensity from the scattering gratings, and a linear fit gives the stiffness per unit intensity ( Supplementary Fig. 11e).
The force exerted on the bead from the resonator-nSWAT trap during an experiment is determined by using a force map generated from finite element COMSOL simulations and the trap stiffness measured above. A 3D COMSOL simulation was performed for a 380 nm polystyrene sphere at 5 nm above a 250 nm × 750 nm Si 3 N 4 waveguide as a function of and displacements from the trap center at 1 W trapping power (defined as the sum of powers in two directions) ( Supplementary Fig. 12). This map is then scaled based on the measured stiffness per unit intensity. Subsequently, the measured ∆ and ∆ displacements of the bead and the local intensity are then used to look up the and forces exerted on the bead by the trap from the force map. The resulting force along the tether can be calculated by sin cos , where is the measured angle of the DNA tether relative the nSWAT waveguides ( Supplementary Fig. 12; Fig. 3). Force along the tether can also be calculated from a single force component alone, by sin ⁄ or cos ⁄ , but with amplified noises at values close to 0 or 2 ⁄ , respectively. The vast majority of traces in this work were calculated by using both force components. In rare scenarios where one force component showed significant image tracking errors, the other force component was used to calculate the force along the tether.

Elastic properties of DNA and theoretical predictions for stretching and unzipping of DNA
dsDNA and ssDNA parameters are both calibrated in a conventional optical tweezers setup in a calibration buffer (15.5 mM Tris-HCl pH 7.8, 0.2 mg/mL BSA, 0.5 mM EDTA, 2.5 mM NaCl, 0.77 mM NaN 3 ), which is nearly identical to the buffer used for experiments on the nSWAT.
The dsDNA parameters were calibrated by stretching 11.5 kb dsDNA, and the ssDNA parameters were calibrated by unzipping a DNA template with 2.2 kbp arms (total) and 4.1 kbp unzipping segment with DNA hairpin end-capping. dsDNA persistence length and dsDNA elastic modulus are obtained by fitting a modified Marko-Siggia model to measured force-extension curves of 11.5 kb dsDNA molecules using a nonlinear least-squares method 6 . ssDNA persistence length and ssDNA elastic modulus are obtained by fitting to the force-extension curve section after dsDNA is fulling unzipped, with the dsDNA extension portion calculated by the modified Marko-Siggia model using previously determined dsDNA parameters and the ssDNA extension portion calculated by a freely-joined-chain model 7,8 . The calibrated parameters were: dsDNA persistence length 56.0 0.7 nm, dsDNA elastic modulus 1199.3 26.2 pN, ssDNA persistence length 0.9 0.01 nm, and ssDNA elastic modulus 669 14 pN.
For comparison, we also directly fit the force-extension curves of single dsDNA tethers shown in Fig. 3c. These fits yielded a persistence length 51.0 1.8 nm and a stretch modulus 1085.0 83.2 pN, which are in a reasonably good agreement with those calibrated above.
These calibrated parameters were used to generate the expected theory curves and calculate the number of base pairs of unzipped DNA (Figs. 3, 4 & 5). The theoretical prediction of dsDNA stretching was calculated using these parameters and the modified Marko-Siggia model. The unzipping theoretical prediction was calculated using an equilibrium statistical mechanical model, which uses a partition function to calculate the expected force and expected number of base pairs unzipped at a given DNA extension 8,9,10 . For this calculation, we used the calibrated dsDNA and ssDNA parameters, the known DNA sequence of the unzipping segment, and an estimated temperature of 25 o C at the specimen plane. Supplementary Figure 6. Return laser power. This schematic explains the notation used under Methods for the analysis of the return laser power. Here, only a single copy resonator-nSWAT is shown. Light is coupled to the device through port 1. For a perfect 50/50 splitter, light will be eventually returned to port 1 without any light exiting port 2. However, for an imbalanced 50/50 splitter, some light also exits port 2. Under Supplementary Methods, we show that the return laser light to port 1 may be monitored by the light output at port 2.

Supplementary
Supplementary Figure 8. Rapid microheater reset allows for an increased manipulation force.
a, Simplified and normalized equation of motion during trap reset. To achieve long-distance motion of the trapped beads, the microheater is reset rapidly after each slow translation of a trap by the trapping potential periodicity, . is the maximum force attainable from nSWAT, proportional to the laser intensity in the waveguide. The trap must be reset fast enough so that the bead remains quasi-stationary during the reset, even under the influence of a force from a DNA molecule attached to the bead . To simplify the equation of motion, is approximated as a constant for small bead displacements during the trap reset. The position of the trap after the onset of the reset follows an exponential decay with a time constant , with ≡ being the normalized time constant and being the viscous drag coefficient of the bead. The bead velocity versus bead position in the absence of a trap reset is shown. There is a single stable equilibrium position and an unstable equilibrium position. An increase in shifts the curve up, bringing the two equilibrium positions closer together until the disappearance of the stable equilibrium. b, Example bead trajectories. The equation of motion was solved with the MATLAB ode45 numerical solver. For each , the at which the bead just arrives at the unstable equilibrium position, is determined. For values of < , the nSWAT array moves fast enough that the bead remains quasi-stationary, resulting in a successful trap reset, while for > , the bead follows the standing wave array trap during the reset, corresponding to an unsuccessful reset.
c, Maximum force that can be achieved during trap reset. A rapid trap reset time increases the achievable force for stretching DNA . These curves provide the maximum force from DNA beyond which a bead can no longer be stably trapped. Therefore a fast trap reset time is critical to achieving a high force during nSWAT long-range transport. d, Power spectrum density of a trapped bead position along at local laser intensity = 1.4 × 10 8 IR intensity unit (IRU). The spectrum was fit by a modified Lorentzian function after corrections of camera blurring and aliasing effects (for details, see Methods section). The fit yielded the corner frequency 273 Hz, the viscous drag coefficient 8.7 × 10 -6 pN sec/nm, and the inherent position detection error 25 nm 2 . Thus, the trap stiffness is 0.015 pN/nm. e, Measured stiffness along versus local IR intensity. Each data point represents the mean stiffness measured from multiple beads trapped on the nSWAT (N = 12). The error bars indicate SEMs. The fitted slope is (1.06 ± 0.01) × 10 -10 pN/nm/IRU. This stiffness calibration was performed for each device that was used for force measurements. Over 30 devices were calibrated, and their calibrations had similar results.