Optical tweezers

Optical tweezers use a single laser beam focused through a high-numerical-aperture microscope objective to trap a particle, typically a silica or polystyrene bead 0.2–5 µm across, in three dimensions near the focus. A particle with a higher refractive index than its surroundings is pulled toward the region of highest intensity, and it behaves as if held by a weak spring. The forces are in the piconewton range, set by laser powers of tens to hundreds of milliwatts, and the trap stiffness is typically of order 0.01–1 pN/nm, roughly proportional to the power. That range matches the forces of single motor proteins and DNA molecules, making optical tweezers a standard tool of single-molecule biophysics. Arthur Ashkin and colleagues demonstrated the single-beam gradient trap in 1986, and Ashkin shared the 2018 Nobel Prize in Physics for the work.

Gradient and scattering forces

Light carries momentum, so a particle that refracts or reflects it feels a force. Two components act. The scattering force, from light reflected and absorbed, pushes the particle along the beam. The gradient force, from refraction in an intensity gradient, pulls a high-index particle toward the brightest point. For a particle much smaller than the wavelength it is proportional to the particle's polarizability times the gradient of the intensity. A stable three-dimensional trap requires the axial gradient force to exceed the scattering force just beyond the focus, which needs very steep focusing: water- or oil-immersion objectives with NA of about 1.2–1.4 are standard. The numerical aperture calculator relates NA to the focusing cone angle. Underfilling the objective's back aperture lowers the effective NA and weakens the axial trap, so the input Gaussian beam is usually expanded to fill or slightly overfill it.

Lasers and wavelength

For biological samples the usual source is a 1064 nm Nd:YAG or ytterbium fiber laser. Near-infrared light is absorbed less by cells than visible light, which reduces photodamage, and is absorbed only weakly by water, though water's absorption coefficient at 1064 nm still heats the focus by several kelvin per watt. Multiple traps can be made by time-sharing one beam with acousto-optic deflectors or by shaping the wavefront with a spatial light modulator, a form of computer-generated holography.

Measuring position and force

The bead position is measured by imaging the forward-scattered trapping light (or a separate detection laser) onto a quadrant photodiode placed conjugate to the back focal plane of the condenser, which gives nanometer resolution at bandwidths of tens of kilohertz. Within the linear region of the trap, typically a displacement of about 100–200 nm, the force is $F = -kx$. At $k = 0.05$ pN/nm, a 100 nm displacement corresponds to 5 pN, comparable to the stall force of the motor protein kinesin, about 6 pN.

Calibration from the power spectrum

The most widely used calibration treats the trapped bead as a Brownian particle in a harmonic well. Its position power spectrum is a Lorentzian whose corner frequency is

$$f_c = \frac{k}{2\pi\gamma},$$

with the Stokes drag coefficient

$$\gamma = 6\pi\eta r.$$

For a 1 µm diameter bead ($r = 0.5$ µm) in water with $\eta = 1.0$ mPa·s, $\gamma \approx 9.4 \times 10^{-9}$ N·s/m. A trap stiffness of 0.05 pN/nm ($5 \times 10^{-5}$ N/m) then gives

$$f_c = \frac{5\times10^{-5}}{2\pi \times 9.4\times10^{-9}} \approx 840\ \text{Hz}.$$

Fitting the measured spectrum gives $f_c$ and hence $k$ once $\gamma$ is known. A cross-check uses equipartition, $k\langle x^2\rangle = k_B T$: at 298 K this predicts an rms displacement of about 9.1 nm at the same stiffness. Detectors must be sampled well above $f_c$, usually at tens of kilohertz, to resolve the spectrum.

Pitfalls

Viscosity depends strongly on temperature, and laser heating raises the local temperature, so $\gamma$ and the calibration shift with power. Near a coverslip the drag increases (Faxén's correction), and a bead a few radii from the surface can be calibrated wrongly by tens of percent if bulk drag is assumed. Spherical aberration from an oil-immersion objective focusing deep into water weakens the trap with depth. The detector sensitivity in nm per volt depends on bead size and must be calibrated for each bead type. Stage and pointing drift appear as spurious motion; dual-trap geometries reduce it.

Common questions

How strong are optical tweezers?

Forces of a few piconewtons are routine and the maximum for micron-sized beads at hundreds of milliwatts is of order 100 pN. That is enough to stretch DNA and stall motor proteins.

Can optical tweezers trap metal particles or atoms?

Small metal nanoparticles can be trapped because their polarizability is large, although absorption heats them strongly. Neutral atoms are trapped by the same dipole force in optical dipole traps, usually with laser light tuned away from an atomic resonance and combined with laser cooling.

Why is 1064 nm used rather than visible light?

Cells absorb less light near 1064 nm, so photodamage is reduced, and high-power, low-noise lasers are readily available at that wavelength. The cost is some heating of water, which is lower at 1064 nm than at longer infrared wavelengths.

References: A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, Opt. Lett. 11, 288 (1986); K. C. Neuman, S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004); K. Berg-Sørensen, H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).