Optical Tweezers

Definition

Optical tweezers trap a microscopic particle at the focus of a tightly focused laser beam, using the force light exerts as it bends through the particle. No physical contact, no wires, no fields you can see — just a beam of light holding a glass bead or a living bacterium suspended in water, steerable in three dimensions by moving the focus.

The key force is the gradient force, which points up the intensity gradient toward the brightest point of the beam:

F_grad  ∝  α · ∇I        (α = polarizability, I = light intensity)

Because the focus is the brightest point in the whole beam, the gradient force pulls a transparent, higher-index particle straight into the focal spot and holds it there. The forces involved are on the order of piconewtons (10⁻¹² N), and the trap works for objects roughly 10 nm to 10 µm across. Arthur Ashkin invented the technique at Bell Labs and won the 2018 Nobel Prize in Physics for it.

How it works

Light carries momentum. When a photon is refracted — bent — as it passes through a transparent bead, its momentum changes direction, and by Newton's third law the bead receives an equal and opposite kick. Sum that kick over the trillions of photons hitting the bead each second, and you get a steady, controllable force.

Two distinct forces emerge from this momentum exchange:

• The gradient force comes from refracted photons. A higher-index particle acts like a tiny lens. When it sits off-center in a beam whose intensity varies across space, more light is bent on the bright side than the dim side, and the net recoil pushes the particle toward the brightest region. In a focused beam, that region is the focus — so the gradient force is restoring in all three directions, behaving like a 3D spring.
• The scattering force (radiation pressure) comes from reflected and absorbed photons, which dump their forward momentum into the particle and shove it downstream, along the direction the beam travels. This force always pushes the particle out of the focus, away from the lens.

A stable trap exists only where the backward axial pull of the gradient force beats the forward push of the scattering force. That balance is delicate: a loosely focused beam has a weak gradient and the scattering force wins, so the particle just gets blown downstream. The trick Ashkin found in 1986 was to focus the beam very steeply with a high numerical-aperture (NA ≳ 1.2) microscope objective. A steep focus means a steep intensity gradient, which boosts the gradient force enough to overpower scattering and create a genuine 3D trap — the single-beam gradient trap that defines optical tweezers today.

Near the center, the trap is well approximated by a linear spring:

F = -k · x        (k = trap stiffness, x = displacement from center)

This single relation is what turns optical tweezers into a force meter. Measure how far the particle has been dragged from the center, multiply by the calibrated stiffness, and you have read the force acting on it.

The two competing forces differ in almost every property — origin, direction, and what they scale with:

Property	Gradient force (the trap)	Scattering force (radiation pressure)
Photon process	Refraction (bending)	Reflection & absorption
Direction	Up the intensity gradient, toward the focus	Forward, along the beam direction
Role in the trap	Restoring — holds the particle	Destabilizing — pushes particle out
Scales as (Rayleigh)	∝ radius³ · ∇I	∝ radius⁶ / λ⁴ · I
Sign depends on	Index contrast m = n_p/n_m (flips if m < 1)	Always positive (forward)
Needs	High numerical aperture for a steep focus	Present even in a loosely focused beam

A worked example — trapping a 1 µm bead

Take a 1 µm polystyrene bead (refractive index n_p ≈ 1.57) suspended in water (n_m ≈ 1.33), held by a 1064 nm laser delivering about 200 mW into the focus of a 1.3 NA objective. A typical resulting trap stiffness is:

k ≈ 0.1 pN/nm

Now suppose a molecular motor (say a kinesin walking along a microtubule) tugs the bead 60 nm off center before stalling. The force it generated is:

F = k · x = 0.1 pN/nm × 60 nm = 6 pN

Six piconewtons — and that number is biologically meaningful: kinesin's measured stall force is right around 5-7 pN. The optical trap didn't just hold the bead, it measured the strength of a single protein machine taking 8 nm steps. To put the scale in perspective, 6 pN is the weight of about a single red blood cell. The trap resolves displacements well under a nanometer, so you can watch individual 8 nm steps as discrete jumps in the position trace.

The other side of the balance: the scattering force on the same bead at 200 mW is also of order a few piconewtons, pushing the bead a small fraction of a micron downstream of the geometric focus — which is why the stable equilibrium point sits slightly past the focus, not exactly at it.

Regimes and variants

How you calculate the force depends on how the particle size compares to the wavelength:

Regime	Particle size vs. wavelength λ	How the force is modeled	Force scaling
Rayleigh regime	radius ≪ λ (e.g. ≲ 50 nm)	Particle is a point dipole in the field; F_grad ∝ α∇I	∝ radius³ (volume)
Mie / intermediate	radius ≈ λ (~0.5-2 µm)	Full electromagnetic Mie scattering; numerical	Complex, resonance ripples
Ray-optics regime	radius ≫ λ (e.g. ≳ 5 µm)	Trace refracted/reflected rays, sum momentum change	Roughly ∝ power, geometry-dependent

Beyond the single-beam trap, the same physics powers a family of tools:

• Holographic optical tweezers. A spatial light modulator splits one laser into dozens of independently steerable traps, letting you arrange many particles at once.
• Counter-propagating dual-beam traps. Two opposed beams cancel each other's scattering force, so you can trap with lower NA and even hold low-index or larger objects.
• Doughnut (Laguerre-Gaussian) beams. A dark center surrounded by a bright ring traps low-index particles (bubbles, hollow shells) that are repelled from bright regions, and carries orbital angular momentum that can spin the particle.
• Optical stretchers. Two opposed weakly focused beams squeeze a cell to measure its elasticity instead of just holding it.

Common pitfalls and misconceptions

• "The laser pushes the bead in like a tractor beam." No — radiation pressure (the scattering force) always pushes away from the lens. The trapping is done by the gradient force, which is a sideways/backward pull toward the bright focus, sourced by refraction, not pushing.
• "You can trap anything with a strong enough laser." If the particle's refractive index is lower than the medium's (an air bubble in water), the gradient force flips sign and ejects it from the focus. More power makes it worse, not better. Low-index objects need dark-center beams.
• "Bigger particles trap better." Only up to a point. Above ~10 µm the focal spot is smaller than the particle, gravity and drag dominate, and the trap can no longer cage the object. Below ~10 nm the gradient force (∝ volume) is too weak to beat Brownian motion.
• "More power is always safer for the sample." Power raises stiffness but also local heating and photodamage. Ashkin's key insight was that wavelength choice matters more than brute force: ~1064 nm sits in water's transparency window, so it traps by refraction with minimal absorption, keeping cells alive.
• "The equilibrium point is at the focus." Not quite. The scattering force shifts the stable trapping point slightly downstream of the geometric focus, by a distance that grows with laser power.
• "It's a static hold." The bead is in constant thermal motion, rattling inside the trap by tens of nanometers. That Brownian jitter is not noise to be eliminated — it is the calibration signal used to measure the trap stiffness.

Applications

• Single-molecule biophysics. Measuring the force and step size of motor proteins (kinesin, myosin, RNA polymerase), and the mechanics of DNA — including the famous ~65 pN overstretching transition where the double helix unzips.
• Cell manipulation. Sorting, positioning, and even fusing individual living cells without touching them; holding a single bacterium under a microscope for hours.
• Microrheology. Dragging a trapped bead through a fluid or gel to map its local viscosity and elasticity at the micron scale.
• Atomic and quantum physics. Optical tweezer arrays now hold individual neutral atoms in vacuum as qubits for quantum computers and simulators.
• Colloidal physics. Assembling and studying ordered arrays of microspheres to probe phase transitions and self-assembly.
• Microsurgery and microfabrication. Combining trapping with cutting lasers to dissect cells or build microscopic structures piece by piece.

Derivation and performance analysis

In the Rayleigh regime (particle much smaller than the wavelength), the particle behaves as an induced point dipole with polarizability α. The time-averaged gradient force on such a dipole in a varying field is:

F_grad = (α / 2) · ∇⟨E²⟩  =  (n_m · α / 2c·ε₀) · ∇I

so the force genuinely tracks the gradient of intensity, ∇I, exactly as the headline relation says. The polarizability for a sphere of radius a is:

α = 4π·ε₀·n_m² · a³ · (m² - 1)/(m² + 2),   m = n_p / n_m

Two facts fall straight out of this. First, α ∝ a³ — the trapping force scales with the particle volume, which is why the trap loses its grip on very small particles. Second, the sign of the (m² − 1) factor flips when n_p < n_m, which is why low-index objects are repelled from the focus.

The scattering force, by contrast, comes from the radiation-pressure cross-section and scales as:

F_scat = (n_m / c) · I · σ_scat,    σ_scat ∝ a⁶ / λ⁴   (Rayleigh)

Because the gradient force scales as a³ but the scattering force as a⁶, smaller particles are relatively easier to trap stably (gradient wins), while larger particles get harder to hold against scattering — yet another reason the practical window tops out near 10 µm.

To turn the trap into a quantitative instrument, calibrate the stiffness k from thermal motion. By the equipartition theorem, each degree of freedom of the trapped bead carries ½k_B·T of energy:

½ k ⟨x²⟩ = ½ k_B T   →   k = k_B T / ⟨x²⟩

Record the bead's position fluctuations, take the variance ⟨x²⟩, and the stiffness drops out. With k ≈ 0.1 pN/nm and position resolution below 1 nm from back-focal-plane interferometry, the trap resolves forces to a fraction of a piconewton and displacements at the nanometer scale — fine enough to watch a single protein take an 8 nm step. That combination of piconewton force resolution and nanometer position resolution is exactly what makes optical tweezers indispensable to single-molecule science.