Why is the potential negative at the center?

We plot U = −U₀ I/I₀ so the force F = −∇U points toward the intensity maximum at r = 0, mimicking a dielectric bead attracted to the bright focus.

How does stiffness depend on power and waist?

Near the focus, k ≈ 4U₀/w₀² with U₀ ∝ P in this toy model: higher power tightens the trap; a larger waist weakens confinement for fixed power.

What causes the jitter?

Thermal kicks from the surrounding fluid compete with the restoring force. Higher temperature or lower drag (smaller bead, lower viscosity) increases Brownian motion.

Scattering force, beam polarization, interface heating, non-Gaussian beams, 3D axial trap structure, and photodamage are not modeled.

Optical Tweezers (Gradient Trap)

Gaussian trap U(r), stiffness k ∝ P/w₀², overdamped Langevin bead with Stokes drag and thermal Brownian jitter; ⟨r²⟩ trace.

Live graphs

About this model

Optical tweezers use the intensity gradient of a focused Gaussian laser beam to trap micrometer-scale dielectric beads. In this toy model the beam profile is I(r) ∝ exp(−2r²/w₀²) and the effective potential is U(r) = −U₀ exp(−2r²/w₀²) with trap depth U₀ scaling with laser power P and stiffness k ≈ 4U₀/w₀² near the focus. The bead follows overdamped Langevin dynamics dx = (F_grad/γ)dt + √(2k_BTdt/γ)N(0,1) with Stokes drag γ = 6πηR. The top view shows the trap intensity, waist circle, bead trajectory, and running mean square displacement ⟨r²⟩; sliders adjust power, waist, bead size, temperature, and viscosity. This is a scalar gradient-force cartoon, not a full vector Mie scattering or scattering-force calculation.

Who it's for: Undergraduate biophysics and optics labs studying laser trapping, Brownian motion in harmonic wells, and single-molecule mechanics.

Key terms

Optical tweezers
Gradient force
Gaussian beam
Optical trap stiffness
Brownian motion
Langevin equation
Stokes drag
Mean square displacement

How it works

Optical tweezers toy model: Gaussian trap, bead potential U(r), stiffness k, and Brownian jitter in overdamped Langevin dynamics.

Key equations

U(r) = −U₀ exp(−2r²/w₀²) · k = 4U₀/w₀²

dx = (F_grad/γ)dt + √(2k_BT dt/γ) N(0,1)

Frequently asked questions

Why is the potential negative at the center?: We plot U = −U₀ I/I₀ so the force F = −∇U points toward the intensity maximum at r = 0, mimicking a dielectric bead attracted to the bright focus.
How does stiffness depend on power and waist?: Near the focus, k ≈ 4U₀/w₀² with U₀ ∝ P in this toy model: higher power tightens the trap; a larger waist weakens confinement for fixed power.
What causes the jitter?: Thermal kicks from the surrounding fluid compete with the restoring force. Higher temperature or lower drag (smaller bead, lower viscosity) increases Brownian motion.
What is left out?: Scattering force, beam polarization, interface heating, non-Gaussian beams, 3D axial trap structure, and photodamage are not modeled.

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