Optical Tweezers

Focused laser beam traps dielectric particles via gradient force — move the beam to manipulate particles

Laser & Trap

Environment

Trap Data

κ (pN/μm)
F_max (pN)
⟨Δx⟩ (nm)
0
Trapped

Physics

F_grad = −∇U
U = −½α⟨E²⟩

For Rayleigh (a≪λ):
F_grad = (2πn_m a³/c)·
  ((m²−1)/(m²+2))·∇I

κ = 2·I₀·α/(c·w₀²)

⟨Δx²⟩ = k_B T / κ
(Brownian fluctuations)
Click canvas to move laser trap. Particles feel gradient force toward focus. Brownian motion adds thermal fluctuations.