Gradient force traps, scattering force pushes — together they levitate a particle
Gaussian Beam + Dielectric Sphere
F_grad = −(n_m²/2c) · α · ∇|E|² (attracts to focus)
F_scat = n_m · σ_scat · I / c (pushes along beam)
Trap: F_grad > F_scat at focus
Drag the particle or click to release it. The gradient force pulls toward the beam axis and slightly before the focus. Scattering force pushes it forward — balance gives 3D trapping.
Force Profile Along Beam Axis
Trap depth ∝ P · α / w₀²
w₀ (beam waist) ∝ λ / (π · NA)
At NA=1.2, w₀ ≈ 200 nm for λ=532 nm
Higher NA focuses tighter → stronger gradient force → deeper trap. The equilibrium point (force=0) lies just past the focus where gradient overcomes scattering.