Optical Tweezers: Axial Trapping Force Balance

Single-beam optical tweezers don't trap a bead exactly where the light is most focused — they trap it a little downstream, at the point where the inward-pulling gradient force finally overtakes the forward-pushing radiation pressure of the scattering force. This simulator renders a real focused Gaussian beam and a bead confined along its optical axis, computing both axial forces from the beam's own waist and Rayleigh range so the trap's equilibrium point and stiffness respond to numerical aperture, laser power and bead size exactly as a real trap would — including the well-known failure mode where too low an NA lets the scattering force win outright and the bead is pushed straight through.