Nanometer-displacement detection of optically trapped metallic particles based on critical angle method for small force detection

We have developed a method of measuring the displacement of optically trapped metallic particles (10 μm in diameter) in water with nanometer resolution to detect small forces. Metallic particles were optically trapped in two dimensions by focusing a laser beam below the particle using an objective lens with a numerical aperture of 0.9. Displacement of a trapped metallic particle was detected using the light reflected from the particle based on the critical angle method. The lateral spring constant was estimated from the equipartition theorem to be on the order of 10^-6 N/m and found to increase as the incident laser power increased. Consequently, a trapped metallic particle can be used to detect small forces (10^-13 N).