Sphere in a focused beam

A tightly focused laser pulls a small particle towards the brightest point of the focus (the gradient force, for particles with a higher refractive index than the medium) while radiation pressure pushes it along the beam (the scattering force). When the gradient force wins, the particle is held stably just behind the focus. Holographic optical trapping shapes the beam with a spatial light modulator to make many traps at once, each working the same way. This calculator gives the exact fields in and around the trapped particle; the tweezers heating calculator gives its temperature.

Mie theory with any incident beam instead of a plane wave: the focused beam is expanded in spherical multipoles (beam-shape coefficients) and the particle's response is exact. The focus itself is computed from vector diffraction theory, valid up to the highest numerical apertures.

A tightly focused radially polarized beam has a strong longitudinal (along-axis) field at the focus and a smaller spot, which drives different particle resonances than linear polarization.

Not yet: it computes the exact fields inside and around the particle in the focus. The heating of a trapped particle is in the optical tweezers heating calculator.