  This paper quantifies the rate at which laser shot noise energy is delivered
to a nanoparticle for the various scenarios commonly encountered in levitated
optomechanics. While previous articles have the same form and dependencies, the
proportionality constants often differ in the literature. This paper resolves
these discrepancies. The rate at which energy is delivered to an optically
trapped particle's respective degrees of freedom depends on the radiation
pattern of scattered light as well as the direction of laser propagation. For a
traveling plane wave with linearly polarized light, in the Rayleigh regime this
leads the translational shot noise heating rate to be proportional to $1/10$ of
the total rate in the laser polarization direction, $7/10$ in the laser
propagation direction, and $2/10$ in the direction perpendicular to both.
Analytical expressions for the shot noise heating rate are provided in the
Rayleigh limit as well as numerical calculations for particles in the Mie
regime for silica and diamond. For completeness, numerical calculations of the
shot noise heating for silica Mie particles at the focus of a strongly focused
laser beam are calculated for varying numerical aperture and common laser
wavelengths. Both numerical calculations show that the Rayleigh expression
generally gives an overestimate of the shot noise heating especially for larger
radii, but is still a good approximation even for incident focal fields. The
exception to the relative decrease is when a Mie resonance is reached which was
found for diamond. Lastly, Rayleigh expressions for the rotational shot noise
heating for a symmetric top-like particle for linear, elliptically, and
unpolarized light are also provided.
