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Stability and dynamics of optically levitated dielectric disks in a Gaussian standing wave beyond the harmonic approximation

Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius $2~μ\text{m}$ with index of refraction $n=1.45$ and $n=2.0$ as well as disks of radius 200 nm with $n=1.45$. Calculations of the forces and torques were conducted both analytically and numerically using a discrete-dipole approximation method. Besides harmonic terms, third order ro-translational coupling terms in the potential energy can be significant and a necessary consideration when describing the dynamics of disks outside of the Rayleigh limit. The coupling terms are a result of the finite extension of the disk coupling to both the Gaussian and standing wave geometry of the beam. The resulting dynamics of the degrees of freedom most affected by the coupling terms exhibit several sidebands as evidenced in the power spectral densities. Simulations show that for Gaussian beam waists of $1-4~μ\text{m}$ the disk remains stably trapped.