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

Abstract

Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius 2 μm with indices 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 rotranslational 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 2-4 μm the disk remains stably trapped.

Nanoscale feedback control of six degrees of freedom of a near-sphere

“…The second mechanism is an effect originating from the anisotropy of the optical trap. Under the generalized Rayleigh-Gans approximation, where we consider the inhomogeneous electric field of the trapping laser inside a nanoparticle and assume that the light scattering by the nanoparticle does not modify the local electric field, the mechanical potential energy of a non-spherical nanoparticle in an anisotropic trap U is obtained by integrating the local interaction potential energy density over the volume of the nanoparticle 10 , 35 , 36 (see Methods for more details). U is dependent on the relative angle between the nanoparticle orientation and the optical trap and is minimized when the longer axis of the particle is aligned to the orientation with the lower translational oscillation frequency (Fig.…”

“…These expressions agree with a theoretical formalism provided in ref. 35 when the radius is sufficiently smaller than the wavelength and the beam waist. The presence of higher order terms shifts the frequencies by about 4 %.…”

Initiating revolutions for optical manipulation: the origins and applications of rotational dynamics of trapped particles

“…In complementary observations, gyroscopic stabilisation of the translational motion [145,213] and the orientation [173] has been observed by rotating particles at high speed. Coupling of rotational and translational degrees of freedom has also been shown for certain lower-symmetry particle morphologies, such as disks [226], while coupling between rotational and translational modes can also be enhanced in an optical cavity [227,228] or by painting a spot on the surface of a sphere and performing a continuous joint measurement of two motional modes [229]. For dumbbell-shaped particles, where the moments of inertia of the various rotational modes are comparable, the spinning motion about the symmetry axis couples the two degrees of librational motion, which results in precessional motion [167,230].…”

Quantum rotations of nanoparticles

“…As a consequence, the associated angular momentum is conserved, leading to rotational precession, see Box 1. This has been observed with symmetric rotors [13,25], and was found to limit rotational feedback cooling schemes [26][27][28]. Rotational precession can be controlled with elliptically polarized light fields [29], which exert a non-conservative radiation-pressure torque in addition to the conservative optical potential.…”

“…State-of-the-art feedback cooling of the centre-of-mass motion achieves phonon occupations in the deep quantum regime [11,71,72]. Rotational feedback cooling [26][27][28] has been recently demonstrated for dumbbell-shaped particles down to sub-Kelvin temperatures [13,14]. In the recent experiment reported in Ref.…”