Optical trapping by Laguerre-Gaussian beams: Far-field matching, equilibria, and dynamics

Abstract

By using the method of far-field matching we obtain the far-field expressions for the optical (radiation) force exerted by Laguerre-Gaussian (LG) light beams on a spherical (Mie) particle and study the optical-force-induced dynamics of the scatterer near the trapping points represented by the equilibrium (zero-force) positions. The regimes of linearized dynamics are described in terms of the stiffness matrix spectrum and the damping constant of the ambient medium. Numerical analysis is performed for both non-vortex and optical vortex LG beams. For the purely azimuthal LG beams, the dynamics is found to be locally non-conservative and is characterized by the presence of conditionally stable equilibria (unstable zero-force points that can be stabilized by the ambient damping). We also discuss effects related to the Mie resonances (maxima of the internal field Mie coefficients) that under certain conditions manifest themselves as the points changing the trapping properties of the particles.

Lorenz-Mie scattering of focused light via complex focus fields: An analytic treatment

“…Scattering of arbitrary fields is described using the generalized Lorenz-Mie theory (GLMT) [15,16], which relies on the decomposition of the incident field in terms of vector multipoles [17][18][19][20] and the fulfillment of boundary conditions through the use of the appropriate T-matrix [12][13][14][15]. Past treatments of the scattering of focused * rgutier2@ur.rochester.edu electromagnetic fields [20][21][22][23][24][25][26][27][28] provide a variety of models for optical tweezers. These models differ from each other primarily in how the focused incident field is described: through field matching [20][21][22], through use of the Richards-Wolf diffraction theory (c.f., [6,29,30]) to focus a paraxial beam by an optical element [23][24][25], or via an ad-hoc extension of paraxial beams to the nonparaxial electromagnetic regime [26][27][28]31].…”

“…Past treatments of the scattering of focused * rgutier2@ur.rochester.edu electromagnetic fields [20][21][22][23][24][25][26][27][28] provide a variety of models for optical tweezers. These models differ from each other primarily in how the focused incident field is described: through field matching [20][21][22], through use of the Richards-Wolf diffraction theory (c.f., [6,29,30]) to focus a paraxial beam by an optical element [23][24][25], or via an ad-hoc extension of paraxial beams to the nonparaxial electromagnetic regime [26][27][28]31]. In all these treatments, the expressions for the coefficients of the vector multipoles in the beam decomposition are typically not analytic; i.e., computation of these expressions requires numerical integration.…”

Scattering of the Radial Polarized Beams on the Metal Spherical Particle: Plasmonic Nanojet Formation

“…In this section, we introduce all necessary notations and briefly describe computational approaches. Previously we already described most of them in our studies [24][25][26].…”

Transfer of orbital angular momentum superposition from asymmetric Laguerre–Gaussian beam to Bose–Einstein Condensate

“…After the pioneering work of Allen et al [13] on optical vortex carrying orbital angular momentum (OAM), associated with its spatial mode structure, there have been remarkable advancement in creation [14][15][16], manipulation [17] and detection [18][19][20] of the OAM states of light along with its utilization to generate the vortex states in BEC [21]. In this regard, the utilization of optical vortex carrying OAM is already established as an attractive opportunity in high-density data transmission [22], manipulating the motion of microparticles in optical tweezers [23], optical trapping of atoms [24][25][26][27][28] and quantum information processing [18,[29][30][31][32]. However, the interaction of an atom with optical vortex, in the dipole approximation, inevitably transfers OAM to the center-of-mass (c.m.)…”