Rotation rate measurement and calculation for calcite crystals in a C-point mode

Abstract

A polarization singularity mode offers a unique tool for actuating an array of birefringent calcite crystals, and measurement of the rotation rates of these crystals is in turn a way to image modes with varying polarization. In this work, we show the calculated and measured rotation rates of individual calcite crystals in a C-point mode and their dependence on three key factors: polarization, mode intensity profile, and crystal size. The C-point is a polarization singularity mode in which the mode has a circularly polarized center surrounded by elliptically polarized regions, with the orientation of the ellipse varying azimuthally and the degree of ellipticity changing radially. The beam is focused into an optical trapping region, and micron-sized birefringent calcite crystals in solution are positioned at key points in the mode. The crystals experience different torques at each location. The spin angular momentum of the light is proportional to the degree of ellipticity and to the intensity at each point in the mode. Our technique for generating C-point modes results in an intensity profile with a nonlinear radial dependence. Our crystal growth process generates crystals of varying width and thickness; the crystal size and shape affect the drag forces and light torque acting on them. We explain the crystal growth process and estimations of torque, demonstrate the rate and direction of rotation of calcite crystals placed at different points in the laser mode, and discuss the difference between the estimated and measured rotation rates.