Transfer of spin angular momentum to birefringent materials is widely used in optical tweezers because of the vast array of applications and the ease with which it is generated. With circularly or elliptically polarized light, spin angular momentum is imparted to internally birefringent materials and objects with shape birefringence. In this work, we use polarimetry to spatially map the change in angular momentum of light traveling through birefringent objects. By directly measuring the change in polarization of light passing through materials, we can infer the transferred torque. Our objects are trapped with a linearly polarized beam at 660 nm and polarimetry is performed using a counter-propagating low-power probe beam at 633 nm. We measure six output polarizations each for a range of different input polarizations of the probe to form a polarization map. Using this technique we perform polarimetry on rhombohedral calcite crystals trapped in two distinct orientations, one face up with one side normal to the probe beam, and one corner up with the optic axis running parallel to the beam axis. The polarization changes significantly where the probe beam travels through an edge or corner of the crystal and is uniform across crystal faces. We show the differences in the polarimetry measurements between these orientations to fully understand the generated torque.
We demonstrate the orientation-dependent torque on regular rhombohedral calcite in an optical trap. It is well known that calcite, a birefringent particle, will experience a torque and rotate when tightly trapped at the focus of an elliptically polarized beam due to the transfer of spin angular momentum. Our calcite is grown using a precipitate technique we developed that results in regular crystals approximately 10 μm long on all edges. The regularity of the crystal shape makes it possible to visually identify the optical axis as well as the ordinary (o) and extraordinary (e) polarization axes. When one of our crystals is trapped in an elliptically polarized beam, it first orients itself such that the propagation direction of the beam is along the corner-to-corner optic axis. While in this orientation, the total torque increases and decreases as the crystal rotates, with significant effects at four different locations corresponding to the e and o axes. Current research in this area assumes that there is one crystal axis that is most significant to the motion. We illustrate this axis-dependent calcite rotation at the top of the sample as well as when crystals are trapped three-dimensionally in the middle of the sample fluid, and calculate the torque on the crystal relative to crystal orientation. This work allows us to predict the motion of calcite, giving us an analytical tool for applications such as fluid stirring or as a handle in micro-machines.
Calcite crystals trapped in an elliptically polarized laser field exhibit intriguing rotational motion. In this paper, we show measurements of the angle-dependent motion, and discuss how the motion of birefringent calcite can be used to develop a reliable and efficient process for determining the polarization ellipticity and orientation of a laser mode. The crystals experience torque in two ways: from the transfer of spin angular momentum (SAM) from the circular polarization component of the light, and from a torque due to the linear polarization component of the light that acts to align the optic axis of the crystal with the polarization axis of the light. These torques alternatingly compete with and amplify each other, creating an oscillating rotational crystal velocity. We model the behavior as a rigid body in an angle-dependent torque. We experimentally demonstrate the dependence of the rotational velocity on the angular orientation of the crystal by placing the crystals in a sample solution in our trapping region, and observing their behavior under different polarization modes. Measurements are made by acquiring information simultaneously from a quadrant photodiode collecting the driving light after it passes through the sample region, and by imaging the crystal motion onto a camera. We finish by illustrating how to use this model to predict the ellipticity of a laser mode from rotational motion of birefringent crystals.
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.
Conference Committee Involvement (2)
Optical Trapping and Optical Micromanipulation XVIII
1 August 2021 | San Diego, California, United States
Optical Trapping and Optical Micromanipulation XVII
24 August 2020 | Online Only, California, United States