An Optical Apparatus for Rotation and Trapping

Abstract

We present details of the design, construction and testing of a single-beam optical tweezers apparatus capable of measuring and exerting torque, as well as force, on microfabricated, optically anisotropic particles (an 'optical torque wrench'). The control of angular orientation is achieved by rotating the linear polarization of a trapping laser with an electro-optic modulator (EOM), which affords improved performance over previous designs. The torque imparted to the trapped particle is assessed by measuring the difference between left-and right-circular components of the transmitted light, and constant torque is maintained by feeding this difference signal back into a custom-designed electronic servo loop. The limited angular range of the EOM (±180°) is extended by rapidly reversing the polarization once a threshold angle is reached, enabling the torque clamp to function over unlimited, continuous rotations at high bandwidth. In addition, we developed particles suitable for rotation in this apparatus using microfabrication techniques. Altogether, the system allows for the simultaneous application of forces (~0.1-100 pN) and torques (~1-10,000 pN nm) in the study of biomolecules. As a proof of principle, we demonstrate how our instrument can be used to study the supercoiling of single DNA molecules.

Alkaline niobate nanowires as opto-mechanical probes

“…In both cases the interaction of the beam with the nanowire creates an imbalance of power of left and right circular components (P L and P R ) in the transmitted beam. By monitoring the imbalance of left and right circular components in the transmitted beam, a direct measure of the torque  is possible [11][12][13][14][15][16][17][18][19] :…”

“…Three different parameters have to be extracted in each measurement and, in particular, in torque system one should quantify: the torque sensitivity   (in V/pN nm) that allows the conversion of the volt signal in pN nm, the maximum torque  0 (in pN nm) and the angular drag coefficient  (in pN nm s). Most of the calibration methods available [16,22] are based on extraction of the cut off frequency f c and the zero frequency amplitude A 0 from the power spectral density of the torque signal taken at =0 (see Figure 3a). This is possible by fitting the power sprectral density curve with a Lorentzian described as   A third variable usually extracted is the amplitude V 0 of the torque signal experienced by the particle (see Figure 3b).…”

Fabrication of quartz microcylinders by laser interference lithography for angular optical tweezers

“…11 Later, the advantages of the cylindrical geometry of a uniaxial-positive material were demonstrated. 12 Protocols based on optical and electron beam lithography 7,12,13 have been successfully used, while recently, a simpler fabrication process based on nanosphere lithography has been developed.…”

“…The orientation of the linear polarization of the laser is dynamically controlled by an electro-optical modulator (EOM) combined with a quarter waveplate. 7,8 In our experiments, we control the frequency ω of rotation of the linear polarization by driving the EOM with a sawtooth voltage signal of variable frequency. The polarization can be set in rotation in both directions with ω in the range from 0 to few kHz.…”

On the birefringence of healthy and malaria-infected red blood cells

“…6,[19][20][21] Upon placing a birefringent material in an optical trap, rotation is induced such that the laser light passes through the more polarizable axis. 22,23 Our earlier experiments 24 have established that malaria-infected RBCs undergo shape distortion and rotational motion upon their interaction with a tightly focused laser beam of the type that is encountered within an optical trap; the normal RBCs do not rotate but align themselves along the direction of laser electric field. The distortion of shape has been characterized in terms of Euler buckling; 25 it plays an important role in the rotational motion by enhancing the spatial anisotropy of the cell's polarizability tensor, α, such that the (α · E) interaction with the optical field gives rise to a torque that, in turn, causes rotation of the trapped RBC (E denotes the amplitude of the laser's optical field).…”