Rotation of polarization of a Gaussian beam passing the two lens system. The electric fields are limited to a disk. (a) Incident electric field. (b) Calculated transmitted electric field in the back focal plane of the second lens. The lines of the contour plot correspond to the rotation of polarization of , , , , 2°, 4°, 6°, and 8°, and gray scales are used to facilitate visualization. The and axes are the first and second bisecting lines. The rotation of polarization of the electric field exiting from the two lens system (c) on the axis for and (d) on the perimeter of (solid), (dotted), (dashed), and (dash-dotted).
Schematic layout of the double optical tweezers setup. Light pathways are indicated for the laser (red), and for the white light used for Köhler illumination and imaging of the sample (yellow).
Light remaining on the back focal plane of the second objective when a polarizer is used to reject the maximum of intensity arising from a single polarized beam after transmission through the microscope.
Schematic layout of the microscope and detection part of the setup. Planes (A1), (A2), (B), (C), and (D) are the ones described in the text.
Ray propagation through the two lens system. The two rays have symmetrical paths, but their rotations of polarization are different as described in the text.
Calculated interference pattern in the back focal plane of the second objective (the contrast is artificially enhanced for visualization). The two interfering beams exhibit perpendicular polarization before entering the microscope, and a polarizer is used to remove one of the two beams. The angular difference between the two beams is and .
Theoretically expected normalized output signal of a position sensitive detector in the presence of the two beams when the mobile beam is deflected and . The fixed trap is translated by along the axis in the detector plane (D). The phase differences between the two beams are 0 (dashed), (dotted), (solid), and (dash-dotted).
Interference pattern seen in the back focal plane of the second objective with two silica beads trapped. The two beads each exhibit a diameter of and are separated by in the sample plane.
Dependence of the parasitic signal on the stiffness and the separation between the two traps. The force is measured on the fixed trap using two unlinked beads. The stiffness of the fixed trap and the total laser power in the back focal plane of the trapping objective are (a) and , (b) and , and (c) and . The displacement velocity between the two traps is , and sampling is done at with an antialias filter of . Individual curves are vertically shifted for clarity [ between subsequent curves in (a), in (b), and in (c)]. Notice the change in vertical axis scaling between (a), (b), and (c).
Schematic layout of our polarization rectifier. The electric fields are given for the first passage through the microscope in the back focal plane of the first objective and in the back focal plane of the second objective . For the second passage, they are given in the back focal plane of the second objective and the back focal plane of the first objective .
Force measurements with two silica beads trapped with the frequency shifter on (bottom: and ) and off (top: and ). The displacement velocity between the two beads is , and sampling is done at with an antialias filter of . The signal measured without the frequency shifter on is shifted vertically for better visualization.
Geometrical parameters describing the deflection of the mobile trap by the piezoelectric mirror mount.
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