AmericanChemicalSociety.com

An optical tweezers corresponds to a tightly focused laser beam, which can trap a micron-sized dielectric object, such as a colloidal bead. A dual-trap tweezers permits the trapping and nanomanipulation of two such beads, and the determination of forces acting between them, including the critical Casimir forces that are the subject of this program. Critical Casimir forces are however tiny, requiring us to be able to resolve nanometer-scale changes in the separation between two beads. This requirement lead us to a major effort to improve the resolution of our dual trap optical tweezers apparatus. To this end, we have developed a novel approach, namely to use acousto-optic deflectors to allow for the creation of multiple traps in conjunction with time-resolved quadrant-photo diode detection, which allows us determine the forces on and positions of beads in multiple traps with nanometer positional resolution and picoNewton force resolution.

Specifically, we created a high-resolution optical tweezers apparatus as follows. The 3 mm-diameter beam from a high-stability, 3 W, 1064 nm laser (Laser Quantum, Stockport, UK) is incident onto two orthogonal acousto-optic deflectors (AOD) (NEOS Technologies). The AODs convert radio-frequency electromagnetic power into sound waves. The resultant periodic density modulations diffract the incident laser beam, through a frequency-dependent angle. In our setup, the frequency of the RF drive power to the AOD may be switched at 40 kHz by means of a field programmable gate array (FPGA), between one, two or more precision frequencies, created by direct-digital synthesis (DDS). As a result, the laser light can be cycled among a number of discrete propagation angles. Because the AOD is located in a plane that is optically conjugate to the back focal plane of the microscope objective (Nikon CFI Plan Fluor x 100, oil immersion, NA 1.3), the different angles generated at the AOD give rise to corresponding laser traps in the object plane of the microscope objective, each of which can trap and manipulate a polystyrene bead. The high precision in frequency that is possible using DDS permits us to control the separation between the beads with sub-nanometer spatial precision. Located between the AOD and the microscope objective is a telescope arrangement that expands the beamsʼ diameters by a factor of two, ensuring that the back pupil of the microscope objective is overfilled, as required for strong trapping.

Beyond the objective, the trapping beams are directed onto a InGaAs quadrant photo-diode (QPD), located in a plane conjugate to the back focal plane of the microscope condenser lens. The QPD consists of four quarter-circular photodiodes. In such a conjugate plane, the total intensity is insensitive to the absolute position of the trap, but is linearly proportional to the displacement of a trapped bead along the beam direction, relative to the center of the trap. At the same time, the difference in intensity between the two left and the two right quadrants and between the top and bottom is proportional to the displacement of the bead from the center of its trap in the corresponding directions transverse to the beam. This method of determining bead positions is called back-focal-plane interferometry (BFPI). In our setup, the QPD signals alternate at 40 kHz among the different beads, and we time-resolve the signals from the InGaAs QPD to determine each beadʼs position. It is necessary to employ an InGaAs QPD, because the more-usual Si QPDs are not fast enough in the case of 1064 nm-wavelength illumination. The InGaAs QPD provides a sensitive measure of the force on a bead, since the force is proportional to its displacement from the trap center. We have implemented a feedback mode of operation, in which the QPD signals are held constant, thus holding constant the applied force. In this way, we apply a force-clamp and can study the evolution as a function of time at fixed applied force. Another feedback system, eliminates problematic laser intensity fluctuations at the back pupil of the objective.

To separately measure the separation between beads, our setup also includes a low-power (60 mW) 785 nm probe laser (Crystalaser), in addition to the trapping laser. The probe laser beam is similarly split by AODs, controlled by DDS and an FPGA, into multiple beams. These beams are focused to be nearly coincident with the foci of the trapping laser, but their locations are fixed. Therefore, in this case, the difference in the signals from any two beads yields a measurement of their separation. In this case, we use a Si QPD, which is fast enough under 785 nm illumination.

A unique advantage of our instrument is that by separating the beams in time, rather than by polarization, which is the more usual practice, the two beams follow almost exactly the same optical path. Thus, any fluctuations in beam position or direction that may occur as a result of air currents, or instrumental resonances or laser pointing fluctuations, affect both beams in a closely similar fashion. It follows that such fluctuations are largely absent from the difference coordinate that reports the separation between the beads, permitting high precision measurements. This approach represents an important innovation. By contrast, other dual trap approaches to eliminating low frequency noise create their two traps using different polarizations. These setups are necessarily limited to two traps, and, there is necessarily a region where the two polarizations are spatially well-separated and therefore subject to different air currents, etc