Probing the dynamics of an optically trapped particle by phase sensitive back focal plane interferometry

The dynamics of an optically trapped particle are often determined by measuring intensity shifts of the back-scattered light from the particle using position sensitive detectors. We present a technique which measures the phase of the back-scattered light using balanced detection in an external Mach-Zender interferometer scheme where we separate out and beat the scattered light from the bead and that from the top surface of our trapping chamber. The technique has improved axial motion resolution over intensity-based detection, and can also be used to measure lateral motion of the trapped particle. In addition, we are able to track the Brownian motion of trapped 1 and 3 $mu$m diameter beads from the phase jitter and show that, similar to intensity-based measurements, phase measurements can also be used to simultaneously determine displacements of the trapped bead as well as the spring constant of the trap. For lateral displacements, we have matched our experimental results with a simulation of the overall phase contour of the back-scattered light for lateral displacements by using plane wave decomposition in conjunction with Mie scattering theory. The position resolution is limited by path drifts of the interferometer which we have presently reduced to obtain a displacement resolution of around 2 nm for 1.1 $mu$m diameter probes by locking the interferometer to a frequency stabilized diode laser.

Measurement of probe displacement to the thermal resolution limit in photonic force microscopy using a miniature quadrant photodetector

A photonic force microscope comprises of an optically trapped micro-probe and a position detection system to track the motion of the probe. Signal collection for motion detection is often carried out using the backscattered light off the probe - however, this mode has problems of low S/N due to the small back-scattering cross-sections of the micro-probes typically used. The position sensors often used in these cases are quadrant photodetectors. To ensure maximum sensitivity of such detectors, it would help if the detector size matched with the detection beam radius after the condenser lens (which for backscattered detection would be the trapping objective itself). To suit this condition, we have used a miniature displacement sensor whose dimensions makes it ideal to work with 1:1 images of micron-sized trapped probes in the back-scattering detection mode. The detector is based on the quadrant photo-IC in the optical pick-up head of a compact disc player. Using this detector, we measured absolute displacements of an optically trapped 1.1 um probe with a resolution of ~10 nm for a bandwidth of 10 Hz at 95% significance without any sample or laser stabilization. We characterized our optical trap for different sized probes by measuring the power spectrum for each probe to 1% accuracy, and found that for 1.1 um diameter probes, the noise in our position measurement matched the thermal resolution limit for averaging times up to 10 ms. We also achieved a linear response range of around 385 nm with crosstalk between axes ~4% for 1.1 um diameter probes. The detector has extremely high bandwidth (few MHz) and low optical power threshold - other factors that can lead to its widespread use in photonic force microscopy.