Direct Measurement of the Oscillation Frequency in an Optical-Tweezers Trap by Parametric Excitation

Abstract

We demonstrate a novel technique for direct measurement of the oscillation frequency in an optical-tweezers trap. The technique uses the phenomenon of parametric resonance in an oscillator when the stiffness of the trapping potential is modulated. The trapped particle is a strongly damped oscillator; hence, the signature of parametric resonance is not an increase in the amplitude but an increase in the size of Brownian fluctuations. The trap frequency is measured with an accuracy of 0.1%, which is better than previous techniques and thus opens up new possibilities in experiments with optical tweezers.

Change in spectrum of Brownian fluctuations of optically trapped red blood cells due to malarial infection

“…19 The output of the QPD was first sampled at 16 kHz for a total data length of 100,000 points. A fast Fourier transform of the data set gave its ͑complex͒ Fourier spectrum.…”

Parametric Resonance of Optically Trapped Aerosols

“…The possibility of pumping mechanical energy into optically trapped particles could open the way to many applications. In optical tweezers, even though it is easy to periodically modulate the laser power, parametric excitation is usually ineffective because of the heavy damping action of the surrounding fluid.Recently it has been reported that modulating the laser power at the parametric resonant frequency in an overdamped system increased the amplitude of mean squared fluctuations [8]. However, these findings have been difficult to reproduce and are in strong contrast with the prediction of Langevin dynamics [9,10,11].…”

Venkataraman, Natarajan, and Kumar Reply:

“…While it is quite possible that some kind of instrumental noise could give rise to this effect, it is unlikely that the effect would show a linear variation with laser power as shown in Fig. 3 of the original Letter [1]. However, we cannot rule out a systematic source for the observation until we do more controlled experiments with and without an AOM.…”

“…In regards to the experimental work of Deng, Forde, and Bechhoefer, the only difference is that the trap modulation is done via direct current modulation, rather than by use of an AOM as in the original experiment [1]. At first glance, this appears unimportant, and indeed it was mentioned in the Letter that the use of direct current modulation should also work.…”

“…In the original Letter [1] the observed effect was explained using the following physical picture. The parametric drive injects energy into the system and this injection is expected to be strongest near 2f.…”