Quantitative assessment of non-conservative radi- ation forces in an optical trap

The forces acting on an optically trapped particle are usually assumed to be conservative. However, the presence of a non-conservative component has recently been demonstrated. Here we propose a technique that permits one to quantify the contribution of such a non-conservative component. This is an extension of a standard calibration technique for optical tweezers and, therefore, can easily become a standard test to verify the conservative optical force assumption. Using this technique we have analyzed optically trapped particles of different size under different trapping conditions. We conclude that the non-conservative effects are effectively negligible and do not affect the standard calibration procedure, unless for extremely low-power trapping, far away from the trapping regimes usually used in experiments. Introduction. – The detection and measurement of forces and torques in microscopic systems is an important goal in many areas such as biophysics, colloidal physics and hydrodynamics of small systems. Since 1993, the photonic force microscope (PFM) has become a standard tool to probe such forces [1–3]. A typical PFM setup comprises an optical trap – an highly-focused Gaussian light beam – that holds a probe – a dielectric or metallic particle of micrometer size – and a position sensing system. Using a PFM it has been possible to measure forces as small as 25 fN [4] and torques as small as 4000 fN · nm [5]. In order to assess the mechanical properties of microscopic systems, the first step is always to have an accurately calibrated optical probe. Modelling the interaction between the light of a focused laser beam and an extended dielectric or metallic object can be a complicated task [6]. The electromagnetic theory is relatively straightforward for the Rayleigh and the geometrical optics regimes [7, 8]. However, most applications of PFM involve particles whose characteristic size is comparable to the wavelength of the light employed. In this case the exact solutions for the force-field are cumbersome to come by. Fortunately there