H. M. Nussenzveig

Theory of trapping forces in optical tweezers

Starting from a Debye–type integral representation valid for a laser beam focused through a high numerical aperture objective, we derive an explicit partial–wave (Mie) representation for the force exerted on a dielectric sphere of arbitrary radius, position and refractive index. In the semi–classical limit, the ray–optics result is shown to follow from the Mie expansion, holding in the sense of a size average. The equilibrium position and trap stiffness oscillate as functions of the circumference–to–wavelength ratio, a signature of interference, not predicted by previous theories. We also present comparisons with experimental results.

Theory of optical tweezers

We derive an exact partial-wave (Mie) expansion of the axial force exerted on a transparent sphere by a laser beam focused through a high numerical aperture objective. The results hold throughout the range of interest for practical applications, as well as in the Rayleigh and geometrical optics limits. They allow, in principle, an absolute calibration of optical tweezers. Starting from the Mie result, we derive a closed analytic representation for the size-averaged short-wavelength limit that takes into account the Abbe sine condition. Numerical plots show large deviations from geometrical optics near the focal region and around the edge of the sphere, and oscillatory behavior of the force as a function of the size parameter. The oscillations are explained in terms of a simple interferometer picture derived from the Mie expansion. The few existing experimental data look more consistent with the present model than with previous ones.

Cell Cytoskeleton and Tether Extraction

We perform a detailed investigation of the force × deformation curve in tether extraction from 3T3 cells by optical tweezers. Contrary to conventional wisdom about tethers extracted from cells, we find that actin filaments are present within them, so that a revised theory of tether pulling from cells is called for. We also measure steady and maximum tether force values significantly higher than previously published ones for 3T3 cells. Possible explanations for these differences are investigated. Further experimental support of the theory of force barriers for membrane tube extension is obtained. The potential of studies on tether pulling force × deformation for retrieving information on membrane-cytoskeleton interaction is emphasized.

Probing the Casimir force with optical tweezers

We propose to use optical tweezers to probe the Casimir interaction between microspheres inside a liquid medium for geometric aspect ratios far beyond the validity of the widely employed proximity force approximation. This setup has the potential for revealing unprecedented features associated to the non-trivial role of the spherical curvatures. For a proof of concept, we measure femtonewton double-layer forces between polystyrene microspheres at distances above 400 nm by employing very soft optical tweezers, with stiffness of the order of fractions of a fN/nm. As a future application, we propose to tune the Casimir interaction between a metallic and a polystyrene microsphere in saline solution from attraction to repulsion by varying the salt concentration. With those materials, the screened Casimir interaction may have a larger magnitude than the unscreened one. This line of investigation has the potential for bringing together different fields including classical and quantum optics, statistical physics and colloid science, while paving the way for novel quantitative applications of optical tweezers in cell and molecular biology.

Polarization effects in optical tweezers

We extend the MDSA (Mie–Debye spherical aberration) theory of trapping forces in optical tweezers, previously developed for circularly polarized trapping beams, to linear polarization. Although it does not significantly affect the trap stiffness, linear polarization may introduce a strong axial asymmetry of the optical forces near the edge of a trapped microsphere, arising from Mie resonance effects.

Absolute calibration of optical tweezers including aberrations

We extend a previous proposal for absolute calibration of optical tweezers by including optical setup aberrations into the first-principles theory, with no fitting parameters. Astigmatism, the dominant term, is determined from images of the focused laser spot. Correcting it can substantially increase stiffness. Comparison with experimental results yields agreement within error bars for a broad range of bead sizes and trap heights, as well as different polarizations. Absolute calibration is established as a reliable and practical method for applications and design of optical tweezers systems.

Towards Casimir force measurements with optical tweezers (Conference Presentation)

We propose to use optical tweezers to probe the Casimir interaction between micro-spheres inside a liquid medium for geometric aspect ratios far beyond the validity of the widely employed proximity force approximation. This setup has the potential for revealing unprecedented features associated to the non-trivial role of the spherical curvatures. For a proof of concept, we measure femtonewton double-layer forces between polystyrene microspheres at distances above 400 nm by employing very soft optical tweezers, with stiffness of the order of fractions of a fN/nm. As a future application, we propose to tune the Casimir interaction between a metallic and a polystyrene microsphere in saline solution from attraction to repulsion by varying the salt concentration. With those materials, the screened Casimir interaction may have a larger magnitude than the unscreened one.

Absolute calibration of optical tweezers: the MDSA+ theory

In this paper will be reported the principal results about absolute calibration of optical tweezers that we have published at reference.1