2.1.1 Physics of optical trapping

There are several theories in physics to describe the interaction between light and matter: from the very fundamental Quantum Electrodynamics of electrons and photons to the Mie scattering of atmospheric particles. Thus, there is an appropriate theory for each scale of energy and mass involved in the interaction. The optical tweezers instruments devoted to experimental biophysics deal with interactions that are correctly described by classical theories (i.e., Maxwell's electromagnetism). In this classical regime, the forces exerted on matter by light are known as radiation pressure. The radiation pressure is the result of light-matter interaction and includes different phenomena such as absorption or scattering of light. The purpose of an optical tweezers setup is to control the radiation pressure of light in order to apply forces on tiny objects.

Although all optical forces exerted on a particle arise from the same physics, they are usually split into two main contributions: the scattering force and the gradient force. In both cases, the change in the light momentum is the ultimate responsible of the force exerted on the particle. The scattering force tends to push the particle along the beam in the direction of propagation, while the gradient force pushes the objects towards the regions of highest light intensity. If the light is correctly conditioned (in terms of collimation, intensity, aberration, etc.) the scattering and gradient forces can be combined to apply controlled forces on the particle. An optical trap is formed by focusing a laser beam in a small region so that a transparent particle feels a restoring force that tends to take it to the region of maximum intensity of light. An optical trap can only be formed if the gradient force along the optical axis is stronger than the scattering force that pushes the bead out of the focal point.

There are three main theoretical approaches to the physics of optical trapping, depending on the ratio between the wavelength $ \lambda $ of the light and the diameter of the particle $ d$. In the ray optics (or Mie) regime, the particle is very large compared to the wavelength ( $ d\gg\lambda$), whereas in the Rayleigh regime the opposite is true ( $ d\ll\lambda$). The calculation of optical forces in the intermediate regime ( $ d\approx\lambda$) is quite complicated and requires the solution of the Maxwell's equations with the appropriate boundary conditions. It can be achieved by means of the Generalized Lorenz-Mie Theory (GLMT) [15]. Most of the work done with optical tweezers in biophysics falls in this last case, where infrared lasers have a wavelength of $ \lambda\simeq 0.8$-1.2 $ \mu $m and the trapped particles are spherical beads of $ d\simeq2$-4$ ~\mu$m.



Subsections
JM Huguet 2014-02-12