On the theory of the optical stretcher : optics, mechanics, and thermal effects

Abstract

The optical stretcher (OS) is dual-beam laser trap capable of capturing and deforming micron-sized particles or biological cells. It can be employed to measure cell-mechanical properties and, thus, to monitor physiological changes, such as differentiation, and to diagnose diseases that affect the structural integrity of cells, like cancer and sickle-cell anemia. To correctly interpret the deformation data, this study presents a versatile physical framework for the electrodynamics, mechanics, and thermodynamics in the OS. Due to the limitations of geometrical optics (GO), an analytical approach based on generalised Lorenz-Mie theory (GLMT) is adopted to describe the electromagnetic fields, intensity, and surface stresses in the OS. To model the optical properties of particles with different internal structures and shapes, the theory is provided for multi-layered spheres and spheroids. The extension to aggregates consisting of numerous coated spheres with arbitrary positioning and dielectric properties is also derived and implemented in a parallel computer code. The theoretical methods are relevant for the scattering from colloidal suspensions and the light transmission through biological tissue, such as the retina. Despite the difference in complexity between GO and GLMT, the stress profiles obtained with both theories for medium-sized spheres and spheroids are in accord with each other. The optical forces on spheres and spheroids with small aspect ratios are found to deviate only slightly, suggesting that the redistribution of the surface stresses during thermo-optical stretching may be neglected. Reflecting the geometry chosen for the electrodynamic theory, an analytical solution for the deformation of a layered, viscoelastic spheroid under axisymmetric loading is presented. The stresses inside the object are deduced from Hooke's law of elasticity. To take the particle's thermal expansion into account, a particular solution for the presence of a temperature gradient is derived. The temperature profile in the OS was determined experimentally using fluorescence ratio thermometry. Homogeneous agarose micro-spheres were manufactured from water-in-oil emulsions and their optical and thermal properties were established for the temperatures reached in the trap. The measured thermo-optical deformations of the agarose spheres were found to be in agreement with the theory. Based on the presented framework a new approach is suggested to reduce the impact of temperature on deformation analysis. This is the first complete, analytical description of all major theoretical aspects of the OS.