Transition of a particle between adjacent optical traps: A study using catastrophe theory

TL;DR

This study uses catastrophe theory to analyze particle transitions between optical traps, providing a new experimental method to validate and parameterize optical tweezers across their entire force-displacement range.

Contribution

It introduces a novel approach linking optical trap transitions to catastrophe theory, enabling comprehensive force-displacement characterization.

Findings

Experimental determination of force-displacement curve for optical traps.

Identification of the transition as a butterfly catastrophe.

Revealed formal resemblance to phase transitions in ferroelectrics.

Abstract

In spite of the widespread use of optical tweezers as a quantitative tool to measure small forces, there exists no unambiguous and simple experimental method for either validating its theoretically predicted form or empirically parameterizing it over the entire range. This problem is addressed by studying the transition of a colloidal particle between two spatially separated optical traps. The transition as a function of the relative intensity of the traps and the separation between them reveals a formal resemblance to the `butterfly catastrophe' which also maps onto to phase transitions observed, for example in ferroelectrics, on a phenomenological level. The method has been used to experimentally determine the force-displacement curve for an optical trap over its entire range.