Detection of pitch rotation to high resolution in an optically trapped hexagonal shaped upconverting particle

A rigid body can have six degrees of freedom, of which three are with rotational origin. In the nomenclature of the airlines, the in-plane degree of rotational freedom can be called yaw, while the first out-of-plane degree of freedom can be called pitch, with the second one called roll. Among these, only the yaw sense has been studied extensively in the optical tweezers literature, while the pitch rotation is starting to be explored. In this paper, we show a way to detect the pitch rotation in a hexagonal-shaped particle using photonic force microscopy using the forward scattered light under crossed polarizers and making it incident on a split photodiode. In this way, the pitch angle can be detected at high resolution and bandwidth. We apply this technique to detect continuous pitch rotation and also exhibit a power spectral density for an anisotropic particle optically trapped in a linearly polarized light and exhibiting Brownian motion.