Wave simulations in infinite spacetime

Chad McKell, Mohammad Sina Nabizadeh, Stephanie Wang, Albert Chern

In progress

Solving the wave equation on an infinite domain has been an ongoing challenge in scientific computing. Conventional approaches to this problem only generate numerical solutions on a small subset of the infinite domain. In this paper, we present a method for solving the wave equation on the entire infinite domain using only finite computation time and memory. Our method is based on the conformal invariance of the scalar wave equation under the Kelvin transformation in Minkowski spacetime. As a result of the conformal invariance, any wave problem with compact initial data contained in a causality cone is equivalent to a wave problem on a bounded set in Minkowski spacetime. We use this fact to perform wave simulations in infinite spacetime using a finite discretization of the bounded spacetime with no additional loss of accuracy introduced by the Kelvin transformation.

arXiv preprint

Optical corral using a standing-wave Bessel beam

Chad McKell, Keith Bonin

Journal of the Optical Society of America B (2018)

Here we create a series of optical corrals and calculate their potential energy profile. A standing-wave Bessel beam is used to form traps in 1D (along the optical axis) and corrals in 2D, in planes perpendicular to the optical axis at the antinodal regions of the standing waves. These optical corrals are formed by an axicon-generated Bessel beam that is retro-reflected back onto itself. We report on Mie calculations of the 2D optical corrals and then compare the resulting probability distributions to those observed for latex particles of diameters 100, 200, and 300 nm. The experimental radial probability density function of tracked particles closely mimics the theoretical optical structure of a Bessel standing-wave corral. The Bessel standing-wave corrals we have characterized are being developed to measure rotational diffusion and torques on micro- and nanorods to help understand microfluidic behavior. The maximum forces on our small beads in the diffraction-free central zone of the Bessel beam standing wave are 𝐹||=0.5  pN and 𝐹⊥=0.1  pN.

Paper