Multiscale Modeling and Computation of Optically Manipulated Nano Devices

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 7, 2019 - 1:55pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Di Liu – Michigan State University
Organizer
Haomin Zhou

We present a multiscale modeling and computational scheme for optical-
mechanical responses of nanostructures. The multi-physical nature of
the problem is a result of the interaction between the electromagnetic
(EM) field, the molecular motion, and the electronic excitation. To
balance accuracy and complexity, we adopt the semi-classical approach
that the EM field is described classically by the Maxwell equations,
and the charged particles follow the Schr ╠łoidnger equations quantum
mechanically. To overcome the numerical challenge of solving the high
dimensional multi-component many- body Schr ╠łodinger equations, we
further simplify the model with the Ehrenfest molecular dynamics to
determine the motion of the nuclei, and use the Time- Dependent
Current Density Functional Theory (TD-CDFT) to calculate the
excitation of the electrons. This leads to a system of coupled
equations that computes the electromagnetic field, the nuclear
positions, and the electronic current and charge densities
simultaneously. In the regime of linear responses, the resonant
frequencies initiating the out-of-equilibrium optical-mechanical
responses can be formulated as an eigenvalue problem. A
self-consistent multiscale method is designed to deal with the well
separated space scales. The isomerization of Azobenzene is presented as a numerical example.