Field–potential finite-difference time-domain (FiPo FDTD) technique for computational electromagnetics

Abstract Modeling light–matter interactions at the nanoscale requires accurate handling of coupled quantum and electromagnetic systems. This coupling requires information about the electric scalar potential $$\phi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> and the magnetic vector potential $${\textbf{A}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> , which are not typically calculated in standard computational electromagnetics implementations. To that end, we have developed a field–potential finite-difference time-domain (FiPo FDTD) algorithm, which solves a set of first-order equations for $$\phi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> and $${\textbf{A}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> alongside equations for the electric and magnetic fields $${\textbf{E}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> and $${\textbf{H}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math> . The FiPo Basic code is essentially conventional FDTD, but with an added module that calculates the potentials. The FiPo Hybrid code self-consistently calculates both fields and potentials and is particularly suitable for coupling with quantum electronic transport solvers because it can be sourced by the potentials themselves. To terminate the domain and mimic infinite space, we have derived and implemented a convolutional perfectly matched layer (CPML) absorbing boundary condition for FiPo FDTD whose performance is on par with state-of-the-art CPMLs for standard FDTD. We present FiPo simulation results on several example systems.