The FDTD Method: Essences, Evolutions, and Applications to Nano-Optics and Quantum Physics

This chapter aims to introduce the recent developments, basic theories, core
techniques, real-world applications, and future directions for the finitedifference
time-domain (FDTD) method. The unified theoretical frameworks
of the FDTD method and its advances (Runge Kutta-FDTD, symplectic FDTD,
alternative direction implicit-FDTD, high-order FDTD, multiresolution-TD,
pseudospectral-TD, etc.) for solving Maxwell’s equations are systematically
reviewed in Section 2.1. Next, we will briefly describe core techniques of the
FDTD method (involving the basic update equations, material averaging
technique, perfectly matched layer, source excitation, near-to-far-field transformation,
periodic boundary condition, and treatment of dispersive media)
and particularly focus on those for nano-optics applications in Section 2.2. In
Section 2.3, we will demonstrate powerful capabilities of the FDTD method to
model versatile physical problems in the nano-optics field. The case studies
on plasmonic solar cells, nanoantennas, spontaneous emissions, and metamaterials
will be discussed with detailed physical understandings. Then,
the numerical analyses and implementations of the FDTD method to simulate
the Schrödinger equation are presented in Section 2.4. In Section 2.5, we
will show several simple examples on the numerical solution of quantum
physics problems with the FDTD method. Finally, the conclusion and future
direction are summarized in Section 2.6.