# Blog

# FDTD Method

## FDTD Method

FDTD method (Finite-difference time-domain) is a method for simulating electromagnetic waves..It discretizes Maxwell's equations and calculates the time evolution of the electric field distribution in the simulation space. Specifically, Maxwell's equations are expanded into difference equations in the space and time domains. In the actual simulation, the computational domain is divided by a unit grid called a Yee grid. The unit lattice is shown in Figure 1.

Figure 1. The Yee lattice

In this lattice, the electric field overlaps the grid of the lattice, but the magnetic field exists at a position that is displaced from the grid by 1/2 in the three-dimensional direction. As an image, one can imagine a lattice representing the electric field and a lattice representing the magnetic field overlapping in a misaligned state. By calculating the electric field in space at each time step, time evolution can be observed virtually.

**Absorption Boundary Condition**

When light reaches the computational domain boundary, the light reflects off the edge surfaces and generates noise in the simulation space. To prevent this phenomenon from occurring, it is necessary to set PML (Perfectly Matched Layer) absorption boundary conditions. By placing it on all end-faces in the simulation space, the light coming to the end-faces is sufficiently attenuated. The PML is shown in Figure 2.

Figure 2. PML absorption boundary conditions

**Applications in Our Laboratory**

In the Photonics and Quantum Matter Lab, pump-probe spectroscopy using an ultrashort pulse light source is used to observe the dynamics of materials in the ultrashort time region. We are attempting to approach the areas that cannot be elucidated experimentally by the FDTD method. Figure 3 shows the transmission spectrum of a designed cavity model with a gold mirror and an incident mid-infrared pulse. It can be seen that the Fabry-Perot mode of the cavity is generated.

Figure 3. Cavity model and transmission spectrum