Nonstandard FDTD Theory

Beginner Course

1. Finite Difference Model
2. 1D Wave Equation
3. 1D Stability
4. 1D Boundary Condition
5. Dimensionless Form
6. 1D Example

Intermediate Course

1. 2D Wave Equation
2. 2D Maxwell's Equations
3. Scattered Field
4. 2D Stability
5. 2D Boundary Condition
6. Scatterer Representation
7. Intensity
8. 2D Example

Advanced Course

1. 3D Wave Equation
2. 3D Maxwell's Equations
3. 3D Stability
4. Conductive Media
5. Perfectly Matched Layer

7. Intensity

Some analytic solutions such as Mie scattering are obtained as standing waves. We can calculate the standing wave in the simulation, but it is difficult to compare the result with the analytic solution due to phase shift. Here we introduce how to calculate time-independent intensity.

The electromagnetic oscillation for a monochromatic wave is given by, ψ(r, t) = Ae^{i(r⋅r±ωt)} where A is the wave amplitude. From the real part of ψ(r, t), the imaginary part is given by

Using the S- and NS-FDTD algorithms, we obtain

Hence the intensity distribution is given by

where ψ(r, t)^* is the complex conjugate.

Copyright (C) 2011 Naoki Okada, All Rights Reserved.