How FDTDX works

How FDTDX works#

The solver is compact enough to understand from first principles. These chapters connect Maxwell’s equations to the objects and arrays visible in Python.

Yee-grid time stepping

Staggered fields, leapfrog updates, stability, and numerical dispersion.

Maxwell on a Yee grid
Grids and boundaries

Uniform and rectilinear cells, PML, periodic/Bloch faces, PEC/PMC, and symmetry.

Grids and boundaries
Sources and detectors

Temporal profiles, plane/mode/TFSF excitation, phasors, flux, fields, and normalization.

Sources and detectors
Materials

Loss, dispersion, full tensors, oriented crystals, and subpixel geometry.

Materials and dispersion
Modes and S-parameters

Cross-sectional eigenmodes, overlap amplitudes, port power, and consistent reference planes.

Modes and S-parameters
Differentiation

Reverse-mode Maxwell gradients, memory strategies, parameter maps, and objective design.

Differentiable FDTD
Pixel and spectral design bases

Swap pixels for cosine, Fourier, or radial waves without changing the FDTD objective.

Pixel and spectral design bases