Theory

These pages explain how BeamZ turns Maxwell’s equations into local field updates, represents material interfaces, absorbs outgoing waves, and launches waveguide modes.

From physics to simulation

Topic	What you will learn
Maxwell Equations	How charges, currents, polarization, and magnetization determine the fields, and why two curl equations drive time evolution.
Yee-update	How staggered space and time samples turn the curl equations into explicit updates, and what limits the time step.
Rasterization	How continuous geometry becomes material coefficients on the field grid, including partially filled cells.
CPML	How absorbing layers approximate an open domain using stretched derivatives and a short memory recurrence.
Mode Sources	How a transverse eigenmode becomes a directional excitation with a defined frequency and power.

Read in order or start with a topic of interest. For runnable workflows, see Getting Started and the simulation examples.

Conventions

Equations use SI units. Bold symbols denote vectors; $\varepsilon$ and $\mu$ denote absolute permittivity and permeability unless a subscript $r$ explicitly indicates a relative value. Physical fields are real. For frequency-domain arguments we use the phasor convention $e^{-i\omega t}$ .

BeamZ’s Material(permittivity=..., permeability=...) takes relative values. For example, Material(permittivity=3.48**2) represents $\varepsilon=\varepsilon_0\,3.48^2$ for a nonmagnetic dielectric. Conductivity is in S/m.

The derivations start with linear, isotropic, nondispersive materials on a uniform grid. BeamZ represents materials with static real coefficients and electric conductivity; its FDTD solver supports diagonal permittivity and restricted full tensor coupling. Polarization, magnetization, and dispersion are discussed as general physics, not as a promise of arbitrary dispersive or magnetic material models. See Rasterization and Mode Sources for current restrictions.

What controls accuracy

A stable calculation can still be inaccurate. Vary resolution, smoothing, source settings, and absorber thickness independently, comparing the quantity you need, such as transmitted power or resonance wavelength.

Start with Maxwell Equations.