# Perfectly matched layer (PML) (2D FDTD)

A **perfectly matched layer (PML)** is an absorbing region around the simulation interior. Its purpose is to attenuate outgoing waves while introducing little reflection at the entrance to the layer.

FDTD CUDA uses a split-field PML. Inside it, the electric field is reconstructed from two directional contributions:

$$
E_z=E_{zx}+E_{zy}
$$

The contributions have separate damping along x and y. Conductivity increases polynomially with depth into the layer, and the magnetic profiles account for the half-cell offsets of the [[fdtd-cuda-yee-grid|Yee grid]]. These profiles are included in the [[fdtd-cuda-update-coefficients|update coefficients]].

`Boundary::Pml` enables the layer. Its thickness, polynomial order, and target reflection are configured by `pml_thickness`, `pml_order`, and `pml_reflection`. The layer must leave a nonempty interior, and sources must be outside it.

An outer PEC wall still terminates the grid. Finite thickness and discretization leave some reflection, so the target reflection is a construction parameter rather than a guaranteed measurement. With zero thickness, this option behaves like PEC.