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Beam Propagation Method

Paraxial wave equation solved with the Crank–Nicolson scheme. Launch a Gaussian beam into a step-index waveguide and watch the intensity evolve along the propagation axis.

Parameters

Propagation
Beam
Grid
Waveguide
Boundary conditions

Crank–Nicolson BPM. Solves the paraxial Helmholtz equation ∂zu = (i/2km) (∂2xu + (k²−km²) u) with a second-order implicit scheme that is unconditionally stable. Absorbing BCs add a quadratic imaginary-n ramp at the window edges to damp outgoing waves.

Intensity |v(x,z)|²