32 - The beam propagation method

Summary

The beam propagation method (BPM) is a simple numerical algorithm for simulating the propagation of a coherent beam of light through a dielectric waveguide (or other structure). Figure 32.1 shows the split-step technique used in the BPM, in which the diffraction of the beam and the phase-shifting action of the guide are separated from each other in repeated sequential steps, of separation Δz. One starts a BPM simulation by defining an initial cross-sectional beam profile in the XY-plane. The beam is then propagated (using classical diffraction formulas) a short distance Δz along the Z-axis before being sent through a phase/amplitude mask. The properties of the mask are derived from the cross-sectional profile of the waveguide (or other structure) in which the beam resides. The above steps of diffraction followed by transmission through a mask are repeated until the beam reaches its destination or until one or more excited modes of the guide become stabilized.

Instead of propagating continuously along the length of the guide, the beam in BPM travels for a short distance in a homogeneous isotropic medium, which has the average refractive index of the guide but lacks the guide's features (e.g., core, cladding, etc.). After this diffraction step, a phase/amplitude mask is introduced in the beam path. To account for the refractive index profile of the guide, the mask must phase-shift certain regions of the beam relative to others.