Beam-Prop

Beam Propagation Method (BPM) for planar photonic integrated circuits (PIC), implemented in MATLAB with finite-differences.

Brief description of the BPM-FD-2D

The BPM is a paraxial spectral-domain stepping algorithm, propagating a transversal spatial excitation at the input facet of structure (e.g. at one port of a PIC waveguide component) down to its output facet, along a well-defined (straight) optical axis; only 'slow' longitudinal perturbations of the structure are allowed, such as tapers, S-type bends or MMI-sections when dealing with PICs. The BPM is implemented with finite differences in 2D, where one axis is the waveguide cross-section (e.g. x), the other axis is the propagation direction (e.g. z). Perfectly matched layers (PML) truncate the cross-section in the lateral x-direction. Both scalar and semi-vector variants are included, corresponding to TE and TM polarized modes in the PIC waveguides. A variable wide-angle (Pade) correction can be used in conjunction with the Crank-Nicolson scheme, for the z-propagation algorithm.

Note that a multi-layer slab waveguide (MLSWG) characteristic equation solver is included, that can be used to calculate the modal excitation fed at the input port of the PIC. It can solve for arbitrary number of slab layers, with complex-valued indices, for both TE and TM polarizations. It can be used to find all modes inside a specified effective-index range, for a given wavelength.

Examples included

Four scripts/examples are included, to ease the understanding of these routines and how to define the various input variables.

1. Solver used for Coupler Supermodes -- Extracts the (super)modes supported by a waveguide coupler, assumed as a "super-waveguide".
2. BPM along a simple coupler -- Excites one port of a waveguide coupler and propagates the field down to the end of the coupler.
3. BPM tap coupler -- Models a realistic 10 dB tap coupler, including S-bends to uncouple the I/O waveguide ports.
4. BPM MZI modulator -- Models an amplitude modulator, including a pair of MZI arms with input/output Y-splitter/combiners, respectively.

Files

Here is a list of the m-files included in this repository

\BPM\BPMFD2D_DoProp.m
    \BPMFD2D_DrawLayout.m
    \BPMFD2D_PreProcLayout.m
\Solver\interpinv.m
       \MLSWG.m
       \MLSWG_CharEq.m
       \myNewtonRaphson.m
\Misc\flwcs.m
     \fmfp.m
     \LVCMv2.m
myScriptExample1_Solver_Supermodes.m
myScriptExample2_BPM_Simple_coupler.m
myScriptExample3_BPM_Tap_coupler.m
myScriptExample4_BPM_MZI_modulator.m

References

If this code is used for research papers, be a pal and please cite some of my relevant works, e.g., this one (thermo-optically tunable plasmonic components) or that one (nonlinear graphene-comprising isolator). Both relate to full-vector finite-element method implementations of the BPM, which I plan to soon^TM add, too.