Solver Algorithm — Lesson 1

Modal Decomposition

The Eigenmode Expansion, or EME, method solves Maxwell's equations in the frequency domain to calculate the supported modes at the cross-section of the waveguide along the propagation direction. In this video, we will show the key working principles of the EME: slicing the waveguide into cells, expressing an arbitrary field as a superposition of the eigenmodes of individual cells, and reconstructing the propagating field using the boundary conditions at the cell interfaces.

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Scattering Matrices

Once the eigenmodes for each cell are found, the solver determines how the modes in the neighboring cells are coupled. In this video, you will learn about the S-matrices which store the information about the coupling between cells.

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Once the S-matrices are calculated, it is possible to propagate the input field to obtain the transmission/reflection of the whole device as well as the profile of the propagating field.

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  1. Bienstman, P. 2001, ‘Rigorous and efficient modelling of wavelength scale photonic components’, Electrical Engineering thesis, Ghent University, Ghent, Belgium