Lumerical’s new 2D/3D bi-directional Eigenmode Expansion (EME) solver in MODE Solutions complements the existing Eigenmode and 2.5D variational FDTD solver (varFDTD) to make MODE Solutions a complete and comprehensive design environment ideal for virtual prototyping of fiber and waveguide components.
The EME method is a fully vectorial and bi-directional technique to solve Maxwell's equations. The methodology relies on the modal decomposition of electromagnetic fields into a basis set of eigenmodes, which are computed by dividing the geometry into multiple cells and then solving for the modes at the interface between adjacent cells. Scattering matrices for each section are formulated by applying boundary conditions at the interface between each section. The solution to each section is then propagated bi-directionally to calculate the total transmission and reflection of the device, as well as the final field profile.
The EME method is very efficient for optimization of large waveguide components. Once the basis set of modes are computed for the EME method, there is very little additional computation required to change the length or number of periods of the device. In addition, only one simulation is required to obtain the result for all input modes and polarizations.
Lumerical provides an intuitive user interface for defining and parameterizing the device geometry. In the EME solver region, the location of the cells as well as the span between each cell can be defined in a simple tabular format.
Figure 1: An MMI coupler simulated using the EME solver. The red lines (left) indicate the location of the interfaces, as specified in the table to the right. The input and output waveguides, as well as the MMI core can be represented with only one cell. The tapered sections require more cells to resolve the geometry.
Figure 2: (Left) A unit cell of a fiber Bragg grating (FBG) can be simulated with 2 cells, one for the higher index region and one for the lower index region. The number of periods can be set arbitrarily. The result of a 20000 period FBG is shown (right). Learn more about this application⇒ (Login required)
Figure 3: Only 3 cells are required to simulate an MMI coupler. Once the modes are calculated at each interface, the length of the core region can be scanned quickly without having to solve for any additional modes.
Non-uniform structures: Spot-Size converter
Figure 4: Compares the transmission for the spot-size converter in  calculated using the EME solver and 3D FDTD. The EME simulation takes 1 minute to simulate 101 different taper lengths (blue squares), whereas 3D FDTD takes 6 hours to simulate 11 different taper lengths (green squares). Learn more about this application⇒(Login required)
Non-uniform structures: Polarization Converter
Figure 5: Shows the transmission into the fundamental TM and second-order TE mode of the output waveguide for a polarization converter . The strength of EME for larger device lengths is seen in comparison with FDTD analysis. The discrepancy between the EME and FDTD results at longer taper lengths is due to FDTD grid dispersion. Accuracy of the FDTD simulation improves as the mesh is increased from 10 grids per wavelength (left) to 14 grids per wavelength (right), at the cost of higher simulation time. Learn more about this application⇒(Login required)
The combination of Lumerical’s advanced meshing algorithms and MODE Solutions multi-threaded mode-solving engine means that the calculation of the basis set of eigenmodes for all interfaces, often the most time consuming part of the EME algorithm, can be carried out quickly, efficiently and accurately.
In MODE Solutions, users have the ability to choose from a variety of optical solvers. This includes the Eigenmode solver, the 2.5D variational FDTD (varFDTD) solver, and the EME solver. MODE Solutions and FDTD Solutions share a familiar CAD environment in which the same structures, simulation mesh and analysis tools can be used across different solvers. The familiar design environment and comprehensive suite of solver tools makes the combination of MODE Solutions and FDTD Solutions ideal for efficient component design workflows.
Figure 6: For the polarization converter in , the Eigenmode solver can be used to identify the regions where mode-crossings occur. This allows one to quickly narrow down the design choices prior to running full simulations of the entire device using the EME solver.Learn more about this application⇒(Login required)
For active components, in addition to optical simulation using MODE Solutions, Lumerical’s charge transport solver DEVICE is required to simulate the steady-state and transient behavior of the charge carriers. Interoperability between Lumerical’s optical solvers and DEVICE allows one to completely characterize optoelectronic components such as modulators and photodetectors using an efficient workflow.
Figure 7: Absorption per unit volume along the Ge photodetector in . This simulation takes under 1 minute to run using the EME solver, and about 4 hours to run with 3D FDTD. Learn more about this application.
The EME solver automatically computes the component S parameters matrix, which can be imported into a library of circuit components in INTERCONNECT and used to study the circuit-level response of a photonic integrated circuit such as the DPSK modulator shown in Figure 8.
Figure 8: A DPSK transceiver circuit  in INTERCONNECT (left). The MMI coupler compact models are based on the S parameters extracted from an EME simulation of the MMI coupler in  (right).
 T. Tsuchizawa et al, “Microphotonics devices based on silicon microfabrication technology”, IEEE J. Select. Topics Quantum Electron., 11, 2005, 232-240.