# Application Gallery

 Results and discussion

The project file used in this example is provided in the top-level page.  Alternatively, the file can be created from scratch by following the steps described in the Modeling Instructions page.  Once the simulation has been set up, it will look as in this screenshot (in the XZ-plane).

Fig: XZ view of the geometry.

There are two rectangles in the Objects Tree.  The silicon "WG" and the "Oxide" cladding.  The simulation region is set up to be a 2D rectangle in the XZ plane.  The simulation boundaries are set up as perfect electrical conductors using the PEC boundary condition.  A mesh constraint object is placed over the waveguide to refine mesh so that the electric field distribution inside the waveguide can be properly resolved.

## Run Simulation

Run the simulation by pressing the RUN button under Simulation section of the FEEM tab.  After the simulation is run, results will be available in the FEEM solver region and the icon will change to indicate that.  Right click on the FEEM object and click 'Visualize' to plot the quantities of interest.

### Simulation Mesh

Right click on FEEM solver object and select visualize>grid.  This opens up the 'grid' dataset which reports the index profile inside the simulation area.  Note that the 'grid' result can also be generated without running the simulation by clicking on the 'Mesh' button.  The figure below shows the index profile along with the finite-element mesh.  Note that the mesh is finer on the surface of the silicon waveguide due to the mesh constraint.

### Optical Modes

Right click on FEEM solver object and select visualize>modeproperties.  The 'modeproperties' dataset reports the effective index and propagation loss of the optical modes. The plot (below) on the left shows the effective index for the first 20 optical modes.  The plot (below) on the right shows the loss of the optical modes.  Note that at 1.55 micron the silicon waveguide is approximately lossless.

The 'fields' dataset also available in the FEEM solver object reports the electric and magnetic field profiles for the different optical modes.  The plots below shows the electric field profiles for the fundamental TE (mode 1) and fundamental TM (mode 2) modes.

 |E| |Ex| |Ey| |Ez| TE TM

### Frequency Sweep (group index)

Next, we will calculate the group index of the fundamental TE mode for SOI waveguide.  To do this we will have to run two simulations at different frequencies and calculate the group index from the slope of the effective index versus frequency (wavelength) plot.  The script file SOI_WG_ng_sweep.lsf is set up to run two simulations, one at 1.55 micron and another at 1.56 micron.  The script will then calculate the group index using, $$n_g(w_1) = n_{eff}(w_1) - \lambda_1\frac{n_{eff}(w_2)-n_{eff}(w_1)}{\lambda_2-\lambda_1}$$, where, $$\lambda_i=\frac{c}{w_i}$$.  The group index of the fundamental TE mode is calculate to be 4.24.  The script will also plot the effective index of the fundamental TE mode as a function of wavelength (plot below).

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