This example file shows how to setup and calculate the modes of a simple Bragg fiber.

## Simulation setup

Ring structures are used to create the layers with alternating indices. Two dielectric materials have been created, one for the high index layers and another for the low index layers. These materials can be modified by opening the material database. The background index (black) is set to 1.

Initially, the boundary conditions should all be set to metal and the number of mesh cells set to 200x200.

## Results

We can switch to Analysis Mode by pressing the run button and clicking Calculate Modes in the Analysis window. Initially we will use a wavelength of 4.116um. Among the several modes found by the solver, we can identify the one shown below, which is the fundamental mode confined at the empty core region and has an effective index of approximately 0.15.

By looking at the E field in cylindrical coordinates, we find that this mode is symmetric with respect to the x and y axes. We can therefore speed up the calculation by changing the x-min and y-min boundary conditions to Symmetric. After making this change, it is a good idea to recalculate the mode and be sure that we can find the same fundamental mode.

To study the loss of this type of structure, it is necessary to switch the boundary conditions to perfectly matched layer (PML) absorbing boundaries at x-max and y-max, as shown below. We did not do this initially because it increases the computation time and can make it harder to find the effective index of the fundamental mode.

When we recalculate the modes, we find that the fundamental mode at 4.116um has an effective index of approximately 0.22 and a loss of 205 dB/mm. Next, we can use the built in frequency sweep feature to calculate the modal dispersion.

It is also possible to determine the coupling sensitivity between this fiber and a simple 3um-diameter fiber for various misalignment conditions. The plot below shows the fraction of fields that overlap between the fundamental modes of the two fibers, as a function of the x and y offsets between the centers of the fibers.

To reproduce these results, run the simulation in bragg_fiber_simple_3um.lms; then, save the mode profile to a Lumerical data file (.ldf), or download a copy of the file bragg_fiber_simple_3um.ldf from this page. Finally, run the script bragg_fiber_simple_overlap.lsf to generate the figure above. The coupling efficiency is low, as expected, given the fact that the mode profiles of the two structures are very different.

## Convergence testing

We start by copying the fundamental mode to the global DECK, as shown below.

We then rename the copied mode to "fundamental", as shown below.

We can now test the convergence by running the sweep contained in the optimization and sweeps window. At each step, the optimization calculates the modes, then identifies the fundamental mode as the one that gives the best overlap with the fundamental mode we have already stored in the DECK. It then records the effective index and loss for these modes as a function of the number of mesh cells used.

Once the sweep is complete, right click on the parameter sweep to get the following plot data in the Visualizer.

Effective index vs mesh cells

Loss vs mesh cells

We see that the effective index is converging by the time we reach 500x500 mesh cells and the final value will be near 0.18; however, more mesh cells would be necessary to have more accuracy. Depending on the amount of memory on your computer, it may be possible to increase the maximum number of cells tested to 600x600 or more. The loss, on the other hand, does not depend much on the number of mesh cells and only varies between 206 dB/mm and 204 dB/mm as we change the number of mesh cells.