The PCF is constructed by perforating a circular fiber of radius 300 um with air holes forming a hexagonal lattice. The lattice constant is 23.2 um, and the air hole radius within the photonic crystal lattice is 5.8 um. The cavity itself is formed by removing a central hole. Since the material of the air hole is specified as "etch" (with mesh order 1), whereas the mesh order of the fiber is 2, MODE will use the refractive index data from the air holes in regions where the two objects overlap. For more details about mesh order, refer to the mesh order page in the Reference Guide.
It is always a good idea to start with a relatively coarse mesh (a good rule of thumb is 50 grid points in each of the x and y direction). This way the simulation will run quickly and still provide reasonable results. When high accuracy is required, increase the number of grid points. Note that the more grid points you use, the more memory required.
It is important to make sure that periodic structures are properly discretized in order to get accurate results. In general, it is always good to ensure that you can fit an integer number of mesh cells within each period of the device, and within the span of the simulation region. In this example, the x and y span are both 12 times the period of the structure along the respective axis, and there are 60/12=5 mesh cells per period.
In the screen shot below (or if you view the mesh in MODE by clicking on VIEW SIMULATION MESH ), it is possible to see that there is a mesh cell at the same point at each period of the hole array. If the mesh lines fall at different locations, each hole will have a slightly different size and shape, reducing the accuracy of the simulation.
Note that by setting the y min boundary condition to symmetric the lowest order mode with electric field polarized along the x axis has been chosen.
Before beginning Modal Analysis, one should always mesh the structure to see that the material properties that will be used in the calculation are correct. Next, we provide an estimate of the mode effective index to the solver. In this case, we use the SEARCH IN RANGE option because we do not yet know the effective index of the fundamental mode. With this setting, MODE will iteratively move through the effective index range (n1 to n2) specified, and locate any modes where the majority of the optical energy is located in the interior (and not along the boundaries) of the computation region. Once you see a number (say, more than 5) modes appear in the index table, press the STOP button on the progress window.
You should now have in front of you the following results:
By selecting various modes within the table, the spatial intensity profile of the mode will be plotted in the window. Note that mode #1, with the highest effective refractive index, consists of a central intensity lobe - this is the fundamental mode that we are looking for (with effective index of approximately 1.4436). We can now use this value to speed up the calculation process when using a finer mesh with the SEARCH NEAR N option. Note that the fundamental mode is found in the first attempt, but now with a higher spatial resolution. The effective index may shift slightly due to the higher resolution meshing.
The modes of interest are typically those that have energy near the center of the photonic crystal fiber (and away from the PML boundary layers). Modes found near the PML boundary conditions tend to be artificial, and are automatically hidden. The ADVANCED OPTIONS tab can be set so that MODE returns all of the modes found, should you be interested in doing so.
For each mode listed in the mode table, the effective index, propagation loss and polarization properties (see Mode List and Deck for a more precise definition) are shown.
The frequency dependence of the effective index and propagation loss of a particular mode can be calculated with the frequency analysis tool. From this the associated modal group velocity, group effective index, modal delay and dispersion can also be determined. This type of analysis is done in the Frequency Analysis Tab. Here we determine the waveguide dispersion of the lowest order mode over a broad range in frequency (or wavelength).
We can get the dispersion plot below by following the instructions in the "Modeling instructions" section. Note that this is the plot of the total dispersion (i.e. material dispersion + waveguide dispersion), which at 1.55 microns is equal to 25.8 ps/(nm×km). To calculate the dispersion to greater precision, the number of grid points could be increased. It is good practice to double the number of grid points and see if the results change significantly.
Now, to determine the fraction of the total measured dispersion results from the waveguide itself, we need to remove the material dispersion from the Corning material. To do this, we need to determine the refractive index of the Corning material at the wavelength of interest (1550nm) using the MATERIAL EXPLORER (press the MATERIAL EXPLORER button in the Material Database):
Note that the material is set to "Corning 7980 Silica". To determine the refractive index, set the min and max wavelengths to 1.55 microns and press "Fit and plot", and read off the real part of the effective index (1.4440) from the Re(index) plot. Once we set the index of the fiber to be a non-dispersive material of index 1.4440 and re-perform the sweep, the frequency sweep plot will show that the (waveguide only) dispersion is equal to about 1.3 ps/(nm×km). Thus, the material dispersion is the dominant component of the total dispersion for this micro-structured fiber design.
The plot below shows that at around .3 meters the loss arising from the bend begins to increase dramatically. For smaller radius of curvature bends, the fundamental mode of interest begins to couple significantly to cladding modes within the photonic crystal fiber, leading to a complicated loss versus bend radius relationship.