Tips for simulating high Q Photonic Crystal (PhC) Cavity

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#1

While there are various approaches to simulate high Q factor using photonic crystal cavity, there are some common considerations to make in order to increase your chance to obtain the results you expect.

  1. Lumerical comes with High Q analysis tool that is available in the object library. Make sure to select the high Q analysis and not the low Q:

  2. To get good results for cavity simulation, it is important to include an integer number of mesh cells per lattice constant in the two directions. We can expect reasonable accuracy with a λ/10 mesh. To make sure that the mesh can actually be an integer number of mesh cells, the simulation (FDTD) span has to fit exactly an integer number of mesh cells inside the boundaries. By clicking the ‘View mesh’ button, it is possible to view the mesh around the structure. It is important that each hole is meshed in the same way. If the mesh lines fall at different locations with respect to the holes, each hole will have a slightly different size and shape in the simulation.

  3. Boundary conditions and the z span of the simulation. Typically, you will use PML boundaries with this type of simulation. PML boundaries absorb incident radiation, and are intended to absorb all radiation propagating away from the cavity. It is important to leave some distance between the cavity and the PML boundaries, particularly in the z direction where it is easy to get too close to the cavity. If the boundaries are too close to the cavity, they will start to absorb the non-propagating local evanescent fields that exist within the cavity. A simple rule is to leave at least half a wavelength of distance above and below the structure. You can also use a 2D field monitor to display the field profile in the z direction to better judge if the PML interaction with the evanescent fields. Here is an example:

    The profile from the 2D field monitor in z direction (log scale):

  4. Make sure to include enough PhC periods in x and y direction. Using low number of periods can result in poor confinement and a leaky cavity that protects you from reaching high Q factor.

  5. Do not include air interface between the slab the PML in x and y direction. Let’s consider a case of PhC created by etch holes in silicon slab. If you include several PhC periods in your simulation and then interface created by silicon slab/air interface before PML, it will likely cause artificial confinement that is introduced by the reflection on the interface. Rather try to place the PML over the slab and use “extend through PML” option in the FDTD region settings to avoid this artificial confinement that could skew your results.

For more information about high Q PhC simulation visit:
PC Micro Cavity Tutorial (FDTD)
Photonic Crystal Fiber (MODE)
Simple high Q example (FDTD)
Quality Factor Calculations - Advanced Notes


L3 Cavity Mode Simulation