Implementing translational and rotational symmetries

[johnaparker]

Implement all of the symmetry options to miepy.cluster

Implementation

• Test the convergence of the current 1D and 2D implementation. A metric of auto-convergence should determine when to stop computing (see [1])
• Implement 3D translational symmetry (ref [2])
• Implement the rotational and mirror symmetries (see miepy/docs for theory)
• For translational symmetries in 2D, define symmetries the major type of lattice (square, rectangle, hexagonal, etc.)

Tests

• FDTD 1d and 2d periodic boundary comparison
• Rotational symmetry compared to exact solution for different integers of rotation symmetry
• Translational symmetry compared to approximation solution (a long chain or large 2D lattice)

References

1. Xu_2013_Scattering of electromagnetic waves by periodic particle arrays.pdf
   1D and 2D periodic
2. josaa-31-2-322.pdf
   3D periodic