Bloch Boundary condition is the general periodic boundary condition to ensure the angled plane wave is excited correctly:
https://optics.ansys.com/hc/en-us/articles/360034382714-Bloch-boundary-conditions-in-FDTD-and-MODE
If you check the theory for bloch modes, you will notice that the envelope is periodic however the wave has extra phase term, which is shown in the above link at the boundary only. eg
and E(x) is spatially periodic as the normal periodic function when incident angle is zero.
The commonly known “periodic boundary condition” is the special case of Bloch boundary condition.
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