We analyze the propagation of electromagnetic fields through tight-binding arrays of coupled photonic waveguides as a symmetry problem in the case of invariant properties of the propagation distance. We consider the Heisenberg-Weyl group and the photonic lattices with that underlying symmetry. Based on this, dispersion relations, impulse functions and normal states can be constructed from the point of view of Gilmore-Perelomov coherent state approach and different classes of propagation invariant input can be constructed.
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