Optical finite representation of the Lorentz group
Abstract
We present a class of photonic lattices with an underlying symmetry given by a finitedimensional representation of the 2+1D Lorentz group. In order to construct such a finitedimensional representation of a noncompact group, we have to design a $\mathcal{PT}$symmetric optical structure. Thus, the array of coupled waveguides may keep or break $\mathcal{PT}$symmetry, leading to a device that behaves like an oscillator or directional amplifier, respectively. We show that the socalled linear $\mathcal{PT}$symmetric dimer belongs to this class of photonic lattices.
 Publication:

Optics Letters
 Pub Date:
 December 2015
 DOI:
 10.1364/OL.40.005682
 arXiv:
 arXiv:1508.05419
 Bibcode:
 2015OptL...40.5682R
 Keywords:

 Physics  Optics
 EPrint:
 11 pages, 4 figures