Abstract
We implement a finite-dimensional representation of the 2+1D Lorentz group with a PT-symmetric waveguide array. Our device can be engineered to behave like a multi-port oscillator or directional coupler with amplification. We show that the two-waveguide coupler with linear losses, the Vernier effect in coupled asymmetric micro-cavity lasers, and the so-called linear PT-symmetric dimer belong to this symmetry class of optical systems.
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