Optical finite representation of the Lorentz group
Abstract
We present a class of photonic lattices with an underlying symmetry given by a finite-dimensional representation of the 2+1D Lorentz group. In order to construct such a finite-dimensional representation of a non-compact 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 so-called linear $\mathcal{PT}$-symmetric dimer belongs to this class of photonic lattices.
- Publication:
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Optics Letters
- Pub Date:
- December 2015
- DOI:
- 10.1364/OL.40.005682
- arXiv:
- arXiv:1508.05419
- Bibcode:
- 2015OptL...40.5682R
- Keywords:
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- Physics - Optics
- E-Print:
- 11 pages, 4 figures