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arXiv · 1508.05419

Optical finite representation of the Lorentz group

B. M. Rodríguez-Lara·J. Guerrero
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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.

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B. M. Rodríguez-Lara, J. Guerrero. 2015-08-21. Optical finite representation of the Lorentz group. https://doi.org/10.1364/ol.40.005682

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