Abstract
The relativistic trajectory of a charged particle driven by the Lorentz force is different from the classical one, by velocity-dependent relativistic acceleration term. Here we show that the evolution of optical polarization states near the polarization singularity can be described in analogy to the relativistic dynamics of charged particles. A phase transition in parity-time symmetric potentials is then interpreted in terms of the competition between electric and magnetic ‘pseudo’-fields applied to polarization states. Based on this Lorentz pseudo-force representation, we reveal that zero Lorentz pseudo-force is the origin of recently reported strong polarization convergence to the singular state at the exceptional point. We also demonstrate the deterministic design of achiral and directional eigenstates at the exceptional point, allowing an anomalous linear polarizer which operates orthogonal to forward and backward waves. Our results linking parity-time symmetry and relativistic electrodynamics show that previous PT-symmetric potentials for the polarization singularity with a chiral eigenstate are the subset of optical potentials for the E×B “polarization” drift.
Highlights
With the universal existence of open systems[1,2] of non-equilibrium and time-dependent[3,4,5] potential energy, the concept of parity-time (PT) symmetry[6,7] has become a multidisciplinary topic[8,9,10,11,12,13,14,15]
Inspired by the polarization equation of motion from the Schrödinger-like form of Maxwell’s equations[36], here we interpret the evolution of optical states of polarizations (SOP) near the EP singularity in direct analogy to the relativistic E×B drift of charged particles[34], which we call the relativistic E×B “polarization” drift of light
The phase transition in PT-symmetric potentials[6,16,17] is understood in view of the competition between electric- and magnetic- ‘pseudo’-fields, and we prove that strong chiral conversion of optical SOP at the EP15,16 corresponds to the accidental cancellation of the Lorentz pseudo-force on the Poincaré hemisphere
Summary
E×B drift received: June 2016 accepted: October 2016 Published: 24 November 2016. The phase transition in PT-symmetric potentials[6,16,17] is understood in view of the competition between electric- and magnetic- ‘pseudo’-fields, and we prove that strong chiral conversion of optical SOP at the EP15,16 corresponds to the accidental cancellation of the Lorentz pseudo-force on the Poincaré hemisphere By employing this “Lorentz-force picture” in the analysis of the polarization singularity, we extend the class of the polarization singularity in vector wave equations[25,26,37,38,39], revealing the existence of achiral and directional eigenstates at the EP. Our approach paves the way for the unconventional control of optical polarizations, such as anomalous directional polarizers
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