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Acceleration toward polarization singularity inspired by relativistic E × B drift

View Article: PubMed Central - PubMed

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.

No MeSH data available.


Directional EP with the achiral eigenstate in linearly-dichroic chiral materials.(a) The relative magnitude of electric and magnetic pseudo-fields as a function of material parameters. The Lorentz pseudo-force acceleration for each phase is shown: (b,e) before the EP with /B/ > /E/, (c,f) at the EP with /B/ = /E/, and (d,g) after the EP with /B/ < /E/, for (b–d) forward and (e–g) backward waves. (h) The operation schematic of an anomalous linear polarizer for randomly-polarized incidences: red and blue arrows denote the anisotropic permittivity with the linear dichroism and dotted arrows represent the coupling through optical chirality.
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f4: Directional EP with the achiral eigenstate in linearly-dichroic chiral materials.(a) The relative magnitude of electric and magnetic pseudo-fields as a function of material parameters. The Lorentz pseudo-force acceleration for each phase is shown: (b,e) before the EP with /B/ > /E/, (c,f) at the EP with /B/ = /E/, and (d,g) after the EP with /B/ < /E/, for (b–d) forward and (e–g) backward waves. (h) The operation schematic of an anomalous linear polarizer for randomly-polarized incidences: red and blue arrows denote the anisotropic permittivity with the linear dichroism and dotted arrows represent the coupling through optical chirality.

Mentions: Figure 4 shows the case of linearly-dichroic (ρ = i·ρi) chiral materials, which derive pseudo-fields of E(ρ, χ) = kρi·e1 and B(ρ, χ) = −ωχoρi·e2 + 2ωχo·e3 with the EP condition of ρi2 = 4χo2/(μ0εo) for /B/ = /E/. The PT-symmetry-like phase transition (Fig. 4b–d) around the EP (marked with red dots in Fig. 4c,f) occurs in linearly-dichroic chiral materials from the competition between E and B (Fig. 4a), and the direction of the E×B drift is controlled by changing ρi for the pseudo-magnetic field B, allowing the realization of the achiral singularity (Sn ~ −e2 in Fig. 4c); in sharp contrast to the case of PT-symmetric potentials. Furthermore, the obtained EP state has the directionality in its propagation due to the wavevector-dependency of Eq. (4) (Fig. 4b–dvsFig. 4e–g, Sn ~ e2 in Fig. 4f), which originates from the broken mirror symmetry of chiral materials for forward and backward waves.


Acceleration toward polarization singularity inspired by relativistic E × B drift
Directional EP with the achiral eigenstate in linearly-dichroic chiral materials.(a) The relative magnitude of electric and magnetic pseudo-fields as a function of material parameters. The Lorentz pseudo-force acceleration for each phase is shown: (b,e) before the EP with /B/ > /E/, (c,f) at the EP with /B/ = /E/, and (d,g) after the EP with /B/ < /E/, for (b–d) forward and (e–g) backward waves. (h) The operation schematic of an anomalous linear polarizer for randomly-polarized incidences: red and blue arrows denote the anisotropic permittivity with the linear dichroism and dotted arrows represent the coupling through optical chirality.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5121894&req=5

f4: Directional EP with the achiral eigenstate in linearly-dichroic chiral materials.(a) The relative magnitude of electric and magnetic pseudo-fields as a function of material parameters. The Lorentz pseudo-force acceleration for each phase is shown: (b,e) before the EP with /B/ > /E/, (c,f) at the EP with /B/ = /E/, and (d,g) after the EP with /B/ < /E/, for (b–d) forward and (e–g) backward waves. (h) The operation schematic of an anomalous linear polarizer for randomly-polarized incidences: red and blue arrows denote the anisotropic permittivity with the linear dichroism and dotted arrows represent the coupling through optical chirality.
Mentions: Figure 4 shows the case of linearly-dichroic (ρ = i·ρi) chiral materials, which derive pseudo-fields of E(ρ, χ) = kρi·e1 and B(ρ, χ) = −ωχoρi·e2 + 2ωχo·e3 with the EP condition of ρi2 = 4χo2/(μ0εo) for /B/ = /E/. The PT-symmetry-like phase transition (Fig. 4b–d) around the EP (marked with red dots in Fig. 4c,f) occurs in linearly-dichroic chiral materials from the competition between E and B (Fig. 4a), and the direction of the E×B drift is controlled by changing ρi for the pseudo-magnetic field B, allowing the realization of the achiral singularity (Sn ~ −e2 in Fig. 4c); in sharp contrast to the case of PT-symmetric potentials. Furthermore, the obtained EP state has the directionality in its propagation due to the wavevector-dependency of Eq. (4) (Fig. 4b–dvsFig. 4e–g, Sn ~ e2 in Fig. 4f), which originates from the broken mirror symmetry of chiral materials for forward and backward waves.

View Article: PubMed Central - PubMed

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 &lsquo;pseudo&rsquo;-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&times;B &ldquo;polarization&rdquo; drift.

No MeSH data available.