Abstract

Chirality is a universal feature in nature, as observed in fermion interactions and DNA helicity. Much attention has been given to chiral interactions of light, not only regarding its physical interpretation, but also focusing on intriguing phenomena in the excitation, absorption, refraction, and topological phases. Although recent progress in metamaterials has spurred artificial engineering of chirality, most approaches are founded on the same principle of the mixing of electric and magnetic responses. Here we propose non-magnetic chiral interactions of light based on low-dimensional eigensystems. Exploiting the mixing of amplifying and decaying electric modes in a complex material, the low dimensionality in polarization space having a chiral eigenstate is realized, in contrast to two-dimensional eigensystems in previous approaches. The existence of an optical-spin black hole from low-dimensional chirality is predicted, and singular interactions between chiral waves are confirmed experimentally in parity-time-symmetric metamaterials.

© 2016 Optical Society of America

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References

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2015 (4)

S. Deffner and A. Saxena, “Jarzynski equality in PT-symmetric quantum mechanics,” Phys. Rev. Lett. 114, 150601 (2015).
[Crossref]

S. Yu, X. Piao, K. Yoo, J. Shin, and N. Park, “One-way optical modal transition based on causality in momentum space,” Opt. Express 23, 24997–25008 (2015).
[Crossref]

X. Piao, S. Yu, J. Hong, and N. Park, “Spectral separation of optical spin based on antisymmetric Fano resonances,” Sci. Rep. 5, 16585 (2015).
[Crossref]

S. Yu, X. Piao, J. Hong, and N. Park, “Bloch-like waves in random-walk potentials based on supersymmetry,” Nat. Commun. 6, 8269 (2015).
[Crossref]

2014 (6)

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113, 093901 (2014).
[Crossref]

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113, 023903 (2014).
[Crossref]

B. Peng, Ş. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

L. Feng, X. Zhu, S. Yang, H. Zhu, P. Zhang, X. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22, 1760–1767 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346, 975–978 (2014).
[Crossref]

2013 (6)

S. Yu, D. R. Mason, X. Piao, and N. Park, “Phase-dependent reversible nonreciprocity in complex metamolecules,” Phys. Rev. B 87, 125143 (2013).
[Crossref]

X. Zhu, L. Feng, P. Zhang, X. Yin, and X. Zhang, “One-way invisible cloak using parity-time symmetric transformation optics,” Opt. Lett. 38, 2821–2824 (2013).
[Crossref]

Z. Li, M. Gokkavas, and E. Ozbay, “Manipulation of asymmetric transmission in planar chiral nanostructures by anisotropic loss,” Adv. Opt. Mater. 1, 482–488 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

S.-C. Jiang, X. Xiong, P. Sarriugarte, S.-W. Jiang, X.-B. Yin, Y. Wang, R.-W. Peng, D. Wu, R. Hillenbrand, and X. Zhang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).
[Crossref]

M.-A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87, 043819 (2013).
[Crossref]

2012 (2)

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

S. Yu, X. Piao, D. R. Mason, S. In, and N. Park, “Spatiospectral separation of exceptional points in PT-symmetric optical potentials,” Phys. Rev. A 86, 031802 (2012).
[Crossref]

2011 (3)

Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

A. Pors, M. G. Nielsen, G. Della Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett. 36, 1626–1628 (2011).
[Crossref]

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

2010 (2)

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

2009 (4)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102, 093903 (2009).
[Crossref]

M. Thiel, M. S. Rill, G. von Freymann, and M. Wegener, “Three‐dimensional bi‐chiral photonic crystals,” Adv. Mater. 21, 4680–4682 (2009).
[Crossref]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

2008 (1)

K. Makris, R. El-Ganainy, D. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

2006 (1)

V. Fedotov, P. Mladyonov, S. Prosvirnin, A. Rogacheva, Y. Chen, and N. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
[Crossref]

2004 (1)

J. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[Crossref]

2002 (2)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[Crossref]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[Crossref]

1999 (1)

S. Chen, D. Katsis, A. Schmid, J. Mastrangelo, T. Tsutsui, and T. Blanton, “Circularly polarized light generated by photoexcitation of luminophores in glassy liquid-crystal films,” Nature 397, 506–508 (1999).
[Crossref]

1998 (1)

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

1996 (1)

N. Hatano and D. R. Nelson, “Localization transitions in non-Hermitian quantum mechanics,” Phys. Rev. Lett. 77, 570–573 (1996).
[Crossref]

Aieta, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Albrektsen, O.

Alù, A.

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113, 023903 (2014).
[Crossref]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Bender, C.

B. Peng, Ş. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

Bender, C. M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Blanton, T.

S. Chen, D. Katsis, A. Schmid, J. Mastrangelo, T. Tsutsui, and T. Blanton, “Circularly polarized light generated by photoexcitation of luminophores in glassy liquid-crystal films,” Nature 397, 506–508 (1999).
[Crossref]

Boettcher, S.

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Bozhevolnyi, S. I.

Brody, D. C.

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[Crossref]

Capasso, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

Chen, S.

S. Chen, D. Katsis, A. Schmid, J. Mastrangelo, T. Tsutsui, and T. Blanton, “Circularly polarized light generated by photoexcitation of luminophores in glassy liquid-crystal films,” Nature 397, 506–508 (1999).
[Crossref]

Chen, Y.

V. Fedotov, P. Mladyonov, S. Prosvirnin, A. Rogacheva, Y. Chen, and N. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
[Crossref]

Choi, M.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011).
[Crossref]

Christodoulides, D.

K. Makris, R. El-Ganainy, D. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Christodoulides, D. N.

H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346, 975–978 (2014).
[Crossref]

M.-A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87, 043819 (2013).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

Cohen, A. E.

Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
[Crossref]

Cong, L.

M. Lawrence, N. Xu, X. Zhang, L. Cong, J. Han, W. Zhang, and S. Zhang, “Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces,” Phys. Rev. Lett. 113, 093901 (2014).
[Crossref]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Deffner, S.

S. Deffner and A. Saxena, “Jarzynski equality in PT-symmetric quantum mechanics,” Phys. Rev. Lett. 114, 150601 (2015).
[Crossref]

Della Valle, G.

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

K. Makris, R. El-Ganainy, D. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Fan, S.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102, 093903 (2009).
[Crossref]

Fedotov, V.

V. Fedotov, P. Mladyonov, S. Prosvirnin, A. Rogacheva, Y. Chen, and N. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97, 167401 (2006).
[Crossref]

Feng, L.

Fleury, R.

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113, 023903 (2014).
[Crossref]

Gaburro, Z.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Genevet, P.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

Gianfreda, M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Gippius, N. A.

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Supplementary Material (3)

NameDescription
» Supplement 1: PDF (4112 KB)      Supplementary material for “Low-dimensional optical chirality in complex potentials”
» Visualization 1: MP4 (3460 KB)      Spin black hole behavior at the EP.
» Visualization 2: MP4 (1516 KB)      Linear polarization (LP) incidence.

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Figures (6)

Fig. 1.
Fig. 1. Eigenvalues and spatial evolution of eigenstates in PT-symmetric chiral material. The real and imaginary parts of the effective permittivity εeig1,2 are shown in (a) and (b) with respect to εi0. (c) The density of chirality χ, normalized by the product of the electric field intensity Ue and βr0 (orange: εκ0=εr0/103>0, blue: εκ0=εr0/103<0, line: eigenstate 1, symbol: eigenstate 2). (d)–(h) Spatial evolution of eigenstates corresponding to points dh marked in (a)–(c). (d) εi0=0, (e) 0<εi0<εκ0, (f) εi0=εκ0, (g) and (h) εi0>εκ0. The red and blue arrows represent the axes of Ey (amplifying mode) and Ez(decaying mode). At the EP (f), the complex eigenstate has the singular form of a modal helix. (i) CIM and (j) CCS as functions of (εi0/εκ0). εr0=12.25 for (a)–(h), and εr0=6.5 for (j). εκ0=εr0/103>0 for (a), (b), (d)–(h), and (j). Leff=103 for (b).
Fig. 2.
Fig. 2. Chiral dynamics within PT-symmetric optical material. The output power ratio of LCP over RCP (IL/IR=|ELT/ERT|2 in dB) is shown for the case of (a) LCP and (b) RCP incidence as a function of the imaginary permittivity (εi0/εr0) and the interaction length (Leff=εr01/2·d/Λ0). The black dotted lines in (a) and (b) represent the EPs, where the dimensionality reduces to one. (c) LCP-convergent spin black hole dynamics on the Poincaré sphere at the EP, demonstrated with randomly polarized incidences. The interaction lengths are Leff=0, 80, 160, and 240, clockwise from the upper left. The movie is shown in Visualization 1. All the results are based on the transfer matrix method. εr0=6.5, and εκ0=εr0/103 in (a) and (b), and εκ0=εr0/200 in (c).
Fig. 3.
Fig. 3. Giant chiral conversion through the resonant structure. (a) Schematics of the chiral resonator for the S-matrix analysis (green: PT-symmetric anisotropic material of d=834  nm, εr0=6.5 and εκ0=εi0=εr0/1000; gray: metallic mirrors, εmetal=100, Λ0=1500  nm). Leff=1.4. The power ratios of the LCP over the RCP in the (b) transmitted and (c) reflected wave for different mirror thicknesses. (d) S-matrix-based spatial evolutions of waves through the resonator. Arrows denote the propagating direction of each wave.
Fig. 4.
Fig. 4. Chiral polar metamaterial for low-dimensional chirality. (a) Schematics of a PT-symmetric, point-wise anisotropic permittivity material for Eq. (1). (b) Lorentz model for an I-shaped patch with different material regimes. The effective anisotropic permittivity of chiral metamaterials (Supplement 1, Section 8): (c) the dielectric realization with propagating mode, and (e) the metallic realization with evanescent mode. The fabricated samples of a chiral metamaterial are shown in (d) and (f). Insets of (c) and (e) are the expanded images of the real and imaginary parts near the EP (red dotted line). The width of each polarized patch in (c) and (d) is set unequally to wy=5.5  μm and wz=7.5  μm, and the other structural parameters are g=1.0  μm, L=34.5  μm, a=20.5  μm, t=100  nm, and d=2  μm. The arm length of each polarized patch in (e) and (f) is set unequally to ay=25  μm and az=40  μm, and the other structural parameters are g=1.5  μm, L=50  μm, w=3.0  μm, t=100  nm, and d=2  μm. See Supplement 1, Fig. S5(a) for the definitions of the structural parameters.
Fig. 5.
Fig. 5. Observation of EP in chiral polar metamaterials. (a), (b) The experimental and (c), (d) the simulated results of CIM are shown in a spectral regime for (a), (c) dielectric and (b), (d) metallic realizations. Dotted lines represent the condition of EPs in spectral and θ domains. All simulated results were obtained using COMSOL Multiphysics.
Fig. 6.
Fig. 6. Chiral waveguides supporting the basis of modal helices. (a) Cross sections of a complex-strip waveguide using isotropic materials (graded color: silicon; purple: titanium; green: silica substrate; graded color represents the effective loss by the titanium layer). The lossless silicon (εSi=12.1) is assumed to compose the strip structure on top of the lossy titanium layer (εTi=1.66i·30.1) above a silica substrate (εSiO2=2.07), supporting both a low-loss y-polarized mode and a high-loss z-polarized mode. The complex-strip waveguide satisfies PT symmetry based on the gauge transformation (Re[εy]=Re[εz] and Im[εz]<Im[εy]<0). The effect of the loss can be controlled by changing the depth of the titanium layer. The red and blue arrows describe a corresponding point-wise anisotropic permittivity. (b) The intensity profile and the polarization (in arrows) of the eigenmodes for the structure (εyz=0. Δ=0). (c) shows the modal chirality by IL/IR as a function of Δ and tTi. (d) The absolute value of the difference between eigenvalues as a function of Δ and tTi. The intensity profile and the local chirality (IL(y,z)/IR(y,z)) at the EP are shown in (e). All results were obtained using COMSOL Multiphysics with an optical wavelength of Λ0=1500  nm. L11=190  nm, L12=300  nm, L21=620  nm, and L22=190  nm.

Equations (5)

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εr=(εr0000εr0+iεi0εκ00εκ0*εr0iεi0),
CIM=|tRLtLR|=|εκ0+εi0εκ0εi0|=|1+εi0εκ01εi0εκ0|,
B0=η1,2β1,2ω·[iεi0±λPTεκ0]·eiβ1,2x.
χ1,2=β1,22·εi0εκ0,
χ1,2=Re[β1,2]2·2εκ0·(εi0εi02εκ02)εκ02+(εi0εi02εκ02)2·e2Im(β1,2)x,

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