Abstract

We present a theoretical analysis on optical spin-sensitive Zitterbewegung (ZB) in metamaterials. By developing some formulas about the dispersions and eigenstates of optical modes we show that spin-sensitive ZB can be obtained in a bianisotropic metamaterial with a proper coupling between the electric and magnetic responses. A close analogue of the developed analytical results with these of Dirac equation is proposed. Numerical simulation proves the existence of ZB on the refracted optical beam along a direction determined by the optical spin of incidence. Furthermore, we show that when the incident optical field is linearly polarized, although ZB on field intensity does not exist, the optical spin possesses an interesting spatial split and trembling phenomena. Significance of this investigation is discussed.

© 2016 Optical Society of America

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2015 (7)

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref] [PubMed]

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable Dirac points and Zitterbewegung in graphene-based photonic superlattices,” Phys. Rev. B 91, 201402(R) (2015).
[Crossref]

Y. Fan, B. Wang, H. Huang, K. Wang, H. Long, and P. Lu, “Plasmonic Zitterbewegung in binary graphene sheet arrays,” Opt. Lett. 40, 2945–2948 (2015).
[Crossref] [PubMed]

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nature Photonics 9, 776–778 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nature Photonics 9, 796–808 (2015).
[Crossref]

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115, 067402 (2015).
[Crossref] [PubMed]

2014 (7)

E. Efrati and W. T. M. Irvine, “Orientation-dependent handedness and chiral design,” Phys. Rev. X 4, 011003 (2014).

C. C. Leary and K. H. Smith, “Unified dynamics of electrons and photons via Zitterbewegung and spin-orbit interaction,” Phys. Rev. A 89, 023831 (2014).
[Crossref]

S. Ding and G. P. Wang, “Plasmonic analogs of Zitterbewegung in nanoscale metal waveguide arrays,” J. Opt. Soc. Am. B 31, 603–606 (2014).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

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] [PubMed]

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

B. M. Rodriguez-Lara and H. M. Moya-Cessa, “Optical simulation of Majorana physics,” Phys. Rev. A 89, 015803 (2014).
[Crossref]

2013 (2)

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

H. X. Cui, X. W. Cao, M. Kang, T. F. Li, M. Yang, T. J. Guo, Q. H. Guo, and J. Chen, “Exceptional points in extraordinary optical transmission through dual subwavelength metallic gratings,” Opt. Express 21, 13368–13379 (2013).
[Crossref] [PubMed]

2012 (2)

A. Regensburger, C. Bersch, M. Mohammad-Ali, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nature Mater. 12, 233–239 (2012).
[Crossref]

2011 (4)

Q. Liang, Y. Yan, and J. Dong, “Zitterbewegung in the honeycomb photonic lattice,” Opt. Lett. 36, 2513–2515 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[Crossref] [PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Advances in Optics and Photonics 3, 161–204 (2011).
[Crossref]

2010 (5)

C. E. Ruter, 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]

S. Longhi, “Optical realization of relativistic non-Hermitian quantum mechanics,” Phys. Rev. Lett. 105, 013903 (2010).
[Crossref] [PubMed]

S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett. 35, 235–237 (2010).
[Crossref] [PubMed]

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18, 10120–10126 (2010).
[Crossref] [PubMed]

F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

2009 (6)

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

L. G. Wang, Z. G. Wang, and S. Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL 86, 47008 (2009).
[Crossref]

S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (2009).
[Crossref] [PubMed]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
[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] [PubMed]

2008 (4)

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101, 253903 (2008).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).
[Crossref] [PubMed]

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
[Crossref] [PubMed]

2007 (1)

K. Y. Bliokh, D. Y. Frolov, and Y. A. Kravtsov, “Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium,” Phys. Rev. A 75, 053821 (2007).
[Crossref]

2006 (3)

P. Brusheim and H. Q. Xu, “Spin Hall effect and Zitterbewegung in an electron waveguide,” Phys. Rev. B 74, 205307 (2006).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref] [PubMed]

J. Cserti and G. David, “Unified description of Zitterbewegung for spintronic, graphene, and superconducting systems,” Phys. Rev. B 74, 172305 (2006).
[Crossref]

2005 (4)

J. Schliemann, D. Loss, and R. M. Westervelt, “Zitterbewegung of electronic wave packets in III–V zinc-blende semiconductor quantum wells,” Phys. Rev. Lett. 94, 206801 (2005)
[Crossref]

M. Lee and C. Bruder, “Charge- and spin-density modulations in semiconductor quantum wires,” Phys. Rev. B 72, 045353 (2005).
[Crossref]

Z. F. Jiang, R. D. Li, S-C. Zhang, and W. M. Liu, “Semiclassical time evolution of the holes from Luttinger Hamiltonian,” Phys. Rev. B 72, 045201 (2005).
[Crossref]

R. Khomeriki and S. Ruffo, “Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index,” Phys. Rev. Lett. 94, 113904 (2005).
[Crossref] [PubMed]

2003 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

2000 (1)

M. Philipp, P. von Brentano, G. Pascovici, and A. Richter, “Frequency and width crossing of two interacting resonances in a microwave cavity,” Phys. Rev. E 62, 1922–1926 (2000).
[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] [PubMed]

Almeida, V. R.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Alu, A.

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

Beri, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref] [PubMed]

Bersch, C.

A. Regensburger, C. Bersch, M. Mohammad-Ali, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nature Photonics 9, 796–808 (2015).
[Crossref]

K. Y. Bliokh, D. Y. Frolov, and Y. A. Kravtsov, “Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium,” Phys. Rev. A 75, 053821 (2007).
[Crossref]

Bruder, C.

M. Lee and C. Bruder, “Charge- and spin-density modulations in semiconductor quantum wires,” Phys. Rev. B 72, 045353 (2005).
[Crossref]

Brusheim, P.

P. Brusheim and H. Q. Xu, “Spin Hall effect and Zitterbewegung in an electron waveguide,” Phys. Rev. B 74, 205307 (2006).
[Crossref]

Cao, H.

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[Crossref] [PubMed]

Cao, X. W.

Cardano, F.

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nature Photonics 9, 776–778 (2015).
[Crossref]

Chen, J.

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115, 067402 (2015).
[Crossref] [PubMed]

H. X. Cui, X. W. Cao, M. Kang, T. F. Li, M. Yang, T. J. Guo, Q. H. Guo, and J. Chen, “Exceptional points in extraordinary optical transmission through dual subwavelength metallic gratings,” Opt. Express 21, 13368–13379 (2013).
[Crossref] [PubMed]

Chen, X.

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable Dirac points and Zitterbewegung in graphene-based photonic superlattices,” Phys. Rev. B 91, 201402(R) (2015).
[Crossref]

Chen, Y. F.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref]

Christodoulides, D. N.

A. Regensburger, C. Bersch, M. Mohammad-Ali, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

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C. E. Ruter, 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]

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nature Mater. 12, 233–239 (2012).
[Crossref]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

Siviloglou, G. A.

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] [PubMed]

Smith, K. H.

C. C. Leary and K. H. Smith, “Unified dynamics of electrons and photons via Zitterbewegung and spin-orbit interaction,” Phys. Rev. A 89, 023831 (2014).
[Crossref]

Soljacic, M.

L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Soukoulis, C. M.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Sounas, D. L.

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

Stone, A. D.

Y. D. Chong, L. Ge, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref]

Sukhorukov, A. A.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref] [PubMed]

Szameit, A.

F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

Tassin, P.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Taylor, A. J.

Trompeter, H.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref] [PubMed]

Tse, W. K.

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nature Mater. 12, 233–239 (2012).
[Crossref]

Tunnermann, A.

F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

Volatier-Ravat, M.

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] [PubMed]

von Brentano, P.

M. Philipp, P. von Brentano, G. Pascovici, and A. Richter, “Frequency and width crossing of two interacting resonances in a microwave cavity,” Phys. Rev. E 62, 1922–1926 (2000).
[Crossref]

Wang, B.

Wang, G. P.

Wang, K.

Wang, L. G.

L. G. Wang, Z. G. Wang, and S. Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL 86, 47008 (2009).
[Crossref]

Wang, Y.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Wang, Z. G.

L. G. Wang, Z. G. Wang, and S. Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL 86, 47008 (2009).
[Crossref]

Westervelt, R. M.

J. Schliemann, D. Loss, and R. M. Westervelt, “Zitterbewegung of electronic wave packets in III–V zinc-blende semiconductor quantum wells,” Phys. Rev. Lett. 94, 206801 (2005)
[Crossref]

Wiersig, J.

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

Xu, H. Q.

P. Brusheim and H. Q. Xu, “Spin Hall effect and Zitterbewegung in an electron waveguide,” Phys. Rev. B 74, 205307 (2006).
[Crossref]

Xu, N.

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] [PubMed]

Xu, Y. L.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Yan, Y.

Yang, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref] [PubMed]

Yang, M.

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Advances in Optics and Photonics 3, 161–204 (2011).
[Crossref]

Ye, F.

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable Dirac points and Zitterbewegung in graphene-based photonic superlattices,” Phys. Rev. B 91, 201402(R) (2015).
[Crossref]

Zayats, A. V.

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nature Photonics 9, 796–808 (2015).
[Crossref]

Zhang, L.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Zhang, S.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref] [PubMed]

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115, 067402 (2015).
[Crossref] [PubMed]

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] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Zhang, S-C.

Z. F. Jiang, R. D. Li, S-C. Zhang, and W. M. Liu, “Semiclassical time evolution of the holes from Luttinger Hamiltonian,” Phys. Rev. B 72, 045201 (2005).
[Crossref]

Zhang, W.

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] [PubMed]

Zhang, X.

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] [PubMed]

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Zheludev, N. I.

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101, 253903 (2008).
[Crossref] [PubMed]

Zhu, S. Y.

L. G. Wang, Z. G. Wang, and S. Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL 86, 47008 (2009).
[Crossref]

Advances in Optics and Photonics (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Advances in Optics and Photonics 3, 161–204 (2011).
[Crossref]

EPL (1)

L. G. Wang, Z. G. Wang, and S. Y. Zhu, “Zitterbewegung of optical pulses near the Dirac point inside a negative-zero-positive index metamaterial,” EPL 86, 47008 (2009).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
[Crossref]

Nat. Mater. (1)

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Nat. Photonics (1)

L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

Nat. Phys. (1)

C. E. Ruter, 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]

Nature (3)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M. Mohammad-Ali, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

Nature Mater. (1)

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nature Mater. 12, 233–239 (2012).
[Crossref]

Nature Photonics (2)

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nature Photonics 9, 776–778 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nature Photonics 9, 796–808 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (3)

C. C. Leary and K. H. Smith, “Unified dynamics of electrons and photons via Zitterbewegung and spin-orbit interaction,” Phys. Rev. A 89, 023831 (2014).
[Crossref]

K. Y. Bliokh, D. Y. Frolov, and Y. A. Kravtsov, “Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium,” Phys. Rev. A 75, 053821 (2007).
[Crossref]

B. M. Rodriguez-Lara and H. M. Moya-Cessa, “Optical simulation of Majorana physics,” Phys. Rev. A 89, 015803 (2014).
[Crossref]

Phys. Rev. B (5)

P. Brusheim and H. Q. Xu, “Spin Hall effect and Zitterbewegung in an electron waveguide,” Phys. Rev. B 74, 205307 (2006).
[Crossref]

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable Dirac points and Zitterbewegung in graphene-based photonic superlattices,” Phys. Rev. B 91, 201402(R) (2015).
[Crossref]

M. Lee and C. Bruder, “Charge- and spin-density modulations in semiconductor quantum wires,” Phys. Rev. B 72, 045353 (2005).
[Crossref]

Z. F. Jiang, R. D. Li, S-C. Zhang, and W. M. Liu, “Semiclassical time evolution of the holes from Luttinger Hamiltonian,” Phys. Rev. B 72, 045201 (2005).
[Crossref]

J. Cserti and G. David, “Unified description of Zitterbewegung for spintronic, graphene, and superconducting systems,” Phys. Rev. B 74, 172305 (2006).
[Crossref]

Phys. Rev. E (1)

M. Philipp, P. von Brentano, G. Pascovici, and A. Richter, “Frequency and width crossing of two interacting resonances in a microwave cavity,” Phys. Rev. E 62, 1922–1926 (2000).
[Crossref]

Phys. Rev. Lett. (18)

J. Schliemann, D. Loss, and R. M. Westervelt, “Zitterbewegung of electronic wave packets in III–V zinc-blende semiconductor quantum wells,” Phys. Rev. Lett. 94, 206801 (2005)
[Crossref]

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115, 067402 (2015).
[Crossref] [PubMed]

F. Dreisow, M. Heinrich, R. Keil, A. Tunnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

X. Zhang, “Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal,” Phys. Rev. Lett. 100, 113903 (2008).
[Crossref] [PubMed]

S. Longhi, “Optical realization of relativistic non-Hermitian quantum mechanics,” Phys. Rev. Lett. 105, 013903 (2010).
[Crossref] [PubMed]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref] [PubMed]

R. Khomeriki and S. Ruffo, “Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index,” Phys. Rev. Lett. 94, 113904 (2005).
[Crossref] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref] [PubMed]

S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (2009).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101, 253903 (2008).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[Crossref] [PubMed]

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

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] [PubMed]

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] [PubMed]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).
[Crossref] [PubMed]

Phys. Rev. X (1)

E. Efrati and W. T. M. Irvine, “Orientation-dependent handedness and chiral design,” Phys. Rev. X 4, 011003 (2014).

Rev. Mod. Phys. (1)

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

Other (2)

D. Dragoman and M. Dragoman, Quantum-Classical Analogies (Springer, 2004).
[Crossref]

W. Greiner, Relativistic Quantum Mechanics (Springer-Verlag, 1990).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Schematic of the unit cell of a bianisotropic metamaterial design.
Fig. 2
Fig. 2 Dispersion relations of (kx, ky) near ky = 0 and the associated Stokes parameter S 3 ( y z ) for (a, c) Δ = 0 and (b, d) Δ ≠ 0. Units of kx and ky are k0. Here ε = 2.8, μ = 1.19, γ = 0.559, and ηm = 0.917. In (a, c) ηe = ηm, and in (b, d) ηe = 0.884. Thin lines in (a) and (b) are these given by Eq. (5), and Eqs. (8) to (9), respectively. Note that in (c) S 3 ( y z ) jumps to zero when ky=0 because here the eigenstates are linearly polarized.
Fig. 3
Fig. 3 Distributions of (a, c) field intensity and (b, d) the trajectory of beam center for (a, b) left-handed and (c, d) right-handed circularly polarized incidences, respectively. Here ε = 3.2, μ = 1.19, γ = 0.559, ηm = 0.917, ηe = 0.826, and w0 = 10 cm.
Fig. 4
Fig. 4 Distributions of (a, c) field intensity and (b, d) the trajectory of beam center for right-handed circularly polarized incidence with (a, b) ε = 2.8, and (c, d) ε = 3.0, respectively. Here ε = 1.19, γ = 0.559, and ηm = 0.917, and η e 2 ε = 2.186. When ε = 2.8 the gap width 2σ equals 0.058k0, and when ε = 3.0, 2σ = 0.114k0.
Fig. 5
Fig. 5 Distribution of the Stoke’s parameter S 3 ( y z ) for the situation displayed in Fig. 3(a).
Fig. 6
Fig. 6 Distributions of (a, c) field intensity and (b, d) Stoke’s parameter S 3 ( y z ) when the incident wave is (a, b) y- and (c, d) z-linearly polarized. All the parameters are the same as these of Figs. 3(b) and Fig. 5.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

D = ε = E + ξ = H ,
B = μ = H ξ = E ,
ε = = ε 0 ε ( 1 0 0 0 1 0 0 0 η e 2 ) , μ = = μ 0 μ ( 1 0 0 0 1 0 0 0 η m 2 ) , ξ = = γ c ( 0 i 0 i 0 0 0 0 0 ) .
[ k 0 2 η m 2 ( ε μ γ 2 ) k y 2 k x k y i γ η m 2 k 0 k x k x k y k 0 2 η m 2 ( ε μ γ 2 ) k x 2 i γ η m 2 k 0 k y i γ k 0 k x i γ k 0 k y k 0 2 η e 2 ε μ k y 2 k x 2 ] [ E x E y E z ] = 0 ,
k x ± = β 0 ± ν k y ,
β 0 = k 0 η ε μ γ 2 , ν = γ ε μ .
η e = η Δ , η m = η + Δ ,
k x + = β 0 + σ + α + 2 k y 2 ,
k x = β 0 σ + α 2 k y 2 ,
σ = k 0 Δ ε μ γ 2 ,
α + = 1 β 0 ( ν 2 η + Δ Δ η η + Δ ) ,
α = 1 β 0 ( ν 2 η Δ Δ + η η Δ ) .
S 3 ( y z ) = i ( E y E z * E y * E z ) .
i ψ x = i κ α ψ y + σ β ψ ,
[ k x + σ i κ k y i κ k y k x σ ] [ E y E z ] = 0 .
k x ± = ± σ 2 + κ 2 k y 2 ± ( σ + 1 2 κ 2 σ k y 2 ) .
ψ + = A ( i κ k y 2 σ ) , ψ = A ( 2 σ i κ k y ) ,
d = 2 π 2 σ = λ 0 2 Δ ε μ γ 2 .
R = 1 2 α ¯ σ = 1 2 α + + α 2 σ

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