Abstract

We study the diffraction of optical waves by a single layer of gyromagnetic cylinders. We show that a nonvanishing rotating dipole momentum is excited in a single gyromagnetic cylinder because of the classic analog of the Zeeman effect on photonic angular momentum states (PAMSs). Consequently, different collective dipole modes are excited in a gyromagnetic cylinder array at opposite incident angles. Nonreciprocal optical diffraction effects can be observed, where the transmission and reflection coefficients depend on the sign of the incident angle. A novel phenomenon of nonreciprocal negative directional transmission is demonstrated and numerically analyzed. This work highlights the potential of PAMSs in manipulating the propagation of optical waves for various applications.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  30. J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
    [CrossRef]

2013 (11)

A. A. Asatryan, L. C. Botten, K. Fang, S. Fan, R. C. McPhedran, “Local density of states of chiral Hall edge states in gyrotropic photonic clusters,” Phys. Rev. B 88, 035127 (2013).
[CrossRef]

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

Y. Hadad, Y. Mazor, B. Z. Steinberg, “Green’s function theory for one-way particle chains,” Phys. Rev. B 87, 035130 (2013).
[CrossRef]

Q. H. Guo, M. Kang, T. F. Li, H. X. Cui, J. Chen, “Slow light from sharp dispersion by exciting dark photonic angular momentum states,” Opt. Lett. 38, 250–252 (2013).
[CrossRef] [PubMed]

Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett. 102, 211906 (2013).
[CrossRef]

M. Yang, T. F. Li, Q. W. Sheng, T. J. Guo, Q. H. Guo, H. X. Cui, J. Chen, “Manipulation of dark photonic angular momentum states via magneto-optical effect for tunable slow-light performance,” Opt. Express 21, 25035–25044 (2013).
[CrossRef] [PubMed]

T. F. Li, T. J. Guo, H. X. Cui, M. Yang, M. Kang, Q. H. Guo, J. Chen, “Guided modes in magneto-optical waveguides and the role in resonant transmission,” Opt. Express 21, 9563–9572 (2013).
[CrossRef] [PubMed]

M. Liu, X. Zhang, “Plasmon-boosted magneto-optics,” Nat. Photonics 7, 429–430 (2013).
[CrossRef]

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, G. Dong, W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett. 110, 163902 (2013).
[CrossRef] [PubMed]

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

2012 (2)

Y. Mazor, B. Z. Steinberg, “Longitudinal chirality, enhanced nonreciprocity, and nanoscale planar one-way plasmonic guiding,” Phys. Rev. B 86, 045120 (2012).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

2011 (5)

J. Wang, K. H. Fung, H. Y. Dong, N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84, 235122 (2011).
[CrossRef]

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef] [PubMed]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

2010 (3)

A. Devilez, B. Stout, N. Bonod, “Mode-balancing far-field control of light localization in nanoantennas,” Phys. Rev. B 81, 245128 (2010).
[CrossRef]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef] [PubMed]

Y. Hadad, B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett. 105, 233904 (2010).
[CrossRef]

2009 (1)

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

2008 (3)

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

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett. 89, 251115 (2006).
[CrossRef]

2005 (1)

A. M. Merzlikin, A. P. Vinogradov, M. Inoue, A. B. Granovsky, “Giant photonic Hall effect in magnetophotonic crystals,” Phys. Rev. E 72, 046603 (2005).
[CrossRef]

2004 (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[CrossRef]

2003 (1)

Asatryan, A. A.

A. A. Asatryan, L. C. Botten, K. Fang, S. Fan, R. C. McPhedran, “Local density of states of chiral Hall edge states in gyrotropic photonic clusters,” Phys. Rev. B 88, 035127 (2013).
[CrossRef]

Belotelov, V. I.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Bettiol, A. A.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Bonod, N.

A. Devilez, B. Stout, N. Bonod, “Mode-balancing far-field control of light localization in nanoantennas,” Phys. Rev. B 81, 245128 (2010).
[CrossRef]

Botten, L. C.

A. A. Asatryan, L. C. Botten, K. Fang, S. Fan, R. C. McPhedran, “Local density of states of chiral Hall edge states in gyrotropic photonic clusters,” Phys. Rev. B 88, 035127 (2013).
[CrossRef]

Breese, M. B. H.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Chan, C. T.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef] [PubMed]

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

Chen, J.

Chen, W. J.

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

Chin, J. Y.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Chui, S. T.

J. Du, Z. Lin, S. T. Chui, G. Dong, W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett. 110, 163902 (2013).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Crozier, K. B.

Cui, H. X.

Devilez, A.

A. Devilez, B. Stout, N. Bonod, “Mode-balancing far-field control of light localization in nanoantennas,” Phys. Rev. B 81, 245128 (2010).
[CrossRef]

Dionne, G. F.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Dong, G.

J. Du, Z. Lin, S. T. Chui, G. Dong, W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett. 110, 163902 (2013).
[CrossRef] [PubMed]

Dong, H. Y.

J. Wang, K. H. Fung, H. Y. Dong, N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84, 235122 (2011).
[CrossRef]

Dong, J. W.

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

Dregely, D.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Du, J.

J. Du, Z. Lin, S. T. Chui, G. Dong, W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett. 110, 163902 (2013).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Evers, J.

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Fan, S.

A. A. Asatryan, L. C. Botten, K. Fang, S. Fan, R. C. McPhedran, “Local density of states of chiral Hall edge states in gyrotropic photonic clusters,” Phys. Rev. B 88, 035127 (2013).
[CrossRef]

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

M. Soljačić, C. Luo, J. D. Joannopoulos, S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Fang, K.

A. A. Asatryan, L. C. Botten, K. Fang, S. Fan, R. C. McPhedran, “Local density of states of chiral Hall edge states in gyrotropic photonic clusters,” Phys. Rev. B 88, 035127 (2013).
[CrossRef]

Fang, N. X.

J. Wang, K. H. Fung, H. Y. Dong, N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84, 235122 (2011).
[CrossRef]

Fung, K. H.

J. Wang, K. H. Fung, H. Y. Dong, N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84, 235122 (2011).
[CrossRef]

Gan, F.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Giessen, H.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Granovsky, A. B.

A. M. Merzlikin, A. P. Vinogradov, M. Inoue, A. B. Granovsky, “Giant photonic Hall effect in magnetophotonic crystals,” Phys. Rev. E 72, 046603 (2005).
[CrossRef]

Guo, M. J.

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

Guo, Q. H.

Guo, T. J.

Hadad, Y.

Y. Hadad, Y. Mazor, B. Z. Steinberg, “Green’s function theory for one-way particle chains,” Phys. Rev. B 87, 035130 (2013).
[CrossRef]

Y. Hadad, B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett. 105, 233904 (2010).
[CrossRef]

Haldane, F. D. M.

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

Hang, Z. H.

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

Hong, M.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Hu, J.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Inoue, M.

A. M. Merzlikin, A. P. Vinogradov, M. Inoue, A. B. Granovsky, “Giant photonic Hall effect in magnetophotonic crystals,” Phys. Rev. E 72, 046603 (2005).
[CrossRef]

Jiang, P.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Joannopoulos, J. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

M. Soljačić, C. Luo, J. D. Joannopoulos, S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Kang, M.

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef] [PubMed]

Khurgin, J. B.

J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett. 89, 251115 (2006).
[CrossRef]

Kim, D. H.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Kimerling, L. C.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Kivshar, Y. S.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef] [PubMed]

Li, H.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Li, T. F.

Lin, Z.

J. Du, Z. Lin, S. T. Chui, G. Dong, W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett. 110, 163902 (2013).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef] [PubMed]

Liu, M.

M. Liu, X. Zhang, “Plasmon-boosted magneto-optics,” Nat. Photonics 7, 429–430 (2013).
[CrossRef]

Lu, W.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Luo, C.

Maier, S. A.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Mazor, Y.

Y. Hadad, Y. Mazor, B. Z. Steinberg, “Green’s function theory for one-way particle chains,” Phys. Rev. B 87, 035130 (2013).
[CrossRef]

Y. Mazor, B. Z. Steinberg, “Longitudinal chirality, enhanced nonreciprocity, and nanoscale planar one-way plasmonic guiding,” Phys. Rev. B 86, 045120 (2012).
[CrossRef]

McPhedran, R. C.

A. A. Asatryan, L. C. Botten, K. Fang, S. Fan, R. C. McPhedran, “Local density of states of chiral Hall edge states in gyrotropic photonic clusters,” Phys. Rev. B 88, 035127 (2013).
[CrossRef]

Merzlikin, A. M.

A. M. Merzlikin, A. P. Vinogradov, M. Inoue, A. B. Granovsky, “Giant photonic Hall effect in magnetophotonic crystals,” Phys. Rev. E 72, 046603 (2005).
[CrossRef]

Moser, H. O.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef] [PubMed]

Ng, B.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Poo, Y.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef] [PubMed]

Potton, R. J.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[CrossRef]

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Raghu, S.

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

Ross, C. A.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Sheng, Q. W.

Sheng, Z.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef] [PubMed]

Simsek, E.

Soljacic, M.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

M. Soljačić, C. Luo, J. D. Joannopoulos, S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

Steinberg, B. Z.

Y. Hadad, Y. Mazor, B. Z. Steinberg, “Green’s function theory for one-way particle chains,” Phys. Rev. B 87, 035130 (2013).
[CrossRef]

Y. Mazor, B. Z. Steinberg, “Longitudinal chirality, enhanced nonreciprocity, and nanoscale planar one-way plasmonic guiding,” Phys. Rev. B 86, 045120 (2012).
[CrossRef]

Y. Hadad, B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett. 105, 233904 (2010).
[CrossRef]

Steinle, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Stout, B.

A. Devilez, B. Stout, N. Bonod, “Mode-balancing far-field control of light localization in nanoantennas,” Phys. Rev. B 81, 245128 (2010).
[CrossRef]

Stritzker, B.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Togan, E.

Turaga, S. P.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Vinogradov, A. P.

A. M. Merzlikin, A. P. Vinogradov, M. Inoue, A. B. Granovsky, “Giant photonic Hall effect in magnetophotonic crystals,” Phys. Rev. E 72, 046603 (2005).
[CrossRef]

Wang, D. W.

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

Wang, H. Z.

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

J. Wang, K. H. Fung, H. Y. Dong, N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84, 235122 (2011).
[CrossRef]

Wang, X.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Wang, Z.

Z. Yu, G. Veronis, Z. Wang, S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Wehlus, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Weiss, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Wu, A.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Wu, J.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Wu, R. X.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef] [PubMed]

Xiao, X.

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

Yang, M.

Yang, T.

Yang, Y.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef] [PubMed]

Yu, Z.

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Zhang, J. X.

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

Zhang, W.

J. Du, Z. Lin, S. T. Chui, G. Dong, W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett. 110, 163902 (2013).
[CrossRef] [PubMed]

Zhang, X.

M. Liu, X. Zhang, “Plasmon-boosted magneto-optics,” Nat. Photonics 7, 429–430 (2013).
[CrossRef]

Zhou, H. T.

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

Zhu, S. Y.

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

Zi, J.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Zou, S.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett. 89, 251115 (2006).
[CrossRef]

Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett. 102, 211906 (2013).
[CrossRef]

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Nat. Commun. (1)

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599–1604 (2013).
[CrossRef] [PubMed]

Nat. Photonics (3)

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5, 758–762 (2011).
[CrossRef]

M. Liu, X. Zhang, “Plasmon-boosted magneto-optics,” Nat. Photonics 7, 429–430 (2013).
[CrossRef]

Z. Yu, S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (5)

Y. Mazor, B. Z. Steinberg, “Longitudinal chirality, enhanced nonreciprocity, and nanoscale planar one-way plasmonic guiding,” Phys. Rev. B 86, 045120 (2012).
[CrossRef]

A. A. Asatryan, L. C. Botten, K. Fang, S. Fan, R. C. McPhedran, “Local density of states of chiral Hall edge states in gyrotropic photonic clusters,” Phys. Rev. B 88, 035127 (2013).
[CrossRef]

Y. Hadad, Y. Mazor, B. Z. Steinberg, “Green’s function theory for one-way particle chains,” Phys. Rev. B 87, 035130 (2013).
[CrossRef]

J. Wang, K. H. Fung, H. Y. Dong, N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84, 235122 (2011).
[CrossRef]

A. Devilez, B. Stout, N. Bonod, “Mode-balancing far-field control of light localization in nanoantennas,” Phys. Rev. B 81, 245128 (2010).
[CrossRef]

Phys. Rev. E (1)

A. M. Merzlikin, A. P. Vinogradov, M. Inoue, A. B. Granovsky, “Giant photonic Hall effect in magnetophotonic crystals,” Phys. Rev. E 72, 046603 (2005).
[CrossRef]

Phys. Rev. Lett. (10)

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

Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, Y. S. Kivshar, “One-way extraordinary optical transmission and nonreciprocal spoof plasmons,” Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef] [PubMed]

Y. Hadad, B. Z. Steinberg, “Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides,” Phys. Rev. Lett. 105, 233904 (2010).
[CrossRef]

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef] [PubMed]

D. W. Wang, H. T. Zhou, M. J. Guo, J. X. Zhang, J. Evers, S. Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[CrossRef] [PubMed]

W. J. Chen, Z. H. Hang, J. W. Dong, X. Xiao, H. Z. Wang, C. T. Chan, “Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking,” Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett. 106, 203903 (2011).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, G. Dong, W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett. 110, 163902 (2013).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[CrossRef]

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Distributions of electric field Re{Ez} when (a) μk = 0, and (b) μk = −0.1064, respectively. Plot (c) shows the definition of φB between k and the axis p representing the asymmetric distribution of Ez.

Fig. 2
Fig. 2

Orientations of p without inter-particle coupling when the angle of incidence θ equals (a) −θ0 and (b) +θ0, respectively. With the consideration of inter-particle coupling, different collective dipole modes are expected in these two configurations, which lead to nonreciprocal diffraction.

Fig. 3
Fig. 3

Transmission coefficients T of the 0th (blue) and −1st (red) orders versus the angle of incidence θ, when μk = 0 (short dashed) and μk = −0.1064 (solid), respectively.

Fig. 4
Fig. 4

Optical diffraction by a single-layer array of YIG cylinders, for nonreciprocal cases of μk = −0.1064 at (a) θ = −40° and (b) θ = +40°, respectively, and for reciprocal case of μk = 0 at (c) θ = +40°.

Fig. 5
Fig. 5

Distributions of electric field Re{Ez} and energy flux (by arrows) at the central three YIG cylinders for nonreciprocal cases of μk = −0.1064 at (a) θ = −40° and (b) θ = +40°, respectively, and for reciprocal case of μk = 0 at (c) θ = +40°.

Fig. 6
Fig. 6

Distributions of electric field Re{Ez} and energy flux at normal incidence, when (a) μk = 0, and (b) μk = −0.1064, respectively.

Fig. 7
Fig. 7

Diffraction coefficients versus frequency at different external applied magnetic field H0 for (a) the −1st diffractive order when θ = −40°, and (b) the reflected beam when θ = +40°, respectively.

Equations (4)

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

μ ¯ ¯ = ( μ r i μ k 0 i μ k μ r 0 0 0 1 ) ,
μ r = 1 + ω m ω k ω k 2 ω 2 ,
μ k = ω m ω ω k 2 ω 2 ,
k | | ( l ) = k 0 sin θ + l 2 π d ,

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