Abstract

Mode properties of circularly symmetric waveguides with one special type of bianisotropy are studied using finite element approach. We find that the polarization degeneracy in circularly symmetric waveguides can be eliminated, by introducing intrinsic crossing coupling between electric and magnetic moments in the constituent units of the waveguide media. Breaking the polarization degeneracy in high order mode groups is also confirmed numerically. With the bianisotropic parameters chosen in this work, the x and y-polarized modes remain decoupled. Typically, the y-polarized modes remain completely unchanged, while the x-polarized modes are turned into leaky modes that are lossy along propagation direction. A perturbation model from coupled mode theory is developed to explain the results and shows excellent agreement. Such asymmetric behavior between different polarizations might be feasible and useful for developing compact polarizers in terahertz or mid-infrared regime.

© 2015 Optical Society of America

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References

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2015 (1)

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[Crossref]

2014 (1)

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

2013 (5)

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

T. Narushima and H. Okamoto, “Circular dichroism nano-imaging of two-dimensional chiral metal nanostructures,” Phys. Chem. Chem. Phys. 15, 13805–13809 (2013).
[Crossref] [PubMed]

L. Wu, Z. Yang, Y. Cheng, Z. Lu, P. Zhang, M. Zhao, R. Gong, X. Yuan, Y. Zheng, and J. Duan, “Electromagnetic manifestation of chirality in layer-by-layer chiral metamaterials,” Opt. Express 21, 5239–5246 (2013).
[Crossref] [PubMed]

T. J. Davis and E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).
[Crossref]

V. I. Kopp, J. Park, M. Wlodawski, J Singer, D. Neugroschl, and A. Z. Genack, “Chiral fibers: microformed optical waveguides for polarization control, sensing, coupling, amplification, and switching,” J. Lightwave Technol. 32, 605–613 (2013).
[Crossref]

2012 (3)

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

M. Schäferling, X. Yin, and H. Giessen, “Formation of chiral fields in a symmetric environment,” Opt. Express 20, 26326–26336 (2012).
[Crossref] [PubMed]

M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2, 031010 (2012).

2011 (3)

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011).
[Crossref]

Y. Cao, J. Li, and Q. Su, “Guided modes in chiral fiber,” J. Opt. Soc. Am. B 28, 319–324 (2011).
[Crossref]

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

2010 (7)

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

C. R. Doerr, P. J. Winzer, Y.-K. Chen, S. Chandrasekhar, M. S. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28, 520–525 (2010).
[Crossref]

J. Li, Q. Su, and Y. Cao, “Circularly polarized guided modes in dielectrically chiral photonic crystal fiber,” Opt. Lett. 35, 2720–2722 (2010).
[Crossref] [PubMed]

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

C. É Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quant. 16, 367–375 (2010).
[Crossref]

2009 (2)

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] [PubMed]

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009).
[Crossref]

2007 (2)

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B. 24, 2333–2342 (2007).
[Crossref]

Q. Wang and J. Yao, “A high speed 2 × 2 electro-optic switch using a polarization modulator,” Opt. Express 15, 16500–16505 (2007).
[Crossref] [PubMed]

2004 (1)

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

2002 (1)

1994 (1)

1992 (1)

1990 (2)

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antennas Propag. 38, 90–98 (1990).
[Crossref]

J. A. M. Svedin, “Propagation analysis of chirowaveguides using the finite-element method,” IEEE Trans. Microw. Theory Techn 38, 1488–1496 (1990).
[Crossref]

1989 (1)

1987 (1)

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory for optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

1984 (1)

1972 (1)

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).
[Crossref]

Abebe, M.

Ang, K.-W.

Argyros, A.

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] [PubMed]

Bao, Y.-J.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Barbosa, A. M.

Barner-Kowollik, C.

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[Crossref]

Bassett, I. M.

Biancalana, F.

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

Burns, W. K.

Cao, Y.

Chan, C. T.

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

Chandrasekhar, S.

Chen, H.

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

Chen, L.

Chen, W. J.

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Chen, X. D.

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Chen, Y.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

Chen, Y.-K.

Cheng, Y.

Cohen, A. E.

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

Conti, C.

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

Davis, T. J.

T. J. Davis and E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).
[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] [PubMed]

Doerr, C. R.

Dong, J. W.

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Dregely, D.

M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2, 031010 (2012).

Duan, J.

Engheta, N.

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antennas Propag. 38, 90–98 (1990).
[Crossref]

N. Engheta and P. Pelet, “Modes in chirowaveguides,” Opt. Lett. 14, 593–595 (1989).
[Crossref] [PubMed]

Fischer, J.

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[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] [PubMed]

Genack, A. Z.

Giessen, H.

M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2, 031010 (2012).

M. Schäferling, X. Yin, and H. Giessen, “Formation of chiral fields in a symmetric environment,” Opt. Express 20, 26326–26336 (2012).
[Crossref] [PubMed]

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009).
[Crossref]

Gong, R.

Gregersen, N.

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

Harrington, R. F.

R. F. Harrington, Time-harmonic Electromagnetic Fields, 2. (Wiley-IEEE, 2001).
[Crossref]

Haus, H. A.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory for optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Hendry, E.

T. J. Davis and E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).
[Crossref]

Hentschel, M.

M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2, 031010 (2012).

Huang, W. P.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory for optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Huang, W.-P.

Jiang, S. J.

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Jin, J. M.

J. M. Jin, The Finite Element Method in Electrodynamics, 2. (Wiley, 2002).

Kampfrath, T.

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011).
[Crossref]

Kang, M. S.

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

Kargarian, M.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Kaschke, J.

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[Crossref]

Kawakami, S.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory for optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Koenderink, A. F.

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011).
[Crossref]

Kong, J. A.

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).
[Crossref]

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2008).

Kopp, V. I.

Kriegler, C. É

C. É Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quant. 16, 367–375 (2010).
[Crossref]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continous Media (Pergamon, 1960).

Lee, H. W.

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

Li, F.

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

Li, H.

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

Li, J.

Li, Z.-F.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continous Media (Pergamon, 1960).

Linden, S.

C. É Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quant. 16, 367–375 (2010).
[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] [PubMed]

Liow, T.-Y.

Liu, H.

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009).
[Crossref]

Liu, N.

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009).
[Crossref]

Lo, G.-Q.

Lodahl, P.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

Lu, X.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Lu, Z.

MacDonald, A. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Ming, N.-B.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Moeller, R. P.

Mørk, J.

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Mueller, J. B.

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[Crossref]

Narushima, T.

T. Narushima and H. Okamoto, “Circular dichroism nano-imaging of two-dimensional chiral metal nanostructures,” Phys. Chem. Chem. Phys. 15, 13805–13809 (2013).
[Crossref] [PubMed]

Neugroschl, D.

Nielsen, T. R.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

Okamoto, H.

T. Narushima and H. Okamoto, “Circular dichroism nano-imaging of two-dimensional chiral metal nanostructures,” Phys. Chem. Chem. Phys. 15, 13805–13809 (2013).
[Crossref] [PubMed]

Paiva, C. R.

Park, J.

Pelet, P.

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antennas Propag. 38, 90–98 (1990).
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N. Engheta and P. Pelet, “Modes in chirowaveguides,” Opt. Lett. 14, 593–595 (1989).
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J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
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Peng, R.-W.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Qiu, M.

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B. 24, 2333–2342 (2007).
[Crossref]

Quick, A. S.

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[Crossref]

Rasras, M. S.

Rill, M. S.

C. É Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quant. 16, 367–375 (2010).
[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] [PubMed]

Russell, J.

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

Saile, V.

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] [PubMed]

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M. Schäferling, X. Yin, and H. Giessen, “Formation of chiral fields in a symmetric environment,” Opt. Express 20, 26326–26336 (2012).
[Crossref] [PubMed]

M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2, 031010 (2012).

Semchenko, I. V.

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Serdyukov, A. N.

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Sersic, I.

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011).
[Crossref]

Shao, J.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Sihvola, A.

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Singer, J

St., P.

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

Su, Q.

Sun, C.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Sun, W.-H.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
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Svedin, J. A. M.

J. A. M. Svedin, “Propagation analysis of chirowaveguides using the finite-element method,” IEEE Trans. Microw. Theory Techn 38, 1488–1496 (1990).
[Crossref]

Tang, Y.

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

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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] [PubMed]

Topa, A. L.

Tretyakov, S. A.

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Tse, W.-K.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Tuambilangana, C.

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011).
[Crossref]

Villarruel, C. A.

von Freymann, G.

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] [PubMed]

Wang, M.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Wang, Q.

Wegener, M.

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[Crossref]

C. É Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quant. 16, 367–375 (2010).
[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] [PubMed]

Weiss, T.

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
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Wlodawski, M.

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G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

Wu, C.

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

Wu, L.

Xiong, X.

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Yan, M.

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B. 24, 2333–2342 (2007).
[Crossref]

Yang, Z.

Yao, J.

Yin, X.

Yu, X.

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

Yuan, X.

Zhang, P.

Zhao, M.

Zheng, Y.

Zhou, L.

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
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Zhu, B. C.

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Zhu, S.

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009).
[Crossref]

Adv. Optical Mater. (1)

J. Fischer, J. B. Mueller, A. S. Quick, J. Kaschke, C. Barner-Kowollik, and M. Wegener, “Exploring the mechanisms in STED-enhanced direct laser writing,” Adv. Optical Mater. 3(2), 221–232 (2015).
[Crossref]

IEEE J. Sel. Top. Quant. (1)

C. É Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quant. 16, 367–375 (2010).
[Crossref]

IEEE Trans. Antennas Propag. (1)

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antennas Propag. 38, 90–98 (1990).
[Crossref]

IEEE Trans. Microw. Theory Techn (1)

J. A. M. Svedin, “Propagation analysis of chirowaveguides using the finite-element method,” IEEE Trans. Microw. Theory Techn 38, 1488–1496 (1990).
[Crossref]

J. Lightwave Technol. (3)

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

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

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

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B. 24, 2333–2342 (2007).
[Crossref]

Nat Commun. (1)

W. J. Chen, S. J. Jiang, X. D. Chen, B. C. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Nat. Photonics (1)

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Phys. Chem. Chem. Phys. (1)

T. Narushima and H. Okamoto, “Circular dichroism nano-imaging of two-dimensional chiral metal nanostructures,” Phys. Chem. Chem. Phys. 15, 13805–13809 (2013).
[Crossref] [PubMed]

Phys. Rev. B (4)

T. J. Davis and E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).
[Crossref]

X. Xiong, W.-H. Sun, Y.-J. Bao, M. Wang, R.-W. Peng, C. Sun, X. Lu, J. Shao, Z.-F. Li, and N.-B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B 81, 075119 (2010).
[Crossref]

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011).
[Crossref]

Phys. Rev. Lett. (2)

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

C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. 107, 177401(2011).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2, 031010 (2012).

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J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).
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Science (3)

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] [PubMed]

G. K. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, P. St., and J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337, 446–449 (2012).
[Crossref] [PubMed]

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

Other (5)

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2008).

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continous Media (Pergamon, 1960).

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

J. M. Jin, The Finite Element Method in Electrodynamics, 2. (Wiley, 2002).

R. F. Harrington, Time-harmonic Electromagnetic Fields, 2. (Wiley-IEEE, 2001).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of a circularly symmetric waveguide (a) which contains bianisotropic medium in the core layer by including structures with split ring resonator (SRR) arrays introducing χ12 (b), and structures with helix arrays introducing χ11 (c).
Fig. 2
Fig. 2 (a) Re(neff), (b) Im(neff), (c) propagation length of x-polarized modes. Symbols with (without) lines refers to y- (x-) polarization modes. The color indicates different size of the radius, i.e., 0.12λ0 (black circles), 0.16λ0 (blue triangles) and 0.2λ0 (red diamonds) respectively, where λ0 is vacuum wavelength. We use ε11 = ε22 = ε33 = 4, μ11 = μ22 = μ33 = 1. The other elements in χ ¯ e h r is set to be zero.
Fig. 3
Fig. 3 (a) Power leakage ratio defined by η versus χ12. η is defined by Eq. (9). (b) Real part of ez normalized by ex (ey) for x-(y-) polarized mode versus χ12. Radius of the waveguide in (a) and (b) is 0.2λ0.
Fig. 4
Fig. 4 Slope of Im(neff) of x-polarized modes calculated according to Eq. (12) (symbols with lines) as well as from Fig. 2(b) (symbols without lines) versus χ12. Radius of the three waveguides are 0.12λ0 (black circles), 0.16λ0 (blue triangles) and 0.2λ0 (red diamonds), respectively.
Fig. 5
Fig. 5 Real part (a) and imaginary part (b) of neff versus χ12. (c) and (d) shows enlarged region of (a) and (b), respectively. (e) Mode profiles of the first high order mode group when χ12 = 0 and (f) χ12 = 0.6. Radius of the waveguide is 0.416λ0.

Equations (13)

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

D = ε ¯ E + χ ¯ e h H , B = μ ¯ H + χ ¯ h e E ,
× E = i ω [ μ ¯ χ ¯ e h 1 D + ( χ ¯ h e μ ¯ χ ¯ e h 1 ε ¯ ) E ] , × ( χ ¯ e h 1 D χ ¯ e h 1 ε ¯ E ) = i ω D .
× μ ¯ r 1 × E ( r , ω ) + k 0 c ¯ 1 × E ( r , ω ) + k 0 × c ¯ 2 E ( r , ω ) + k 0 2 ( d ¯ 1 + d ¯ 2 ) E ( r , ω ) = 0 ,
L = S d x d y 1 μ ¯ r Curl E ( x , y , β ) Curl F * ( x , y , β ) + S F * ( x , y , β ) [ 1 μ ¯ r n × Curl E ( x , y , β ) ] d l + S d x d y k 0 [ c ¯ 1 × + × c ¯ 2 + k 0 ( d ¯ 1 + d ¯ 2 ) ] E ( x , y , β ) F * ( x , y , β ) ,
D x = ε 0 ( ε 11 e x + i χ 12 h y ) , B x = μ 0 μ 11 h x ; D y = ε 0 ε 22 e y , B y = μ 0 ( i χ 12 e x + μ 22 h y ) ; D z = ε 0 ε 33 e z , B z = μ 0 μ 33 h z .
t × e 2 d i β z × e 2 d = i k 0 ( μ ¯ r h 2 d + χ ¯ h e r e 2 d ) ,
t × h 2 d i β z × h 2 d = i k 0 ( ε ¯ r e 2 d + χ ¯ e h r h 2 d ) ,
Δ β = i ( e × h 0 * ) n d l + { ( k 0 μ ¯ r h ) h 0 * ( k 0 ε ¯ r e 0 * ) e } d x d y z ( e × h 0 * ) d x d y i k 0 Δ χ 12 c o r e e x h 0 y * d x d y z ( e × h 0 * ) d x d y ,
i ( e 0 2 d × [ h 0 2 d ] * ) n d l = { ( k 0 μ ¯ r h 0 2 d ) [ h 0 2 d ] * ( k 0 ε ¯ r [ e 0 2 d ] * ) e 0 2 d } d x d y .
η = { ( k 0 μ ¯ r h 0 ) h 0 * ( k 0 ε ¯ r e 0 * ) e 0 } d x d y { ( k 0 μ ¯ r h 0 ) h 0 * + ( k 0 ε ¯ r e 0 * ) e 0 } d x d y .
e z = 1 i β ε 33 ( t ε ¯ r 2 × 2 e t + t χ ¯ e h r , 2 × 2 h t ) ,
P x = Re { i [ e y Im ( h z ) + h y Im ( e z ) ] + [ e y Re ( h z ) h y Re ( e z ) ] } = e y Re ( h z ) h y Re ( e z ) , P y = Re { i [ Im ( e z ) h x + Im ( h z ) e x ] + [ h x Re ( e z ) e x Re ( h z ) ] } = h y Re ( e z ) e y Re ( h z ) ,
Δ Im ( n e f f ) Δ χ 12 = c o r e e 0 x h 0 y * d x d y ( e 0 x h 0 y * e 0 y h 0 x * ) d x d y .

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