Abstract

Chiral defect waveguides and waveguide bend geometry were designed in diamond photonic crystal to mold the flow of light in three dimensions. Propagations of electromagnetic waves in chiral waveguides are robust against isotropic obstacles, which would suppress backscattering in waveguides or integrated devices. Finite-difference time-domain simulations demonstrate that high coupling efficiency through the bend corner is preserved in the polarization gap, as it provides an additional constraint on the polarization state of the backscattered wave. Transport robustness is also demonstrated by inserting two metallic slabs into the waveguide bend.

© 2013 Optical Society of America

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  1. K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
    [CrossRef]
  2. F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands .
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2013 (1)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

2012 (2)

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

V. Yannopapas, New J. Phys. 14, 113017 (2012).
[CrossRef]

2011 (2)

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

Y. Poo, R.-X. Wu, Z. F. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

2010 (3)

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, Appl. Phys. Lett. 97, 041112 (2010).
[CrossRef]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

2009 (3)

T. Ochiai and M. Onoda, Phys. Rev. B 80, 155103 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

X. Ao, Z. F. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

2008 (3)

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

2005 (1)

C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[CrossRef]

1998 (1)

A. Chutinan and S. Noda, Phys. Rev. B 57, R2006 (1998).
[CrossRef]

1988 (1)

F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
[CrossRef]

1980 (1)

K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
[CrossRef]

Ao, X.

X. Ao, Z. F. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Bermei, P.

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Chan, C. T.

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

Y. Poo, R.-X. Wu, Z. F. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

X. Ao, Z. F. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Chen, W.-J.

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

Chen, X.-L.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Chen, Y.-F.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

Chutinan, A.

A. Chutinan and S. Noda, Phys. Rev. B 57, R2006 (1998).
[CrossRef]

Dong, J.-W.

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

Dorda, G.

K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
[CrossRef]

Dreisow, F.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Fu, J.-X.

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, Appl. Phys. Lett. 97, 041112 (2010).
[CrossRef]

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
[CrossRef]

Hang, Z. H.

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

He, C.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Ibanescu, M.

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

Johnson, S. G.

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Kane, C. L.

C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[CrossRef]

Kargarian, M.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

Li, X.-F.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Li, Z.-Y.

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, Appl. Phys. Lett. 97, 041112 (2010).
[CrossRef]

Lin, Z. F.

Y. Poo, R.-X. Wu, Z. F. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

X. Ao, Z. F. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

Liu, R.-J.

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, Appl. Phys. Lett. 97, 041112 (2010).
[CrossRef]

Lu, M.-H.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Lumer, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

MacDonald, A. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

Mele, E. J.

C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[CrossRef]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

Noda, S.

A. Chutinan and S. Noda, Phys. Rev. B 57, R2006 (1998).
[CrossRef]

Nolte, S.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Ochiai, T.

T. Ochiai and M. Onoda, Phys. Rev. B 80, 155103 (2009).
[CrossRef]

Onoda, M.

T. Ochiai and M. Onoda, Phys. Rev. B 80, 155103 (2009).
[CrossRef]

Oskool, A. F.

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Pepper, M.

K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
[CrossRef]

Plotnik, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Podolsky, D.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Poo, Y.

Y. Poo, R.-X. Wu, Z. F. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Qian, X.-S.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Raghu, S.

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

Rechtsman, M. C.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Roundy, D.

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Segev, M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

Soljacic, M.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

Szameit, A.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Tse, W.-K.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

von Klitzing, K.

K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
[CrossRef]

Wan, W.-W.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Wang, H.-Z.

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

Wang, Z.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

Wu, R.-X.

Y. Poo, R.-X. Wu, Z. F. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Xiao, X.

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

Yang, Y.

Y. Poo, R.-X. Wu, Z. F. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Yannopapas, V.

V. Yannopapas, New J. Phys. 14, 113017 (2012).
[CrossRef]

Yin, R.-C.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Zeuner, J. M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Appl. Phys. Lett. (2)

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, Appl. Phys. Lett. 97, 041112 (2010).
[CrossRef]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, Appl. Phys. Lett. 96, 111111 (2010).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskool, D. Roundy, M. Ibanescu, P. Bermei, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Nat. Mater. (1)

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nat. Mater. 12, 233 (2012).
[CrossRef]

Nature (2)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[CrossRef]

New J. Phys. (1)

V. Yannopapas, New J. Phys. 14, 113017 (2012).
[CrossRef]

Phys. Rev. A (1)

S. Raghu and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008).
[CrossRef]

Phys. Rev. B (3)

X. Ao, Z. F. Lin, and C. T. Chan, Phys. Rev. B 80, 033105 (2009).
[CrossRef]

A. Chutinan and S. Noda, Phys. Rev. B 57, R2006 (1998).
[CrossRef]

T. Ochiai and M. Onoda, Phys. Rev. B 80, 155103 (2009).
[CrossRef]

Phys. Rev. Lett. (7)

W.-J. Chen, Z. H. Hang, J.-W. Dong, X. Xiao, H.-Z. Wang, and C. T. Chan, Phys. Rev. Lett. 107, 023901 (2011).
[CrossRef]

Y. Poo, R.-X. Wu, Z. F. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
[CrossRef]

F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
[CrossRef]

C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[CrossRef]

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

Other (1)

http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands .

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the chiral waveguide and the dispersion relation. (a) An LH spiral formed by connecting lattice points in diamond lattices. The black frame represents a cubic unit cell. (b) LH chiral defect by removing the LH spiral in diamond PhC. The blue frame denotes the edges of the chiral defect. (c) Segment removed from diamond PhC. (d) Iso-amplitude surface of magnetic field for the LH waveguide mode at 0.49(c/a). (e) Dispersion relation of LH waveguide along the z direction in diamond PhC.

Fig. 2.
Fig. 2.

Two schematic diagrams for bends between waveguides in the z and x directions. (a) WGZ-WGX (L2L): LH waveguides in both directions. (b) WGZ-WGX (L2R): LH waveguide in the z direction and RH waveguide in the x direction. Three cubic cells are shown in both figures. Each arrow near the entrance/exit denotes either the incident or the transmitted wave, and the circular arrow around it denotes the rotational direction of electromagnetic fields.

Fig. 3.
Fig. 3.

Transmission spectra (red) for three types of bend waveguides: (a) WGZ-WGX (L2L) shown in Fig. 2(a), (b) WGZ-WGX (L2R) shown in Fig. 2(b), and (c) double-bend waveguide WGZ-WGY-WGX (L2L). The transmission spectra for the straight waveguide WGZ (L2L) are also plotted (black). Here, L2L means both the input and output waveguides are LH. L2R means that the input and output waveguides are LH and RH, respectively. The light blue box highlights the polarization gap. The blue line in (b) refers to WGZ-WGX (L2R) with two PEC obstacles inside.

Fig. 4.
Fig. 4.

Amplitude profile of energy flow for two types of single bend waveguides in the xz plane at the frequency of 0.49(c/a): (a) and (b) are for the bend geometries in Figs. 2(a) and 2(b), while (c) is the same as (b) but with two PEC slabs inside.

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