Abstract

A system composed of air holes in a dielectric host to form two square photonic crystals, with the same orientation and lattice constant but different scatterer radii, making an interface along their body diagonals, is numerically demonstrated to facilitate unidirectional light transmission. Band structure computations are carried out via the plane wave expansion method, whereas finite-difference time-domain simulations are carried out to investigate the transient behavior. Unidirectional light transmission is achieved over two adjacent stop bands along the ΓX direction, which are circumvented in the forward direction by scaling down the wave vector and rotating the surface normal. Contrast ratios as high as 0.9 are attained within the lower stop band.

© 2012 Optical Society of America

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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

A. Cicek, O. A. Kaya, and B. Ulug, Appl. Phys. Lett. 100, 111905 (2012).
[CrossRef]

S. Feng, C. Ren, W. Wang, and Y. Wang, Europhys. Lett. 97, 64001 (2012).
[CrossRef]

2011

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

2010

2009

A. E. Serebryannikov, Phys. Rev. B 80, 155117 (2009).
[CrossRef]

A. E. Serebryannikov and E. Ozbay, Opt. Express 17, 13335 (2009).
[CrossRef]

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

2008

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

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

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

2007

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

2005

2001

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

1994

J. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1990

K. M. Ho, C. T. Chan, and C. M. Soukolis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef]

1967

R. Courant, K. Friedrichs, and H. Lewy, IBM J. Res. Dev. 11, 215 (1967).
[CrossRef]

1966

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Beauvillain, P.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Berenger, J.

J. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Cakmak, A. O.

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukolis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef]

Checoury, X.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Chen, Y.-F.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

Chong, Y. D.

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

Cicek, A.

A. Cicek, O. A. Kaya, and B. Ulug, Appl. Phys. Lett. 100, 111905 (2012).
[CrossRef]

Citrin, D. S.

Colak, E.

Courant, R.

R. Courant, K. Friedrichs, and H. Lewy, IBM J. Res. Dev. 11, 215 (1967).
[CrossRef]

Dagens, B.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Fainman, Y.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Fan, S.

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Feng, L.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Feng, S.

S. Feng, C. Ren, W. Wang, and Y. Wang, Europhys. Lett. 97, 64001 (2012).
[CrossRef]

Figotin, A.

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Friedrichs, K.

R. Courant, K. Friedrichs, and H. Lewy, IBM J. Res. Dev. 11, 215 (1967).
[CrossRef]

Gralak, B.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Haldane, F. D. M.

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

He, C.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukolis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef]

Huang, J.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Joannopoulos, J. D.

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

John, S.

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Kaya, O. A.

A. Cicek, O. A. Kaya, and B. Ulug, Appl. Phys. Lett. 100, 111905 (2012).
[CrossRef]

Kurt, H.

Lewy, H.

R. Courant, K. Friedrichs, and H. Lewy, IBM J. Res. Dev. 11, 215 (1967).
[CrossRef]

Li, X.-F.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

Lourtioz, J.-M.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Lu, M.-H.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Magdenko, L.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Ni, X.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Ozbay, E.

Postava, K.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Raghu, S.

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

Ren, C.

S. Feng, C. Ren, W. Wang, and Y. Wang, Europhys. Lett. 97, 64001 (2012).
[CrossRef]

Scherer, A.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Serebryannikov, A. E.

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Smigaj, W.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Soljacic, M.

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

Soukolis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukolis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef]

Takeda, H.

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Ulug, B.

A. Cicek, O. A. Kaya, and B. Ulug, Appl. Phys. Lett. 100, 111905 (2012).
[CrossRef]

Vanwolleghem, M.

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Vitebsky, I.

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Wang, W.

S. Feng, C. Ren, W. Wang, and Y. Wang, Europhys. Lett. 97, 64001 (2012).
[CrossRef]

Wang, Y.

S. Feng, C. Ren, W. Wang, and Y. Wang, Europhys. Lett. 97, 64001 (2012).
[CrossRef]

Wang, Z.

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

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Xu, Y.-L.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

Yee, K. S.

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

Yu, Z.

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Appl. Phys. Lett.

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

A. Cicek, O. A. Kaya, and B. Ulug, Appl. Phys. Lett. 100, 111905 (2012).
[CrossRef]

Europhys. Lett.

S. Feng, C. Ren, W. Wang, and Y. Wang, Europhys. Lett. 97, 64001 (2012).
[CrossRef]

IBM J. Res. Dev.

R. Courant, K. Friedrichs, and H. Lewy, IBM J. Res. Dev. 11, 215 (1967).
[CrossRef]

IEEE Trans. Antennas Propag.

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

J. Comput. Phys.

J. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Opt. Express

Phys. Rev. A

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Phys. Rev. B

M. Vanwolleghem, X. Checoury, W. Smigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, Phys. Rev. B 80, 121102(R) (2009).
[CrossRef]

A. E. Serebryannikov, Phys. Rev. B 80, 155117 (2009).
[CrossRef]

Phys. Rev. E

A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Phys. Rev. Lett.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
[CrossRef]

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

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

K. M. Ho, C. T. Chan, and C. M. Soukolis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef]

Science

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Definition of geometrical parameters of the PC diode (a) and the variations of the stop-band edges along the ΓX direction with the r/a ratio (b) for the TM polarization. The dashed line denotes the r/a value maximizing the total stop-band width. The circle and diamond in (b) denote the frequencies (ωa/2πc=0.32 and 0.37, respectively) at which the diode action is investigated. Inset in (b) presents the stop bands up to the 10th band, where the vertical solid line indicates the limits of 2nd PCL TM band for r/a=0.460.

Fig. 2.
Fig. 2.

EFCs at ωa/2πc=0.32 and 0.37 of PCL (a) and PCR (b) for the TM polarization. The dashed arcs in (a) represent the corresponding EFCs in the host material, while the hollow and solid arrows, not to scale, denote the wave vectors and the propagation directions, respectively. The dotted–dashed lines represent the relevant construction lines.

Fig. 3.
Fig. 3.

FDTD simulations of waves travelling to the right (a) and left (b) for ωa/2πc=0.32 (top) and 0.37 (bottom). Arrows on the top denote the propagation directions. The dashed rectangular regions in (a) represent the areas over which the transmission data for TR, TL, TU, and TD are calculated.

Fig. 4.
Fig. 4.

Variation of transmission to the right and left (left axis) accompanied by the contrast ratio (right axis) (a), as well as the leakage to upper (TU) and lower (TD) ports of the system (b) with respect to the normalized frequency.

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