Abstract

We investigate the propagation of electromagnetic waves in a one-dimensional photonic crystal containing a defect layer made of an isotropic chiral medium. Using the invariant imbedding method, we calculate the transmission spectrum for both linearly- and circularly-polarized incident waves. In the normal incidence case, there is one defect mode, which does not depend on the chiral index and the polarization of the incident wave. When the waves are incident obliquely, however, we find that there appear double defect modes regardless of the polarization. The interval between the two defect frequencies increases monotonically as the chiral index or the incident angle increases. We argue that this phenomenon occurs due to the coupling and conversion between s and p waves inside the chiral defect layer.

© 2014 Optical Society of America

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References

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  5. K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, “One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films,” J. Appl. Phys. 103, 083107 (2008).
    [Crossref]
  6. A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
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    [Crossref]
  26. K. Kim, H. Yoo, and H. Lim, “Exact analytical expressions for the dispersion relation of one-dimensional chiral photonic crystals,” Waves Random Complex Media 16, 75–84 (2006).
    [Crossref]
  27. R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express 18, 14553–14567 (2010).
    [Crossref] [PubMed]

2014 (1)

Y. Cao and J. Li, “Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality,” Phys. Rev. B 89, 115420 (2014).
[Crossref]

2013 (2)

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crystal structures,” Opt. Express 21, 28817–28823 (2013).
[Crossref]

Z. Li, M. Mutlu, and E. Ozbay, “Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission,” J. Opt. 15, 023001 (2013).
[Crossref]

2011 (1)

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
[Crossref]

2010 (2)

2009 (5)

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[Crossref]

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3, 85–90 (2009).
[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]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
[Crossref]

2008 (3)

N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7, 43–47 (2008).
[Crossref]

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, “All-optical swiching and multistability in photonic structures with liquid crystal defects,” Appl. Phys. Lett. 92, 253306 (2008).
[Crossref]

K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, “One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films,” J. Appl. Phys. 103, 083107 (2008).
[Crossref]

2007 (2)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[Crossref]

L. Jin, J. Li, H. Li, Q. Lin, and C. Li, “Improving sideband of chiral photonic crystal based on PSTD approach,” Opt. Comm. 279, 43–49 (2007).
[Crossref]

2006 (5)

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photon. Tech. Lett. 18, 1261–1264 (2006).
[Crossref]

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
[Crossref]

G. Ma, J. Shen, Z. Zhang, Z. Hua, and S. H. Tang, “Ultrafast all-optical switching in one-dimensional photonic crystal with two defects,” Opt. Express 14, 858–865 (2006).
[Crossref] [PubMed]

K. Kim and D. H. Lee, “Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity,” Phys. Plasmas 13, 042103 (2006).
[Crossref]

K. Kim, H. Yoo, and H. Lim, “Exact analytical expressions for the dispersion relation of one-dimensional chiral photonic crystals,” Waves Random Complex Media 16, 75–84 (2006).
[Crossref]

2005 (1)

K. Kim, D. H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” EPL 69, 207–213 (2005).
[Crossref]

2004 (2)

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[Crossref] [PubMed]

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

1996 (1)

J. Lekner, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[Crossref]

Altug, H.

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
[Crossref]

Arakawa, Y.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
[Crossref]

Arkhipkin, V. G.

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[Crossref]

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]

Brasselet, E.

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, “All-optical swiching and multistability in photonic structures with liquid crystal defects,” Appl. Phys. Lett. 92, 253306 (2008).
[Crossref]

Cao, Y.

Y. Cao and J. Li, “Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality,” Phys. Rev. B 89, 115420 (2014).
[Crossref]

Chan, H. L. W.

K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, “One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films,” J. Appl. Phys. 103, 083107 (2008).
[Crossref]

Chao, N.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[Crossref] [PubMed]

Choy, C. L.

K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, “One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films,” J. Appl. Phys. 103, 083107 (2008).
[Crossref]

Churikov, V. M.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[Crossref] [PubMed]

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]

Dong, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Dudley, J. M.

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3, 85–90 (2009).
[Crossref]

Englund, D.

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
[Crossref]

Fedotov, V. A.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[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.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[Crossref] [PubMed]

Guimard, D.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
[Crossref]

Gunyakov, V. A.

Ha, N. Y.

N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7, 43–47 (2008).
[Crossref]

Hua, Z.

Ishida, S.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
[Crossref]

Ishikawa, K.

N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7, 43–47 (2008).
[Crossref]

Iwamoto, S.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
[Crossref]

Jeong, S. M.

N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7, 43–47 (2008).
[Crossref]

Jim, K. L.

K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, “One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films,” J. Appl. Phys. 103, 083107 (2008).
[Crossref]

Jin, L.

L. Jin, J. Li, H. Li, Q. Lin, and C. Li, “Improving sideband of chiral photonic crystal based on PSTD approach,” Opt. Comm. 279, 43–49 (2007).
[Crossref]

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photon. Tech. Lett. 18, 1261–1264 (2006).
[Crossref]

Kafesaki, M.

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
[Crossref]

Kim, K.

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crystal structures,” Opt. Express 21, 28817–28823 (2013).
[Crossref]

K. Kim and D. H. Lee, “Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity,” Phys. Plasmas 13, 042103 (2006).
[Crossref]

K. Kim, H. Yoo, and H. Lim, “Exact analytical expressions for the dispersion relation of one-dimensional chiral photonic crystals,” Waves Random Complex Media 16, 75–84 (2006).
[Crossref]

K. Kim, D. H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” EPL 69, 207–213 (2005).
[Crossref]

Kivshar, Y. S.

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, “All-optical swiching and multistability in photonic structures with liquid crystal defects,” Appl. Phys. Lett. 92, 253306 (2008).
[Crossref]

Kopp, V. I.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[Crossref] [PubMed]

Koschny, T.

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express 18, 14553–14567 (2010).
[Crossref] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[Crossref]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
[Crossref]

Lee, D. H.

K. Kim and D. H. Lee, “Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity,” Phys. Plasmas 13, 042103 (2006).
[Crossref]

K. Kim, D. H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” EPL 69, 207–213 (2005).
[Crossref]

Lee, K. J.

Lee, W.

Lekner, J.

J. Lekner, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[Crossref]

Leung, C. W.

K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, “One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films,” J. Appl. Phys. 103, 083107 (2008).
[Crossref]

Li, C.

L. Jin, J. Li, H. Li, Q. Lin, and C. Li, “Improving sideband of chiral photonic crystal based on PSTD approach,” Opt. Comm. 279, 43–49 (2007).
[Crossref]

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photon. Tech. Lett. 18, 1261–1264 (2006).
[Crossref]

Li, H.

L. Jin, J. Li, H. Li, Q. Lin, and C. Li, “Improving sideband of chiral photonic crystal based on PSTD approach,” Opt. Comm. 279, 43–49 (2007).
[Crossref]

Li, J.

Y. Cao and J. Li, “Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality,” Phys. Rev. B 89, 115420 (2014).
[Crossref]

L. Jin, J. Li, H. Li, Q. Lin, and C. Li, “Improving sideband of chiral photonic crystal based on PSTD approach,” Opt. Comm. 279, 43–49 (2007).
[Crossref]

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photon. Tech. Lett. 18, 1261–1264 (2006).
[Crossref]

Li, L.

J. Li, L. Jin, L. Li, and C. Li, “Bandgap separation and optical switching in nonlinear chiral photonic crystal with layered structure,” IEEE Photon. Tech. Lett. 18, 1261–1264 (2006).
[Crossref]

Li, Z.

Z. Li, M. Mutlu, and E. Ozbay, “Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission,” J. Opt. 15, 023001 (2013).
[Crossref]

Lim, H.

K. Kim, H. Yoo, and H. Lim, “Exact analytical expressions for the dispersion relation of one-dimensional chiral photonic crystals,” Waves Random Complex Media 16, 75–84 (2006).
[Crossref]

K. Kim, D. H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” EPL 69, 207–213 (2005).
[Crossref]

Lin, Q.

L. Jin, J. Li, H. Li, Q. Lin, and C. Li, “Improving sideband of chiral photonic crystal based on PSTD approach,” Opt. Comm. 279, 43–49 (2007).
[Crossref]

Lindell, I. V.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

Linden, S.

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]

Ma, G.

Miroshnichenko, A. E.

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, “All-optical swiching and multistability in photonic structures with liquid crystal defects,” Appl. Phys. Lett. 92, 253306 (2008).
[Crossref]

Mutlu, M.

Z. Li, M. Mutlu, and E. Ozbay, “Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission,” J. Opt. 15, 023001 (2013).
[Crossref]

Myslivets, S. A.

Neugroschl, D.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[Crossref] [PubMed]

Nishimura, S.

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N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7, 43–47 (2008).
[Crossref]

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N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7, 43–47 (2008).
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A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
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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).
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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).
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Zhao, R.

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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
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[Crossref]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
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B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
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IEEE Photon. Tech. Lett. (1)

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K. L. Jim, D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, “One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films,” J. Appl. Phys. 103, 083107 (2008).
[Crossref]

J. Opt. (1)

Z. Li, M. Mutlu, and E. Ozbay, “Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission,” J. Opt. 15, 023001 (2013).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
[Crossref]

Nat. Mater. (1)

N. Y. Ha, Y. Ohtsuka, S. M. Jeong, S. Nishimura, G. Suzaki, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals,” Nat. Mater. 7, 43–47 (2008).
[Crossref]

Nat. Photonics (3)

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3, 85–90 (2009).
[Crossref]

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5, 91–94 (2011).
[Crossref]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[Crossref]

Nat. Phys. (1)

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484–488 (2006).
[Crossref]

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L. Jin, J. Li, H. Li, Q. Lin, and C. Li, “Improving sideband of chiral photonic crystal based on PSTD approach,” Opt. Comm. 279, 43–49 (2007).
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Y. Cao and J. Li, “Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality,” Phys. Rev. B 89, 115420 (2014).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
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Science (3)

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, “Chiral fiber gratings,” Science 305, 74–75 (2004).
[Crossref] [PubMed]

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]

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

Waves Random Complex Media (1)

K. Kim, H. Yoo, and H. Lim, “Exact analytical expressions for the dispersion relation of one-dimensional chiral photonic crystals,” Waves Random Complex Media 16, 75–84 (2006).
[Crossref]

Other (2)

A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials (Gordon and Breach, 2001).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

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Figures (7)

Fig. 1
Fig. 1 Sketch of a one-dimensional photonic crystal with one defect layer made of an isotropic chiral medium.
Fig. 2
Fig. 2 Total transmittances for (a) s-polarized and (b) p-polarized incident waves in the absence of a defect versus normalized frequency in the frequency region where the first band gap appears, when the total number of periods is 16 and the incident angle θ is 30°. These results are compared with the total transmittances for (c) s-polarized and (d) p-polarized incident waves in the presence of an achiral defect with the refractive index n = 1.5 and γ = 0, and (e) s-polarized, (f) p-polarized, (g) RCP and (h) LCP incident waves in the presence of a chiral defect with n = 1.5 and γ = 0.5 versus normalized frequency, when θ = 30° and N = 8. When there is an achiral defect, only one defect mode appears at (c) ωΛ/c = 1.842 and (d) ωΛ/c = 1.841. When there is a chiral defect, however, two split defect modes with different frequencies ωΛ/c = 1.837 and 1.859 are clearly seen inside the photonic band gap, even though there is only one defect layer in our structure.
Fig. 3
Fig. 3 Total transmittance versus normalized frequency, when θ = 0° and N = 8. Only one defect mode, which is independent of the value of γ and the polarization of the incident wave, is observed in the normal incidence case.
Fig. 4
Fig. 4 Total transmittances of defect modes for incident s, p, RCP and LCP waves, Ts, Tp, T+ and T, versus normalized frequency, when θ = 30°, N = 8 and γ = 0.1 (black), 0.3 (red), 0.5 (blue).
Fig. 5
Fig. 5 Transmittances Tss (black), Tpp (red), Tsp (blue) and Tps (blue) versus normalized frequency, when θ = 30°, N = 8 and γ = 0.5. Tsp and Tps represent the conversion between s and p waves caused by the chiral defect layer.
Fig. 6
Fig. 6 Tp versus normalized frequency for incident angles θ = 15° (black), 30° (red) and 45° (blue), when γ = 0.5 and N = 8.
Fig. 7
Fig. 7 Tp versus normalized frequency for N = 6 (black), 8 (red) and 10 (blue), when θ = 30° and γ = 0.5.

Equations (7)

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D = ε E + i γ H , B = μ H i γ E ,
( E y H y ) 1 ε μ γ 2 ( ε μ γ γ i ( μ γ i γ μ ) i ( ε γ + γ ε ) μ ε γ γ ) ( E y H y ) + ( k 2 ( ε μ + γ 2 ) q 2 2 i k 2 μ γ 2 i k 2 ε γ k 2 ( ε μ + γ 2 ) q 2 ) ( E y H y ) = ( 0 0 ) ,
d 2 ψ d z 2 d d z 1 ( z ) d ψ d z + [ k 2 ( z ) ( z ) q 2 I ] ψ = 0 ,
= ( μ i γ i γ ε ) , = ( ε i γ i γ μ ) .
1 i k cos θ d r d l = r + r + 1 2 ( r + I ) [ + tan 2 θ ( 1 ) ] ( r + I ) ,
1 i k cos θ d t d l = t + 1 2 t [ + tan 2 θ ( 1 ) ] ( r + I ) ,
t + + = 1 2 ( t p p + t s s ) + i 2 ( t s p t p s ) , t + = 1 2 ( t p p t s s ) + i 2 ( t s p + t p s ) , t + = 1 2 ( t p p + t s s ) i 2 ( t s p + t p s ) , t = 1 2 ( t p p + t s s ) i 2 ( t s p t p s ) .

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