Abstract

We realize a unidirectional transmission by cascading two nonparallel gratings (NPGs) made of isotropic, lossless, and linear media. For a pair of orthogonal linear polarizations, one of the gratings is designed as a polarizer, which is a reflector for one polarization and a transmitter for the other; another grating is designed as a polarization converter, which converts most of one polarized incident wave into another polarized transmitted wave. It is demonstrated by numerical calculation that more than 85% of the incident light energy can be transmitted with less than 1% transmission in the opposite direction for linearly polarized light at normal incidence, and the relative bandwidth of the unidirectional transmission is nearly 9%. The maximum transmission contrast ratio between the two directions is 62dB. Unlike one-way diffraction grating, the transmitted light of the NPGs is collinear with the incident light, but their polarizations are orthogonal.

© 2011 Optical Society of America

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References

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  1. R. J. Potton, Rep. Prog. Phys. 67, 717 (2004).
    [Crossref]
  2. A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
    [Crossref] [PubMed]
  3. X. Hu, C. Xin, Z. Li, and Q. Gong, New J. Phys. 12, 023029 (2010).
    [Crossref]
  4. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
    [Crossref] [PubMed]
  5. V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
    [Crossref]
  6. C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
    [Crossref] [PubMed]
  7. M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, Phys. Rev. E 74, 056611 (2006).
    [Crossref]
  8. A. E. Serebryannikov, Phys. Rev. B 80, 155117 (2009).
    [Crossref]
  9. W.-M. Ye, X.-D. Yuan, C.-C. Guo, and C. Zeng, Opt. Express 18, 7590 (2010).
    [Crossref] [PubMed]
  10. R. Magnusson and M. Shokooh-Saremi, Opt. Express 16, 3456 (2008).
    [Crossref] [PubMed]
  11. R. Magnusson, M. Shokooh-Saremi, and E. G. Johnson, Opt. Lett. 35, 2472 (2010).
    [Crossref] [PubMed]

2010 (5)

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[Crossref] [PubMed]

X. Hu, C. Xin, Z. Li, and Q. Gong, New J. Phys. 12, 023029 (2010).
[Crossref]

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

W.-M. Ye, X.-D. Yuan, C.-C. Guo, and C. Zeng, Opt. Express 18, 7590 (2010).
[Crossref] [PubMed]

R. Magnusson, M. Shokooh-Saremi, and E. G. Johnson, Opt. Lett. 35, 2472 (2010).
[Crossref] [PubMed]

2009 (1)

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

2008 (1)

2007 (1)

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
[Crossref]

2006 (2)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, Phys. Rev. E 74, 056611 (2006).
[Crossref]

2004 (1)

R. J. Potton, Rep. Prog. Phys. 67, 717 (2004).
[Crossref]

Chen, Y.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

Fedotov, V. A.

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

Gong, Q.

X. Hu, C. Xin, Z. Li, and Q. Gong, New J. Phys. 12, 023029 (2010).
[Crossref]

Guo, C.-C.

Helgert, C.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, Phys. Rev. E 74, 056611 (2006).
[Crossref]

Hu, X.

X. Hu, C. Xin, Z. Li, and Q. Gong, New J. Phys. 12, 023029 (2010).
[Crossref]

Johnson, E. G.

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[Crossref] [PubMed]

Khardikov, V. V.

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
[Crossref]

Kivshar, Y. S.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[Crossref] [PubMed]

Kley, E.-B.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

Lederer, F.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

Li, Z.

X. Hu, C. Xin, Z. Li, and Q. Gong, New J. Phys. 12, 023029 (2010).
[Crossref]

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, Phys. Rev. E 74, 056611 (2006).
[Crossref]

Magnusson, R.

Menzel, C.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

Mladyonov, P. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[Crossref] [PubMed]

Pertsch, T.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

Potton, R. J.

R. J. Potton, Rep. Prog. Phys. 67, 717 (2004).
[Crossref]

Prosvirnin, S. L.

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

Rockstuhl, C.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

Rogacheva, A. V.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, Phys. Rev. E 74, 056611 (2006).
[Crossref]

Schwanecke, A. S.

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
[Crossref]

Serebryannikov, A. E.

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

Shokooh-Saremi, M.

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[Crossref] [PubMed]

Tünnermann, A.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

White, K. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, Phys. Rev. E 74, 056611 (2006).
[Crossref]

Xin, C.

X. Hu, C. Xin, Z. Li, and Q. Gong, New J. Phys. 12, 023029 (2010).
[Crossref]

Ye, W.-M.

Yuan, X.-D.

Zeng, C.

Zheludev, N. I.

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

Nano Lett. (1)

V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, Nano Lett. 7, 1996 (2007).
[Crossref]

New J. Phys. (1)

X. Hu, C. Xin, Z. Li, and Q. Gong, New J. Phys. 12, 023029 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

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

Phys. Rev. E (1)

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, Phys. Rev. E 74, 056611 (2006).
[Crossref]

Phys. Rev. Lett. (3)

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[Crossref] [PubMed]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[Crossref] [PubMed]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

R. J. Potton, Rep. Prog. Phys. 67, 717 (2004).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the proposed NPGs and the definition of the coordinate system.

Fig. 2
Fig. 2

Normal incident transmittance spectra of the linearly polarized light through a single-layer Si / SiO 2 grating (period a, thickness h = 0.37 a , filling factor of Si f = 0.2 , infinite in the x direction and periodic in the y direction).

Fig. 3
Fig. 3

(a) Normal incident transmittance spectra and (b) phase difference and efficient transmittance defined by Eq. (1) of x and y polarization through a single-layer Si / SiO 2 grating (period a, thickness h = 0.8 a , filling factor of Si f = 0.16 , infinite in the x direction and periodic in the y direction).

Fig. 4
Fig. 4

Relative polarization transmittance spectra of a normal incident x polarization through a single-layer Si / SiO 2 grating (period a, thickness h = 0.8 a , filling factor of Si f = 0.16 , infinite in the direction at 45 ° to the x direction and periodic in the direction at 135 ° to the x direction).

Fig. 5
Fig. 5

(a), (c) Relative polarization transmittance spectra of a normal incident x and y polarization traveling through the proposed NPGs in the negative z direction and (b), (d) that in the positive z direction.

Equations (1)

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T eff = 1 4 sin 2 ( 2 α ) ( t x 2 + t y 2 2 t x t y cos φ ) .

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