Abstract

We demonstrate that the wavelength sensitivity of a self-collimation superprism in photonic crystals (PhCs) can be greatly improved via slow light. With the help of a saddle point Van Hove singularity, we present an approach to obtain such a wavelength-sensitive self-collimation superprism. Our superprism not only has extremely high wavelength sensitivity, but also can suppress beam divergence, irregular beam generation, and wavelength channel dropout, overcoming the limitations of traditional PhC-based superprisms. Based on our superprism, a high-performance compact demultiplexer is also proposed.

© 2014 Optical Society of America

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  1. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
    [Crossref]
  2. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
    [Crossref]
  3. S. Foteinopoulou, Physica B 407, 4056 (2012).
    [Crossref]
  4. B. Gralak, S. Enoch, and G. Tayeb, in Metamaterials: Physics and Engineering Explorations, N. Engheta and R. Ziolkowski, eds. (Wiley, 2006).
  5. J. Joannopoulos, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).
  6. H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).
  7. T. Matsumoto, S. Fujita, and T. Baba, Opt. Express 13, 10768 (2005).
    [Crossref]
  8. B. Momeni and A. Adibi, Appl. Opt. 45, 8466 (2006).
    [Crossref]
  9. B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, Opt. Express 14, 2413 (2006).
    [Crossref]
  10. T. Baba and M. Nakamura, IEEE J. Quantum Electron. 38, 909 (2002).
    [Crossref]
  11. S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 72, 165112 (2005).
    [Crossref]
  12. D. Bernier, X. L. Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, Opt. Express 16, 17209 (2008).
    [Crossref]
  13. T. Baba and T. Matsumoto, Appl. Phys. Lett. 81, 2325 (2002).
    [Crossref]
  14. M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
    [Crossref]
  15. The relation between q and vg can be illustrated by Eq. (15) in Ref. [14], i.e., q=((kn/kx)(p/ω˜))+((1/|vg|2)((ω˜,χω˜,ηχ)−(ω˜,ηω˜,χχ)/(ω˜,χ))). Near the self-collimation region, we have p≃0, and the second term of the equation can be reduced by L’Hospital Rule. As a result, the equation becomes q≃(1/|vg|2)((−ω˜,ηω˜,χχχ)/(ω˜,χχ)). So we have q∝1/|vg|2.
  16. T. Baba, Nat. Photonics 2, 465 (2008).
    [Crossref]
  17. M. Ibanescu, E. Reed, and J. Joannopoulos, Phys. Rev. Lett. 96, 033904 (2006).
    [Crossref]
  18. X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, Opt. Express 21, 30140 (2013).
    [Crossref]
  19. T. Matsumoto and T. Baba, J. Lightwave Technol. 22, 917 (2004).
    [Crossref]
  20. EastFDTD V3.0, DONGJUN Information Technology Co., Ltd., China. See http://www.eastfdtd.com .
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    [Crossref]
  22. L. Wu, M. Mazilu, and T. Krauss, J. Lightwave Technol. 21, 561 (2003).
    [Crossref]
  23. A. Bakhtazad and A. Kirk, J. Lightwave Technol. 25, 1322 (2007).
    [Crossref]
  24. B. Momeni and A. Adibi, IEEE J. Sel. Areas Commun. 23, 1355 (2005).
    [Crossref]
  25. B. Momeni and A. Adibi, Appl. Phys. B 77, 555 (2003).
    [Crossref]
  26. The proportional coefficient, ζ∼(θT3/[(∇κ(θi),0)×(∇κ(θc),0)]z2), can be derived from the Eqs. (23) and (24) in Ref. [14], where all the symbols are the same as those in the Ref. [14].

2013 (2)

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, Opt. Express 21, 30140 (2013).
[Crossref]

2012 (2)

W. Li, Z. Liu, X. Zhang, and X. Jiang, Appl. Phys. Lett. 100, 161108 (2012).
[Crossref]

S. Foteinopoulou, Physica B 407, 4056 (2012).
[Crossref]

2008 (2)

2007 (1)

2006 (3)

2005 (4)

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 72, 165112 (2005).
[Crossref]

T. Matsumoto, S. Fujita, and T. Baba, Opt. Express 13, 10768 (2005).
[Crossref]

B. Momeni and A. Adibi, IEEE J. Sel. Areas Commun. 23, 1355 (2005).
[Crossref]

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

2004 (1)

2003 (2)

2002 (2)

T. Baba and T. Matsumoto, Appl. Phys. Lett. 81, 2325 (2002).
[Crossref]

T. Baba and M. Nakamura, IEEE J. Quantum Electron. 38, 909 (2002).
[Crossref]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Adibi, A.

Askari, M.

Baba, T.

T. Baba, Nat. Photonics 2, 465 (2008).
[Crossref]

T. Matsumoto, S. Fujita, and T. Baba, Opt. Express 13, 10768 (2005).
[Crossref]

T. Matsumoto and T. Baba, J. Lightwave Technol. 22, 917 (2004).
[Crossref]

T. Baba and M. Nakamura, IEEE J. Quantum Electron. 38, 909 (2002).
[Crossref]

T. Baba and T. Matsumoto, Appl. Phys. Lett. 81, 2325 (2002).
[Crossref]

Bakhtazad, A.

Bassi, P.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Bernier, D.

Cassan, E.

Chen, L.

Eggleton, B.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Enoch, S.

B. Gralak, S. Enoch, and G. Tayeb, in Metamaterials: Physics and Engineering Explorations, N. Engheta and R. Ziolkowski, eds. (Wiley, 2006).

Foteinopoulou, S.

S. Foteinopoulou, Physica B 407, 4056 (2012).
[Crossref]

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 72, 165112 (2005).
[Crossref]

Fujita, S.

Gan, F.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

Gralak, B.

B. Gralak, S. Enoch, and G. Tayeb, in Metamaterials: Physics and Engineering Explorations, N. Engheta and R. Ziolkowski, eds. (Wiley, 2006).

Grillet, C.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Huang, J.

Ibanescu, M.

M. Ibanescu, E. Reed, and J. Joannopoulos, Phys. Rev. Lett. 96, 033904 (2006).
[Crossref]

Jiang, X.

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, Opt. Express 21, 30140 (2013).
[Crossref]

W. Li, Z. Liu, X. Zhang, and X. Jiang, Appl. Phys. Lett. 100, 161108 (2012).
[Crossref]

Joannopoulos, J.

M. Ibanescu, E. Reed, and J. Joannopoulos, Phys. Rev. Lett. 96, 033904 (2006).
[Crossref]

J. Joannopoulos, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Kirk, A.

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Krauss, T.

Li, H.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

Li, W.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

W. Li, Z. Liu, X. Zhang, and X. Jiang, Appl. Phys. Lett. 100, 161108 (2012).
[Crossref]

Lin, X.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, Opt. Express 21, 30140 (2013).
[Crossref]

Liu, Z.

W. Li, Z. Liu, X. Zhang, and X. Jiang, Appl. Phys. Lett. 100, 161108 (2012).
[Crossref]

Lupu, A.

Marris-Morini, D.

Martijn de Sterke, C.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Matsumoto, T.

Mazilu, M.

McPhedran, R.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Mohammadi, S.

Momeni, B.

Nakamura, M.

T. Baba and M. Nakamura, IEEE J. Quantum Electron. 38, 909 (2002).
[Crossref]

Norton, A.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Qiu, C.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

Rakhshandehroo, M.

Reed, E.

M. Ibanescu, E. Reed, and J. Joannopoulos, Phys. Rev. Lett. 96, 033904 (2006).
[Crossref]

Roux, X. L.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Sheng, Z.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

Soljacic, M.

Soltani, M.

Soukoulis, C. M.

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 72, 165112 (2005).
[Crossref]

Steel, M.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Tayeb, G.

B. Gralak, S. Enoch, and G. Tayeb, in Metamaterials: Physics and Engineering Explorations, N. Engheta and R. Ziolkowski, eds. (Wiley, 2006).

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

Vivien, L.

Wang, X.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

Wu, A.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

Wu, L.

Zhang, X.

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, Opt. Express 21, 30140 (2013).
[Crossref]

W. Li, Z. Liu, X. Zhang, and X. Jiang, Appl. Phys. Lett. 100, 161108 (2012).
[Crossref]

Zoli, R.

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Zou, S.

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

Appl. Opt. (1)

Appl. Phys. B (1)

B. Momeni and A. Adibi, Appl. Phys. B 77, 555 (2003).
[Crossref]

Appl. Phys. Lett. (3)

W. Li, Z. Liu, X. Zhang, and X. Jiang, Appl. Phys. Lett. 100, 161108 (2012).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[Crossref]

T. Baba and T. Matsumoto, Appl. Phys. Lett. 81, 2325 (2002).
[Crossref]

IEEE J. Quantum Electron. (1)

T. Baba and M. Nakamura, IEEE J. Quantum Electron. 38, 909 (2002).
[Crossref]

IEEE J. Sel. Areas Commun. (1)

B. Momeni and A. Adibi, IEEE J. Sel. Areas Commun. 23, 1355 (2005).
[Crossref]

IEEE Photon. J. (1)

H. Li, A. Wu, W. Li, X. Lin, C. Qiu, Z. Sheng, X. Wang, S. Zou, and F. Gan, IEEE Photon. J. 5, 201306 (2013).

J. Lightwave Technol. (3)

Nat. Photonics (1)

T. Baba, Nat. Photonics 2, 465 (2008).
[Crossref]

Opt. Express (4)

Phys. Rev. B (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[Crossref]

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 72, 165112 (2005).
[Crossref]

Phys. Rev. E (1)

M. Steel, R. Zoli, C. Grillet, R. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. Eggleton, Phys. Rev. E 71, 056608 (2005).
[Crossref]

Phys. Rev. Lett. (1)

M. Ibanescu, E. Reed, and J. Joannopoulos, Phys. Rev. Lett. 96, 033904 (2006).
[Crossref]

Physica B (1)

S. Foteinopoulou, Physica B 407, 4056 (2012).
[Crossref]

Other (5)

B. Gralak, S. Enoch, and G. Tayeb, in Metamaterials: Physics and Engineering Explorations, N. Engheta and R. Ziolkowski, eds. (Wiley, 2006).

J. Joannopoulos, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

The relation between q and vg can be illustrated by Eq. (15) in Ref. [14], i.e., q=((kn/kx)(p/ω˜))+((1/|vg|2)((ω˜,χω˜,ηχ)−(ω˜,ηω˜,χχ)/(ω˜,χ))). Near the self-collimation region, we have p≃0, and the second term of the equation can be reduced by L’Hospital Rule. As a result, the equation becomes q≃(1/|vg|2)((−ω˜,ηω˜,χχχ)/(ω˜,χχ)). So we have q∝1/|vg|2.

EastFDTD V3.0, DONGJUN Information Technology Co., Ltd., China. See http://www.eastfdtd.com .

The proportional coefficient, ζ∼(θT3/[(∇κ(θi),0)×(∇κ(θc),0)]z2), can be derived from the Eqs. (23) and (24) in Ref. [14], where all the symbols are the same as those in the Ref. [14].

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Figures (4)

Fig. 1.
Fig. 1.

(a) EFCs of the 2D rod-type PhC with rectangular lattice. The saddle point Van Hove singularity is labeled by a blue dot. The structure of the PhC is schematically shown in the inset picture. The region inside the rectangle is the selected region that contains a self-collimation region. (b) EFCs of the selected region, crosses an EIAP with 0.028 rad. (c) Group velocity scale color map. The arrows indicate the direction of the group velocity of light.

Fig. 2.
Fig. 2.

Logarithmic scale color maps of the parameters. (a) log|1/p|; (b) log|q|; (c) log|r|. The purple lines and the bold black solid lines indicate the EFCs and the EIAP, respectively.

Fig. 3.
Fig. 3.

Superprism effect of the PhC. Three Gaussian beams with three frequencies ω˜1=0.375, ω˜2=0.382, and ω˜3=0.385 are, respectively, incident into the PhCs, and the deflected beams are shown in (a), (b), and (c), respectively.

Fig. 4.
Fig. 4.

(a) Model of the demultiplexer structure. (b) Intensity distribution of the deflected beams with three frequencies versus the deflected angle. The intensity is normalized by the average intensity of the right periphery of the semi-circle-type superprism. (c) Deflected angle versus frequency.

Equations (2)

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q1/|vg|2,
Nc4ζr2A,

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