Abstract

We present a positive–negative refraction effect in which, under certain conditions, an incident plane wave launched into a photonic crystal excites a positive-refracted Bloch wave and a negative-refracted Bloch wave simultaneously, both of which maintain the polarization. By utilizing this phenomenon, wide-angle beam splitting can be realized at the microscale level. Numerical simulations are employed to demonstrate this anomalous refraction behavior.

© 2004 Optical Society of America

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  1. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
    [CrossRef]
  2. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
    [CrossRef]
  3. H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
    [CrossRef]
  4. M. Notomi, Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  5. B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
    [CrossRef]
  6. J. Bravo-Abad, T. Ochiai, and J. Sanchez-Dehesa, Phys. Rev. B 67, 115116 (2003).
    [CrossRef]
  7. T. Baba and M. Nakamura, IEEE J. Quantum Electron. 38, 909 (2002).
    [CrossRef]
  8. S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  9. R. W. Ziolkowski and M. Tanaka, Opt. Quantum Electron. 31, 843 (1999).
    [CrossRef]
  10. T. Sondergaard and K. H. Dridi, Phys. Rev. B 61, 15688 (2000).
    [CrossRef]
  11. M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phys. Lett. 77, 3902 (2000).
    [CrossRef]
  12. K. Ohtaka, T. Ueta, and K. Amemiya, Phys. Rev. B 57, 2550 (1998).
    [CrossRef]
  13. L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, J. Opt. Soc. Am. A 17, 2165 (2000).
    [CrossRef]
  14. L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
    [CrossRef]

2003 (2)

J. Bravo-Abad, T. Ochiai, and J. Sanchez-Dehesa, Phys. Rev. B 67, 115116 (2003).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

2002 (1)

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

2001 (1)

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[CrossRef]

2000 (6)

L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, J. Opt. Soc. Am. A 17, 2165 (2000).
[CrossRef]

T. Sondergaard and K. H. Dridi, Phys. Rev. B 61, 15688 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phys. Lett. 77, 3902 (2000).
[CrossRef]

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
[CrossRef]

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

1999 (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

R. W. Ziolkowski and M. Tanaka, Opt. Quantum Electron. 31, 843 (1999).
[CrossRef]

1998 (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

K. Ohtaka, T. Ueta, and K. Amemiya, Phys. Rev. B 57, 2550 (1998).
[CrossRef]

Amemiya, K.

K. Ohtaka, T. Ueta, and K. Amemiya, Phys. Rev. B 57, 2550 (1998).
[CrossRef]

Asatryan, A. A.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[CrossRef]

L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, J. Opt. Soc. Am. A 17, 2165 (2000).
[CrossRef]

Baba, T.

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

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phys. Lett. 77, 3902 (2000).
[CrossRef]

Botten, L. C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[CrossRef]

L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, J. Opt. Soc. Am. A 17, 2165 (2000).
[CrossRef]

Bravo-Abad, J.

J. Bravo-Abad, T. Ochiai, and J. Sanchez-Dehesa, Phys. Rev. B 67, 115116 (2003).
[CrossRef]

de Sterke, C. M.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[CrossRef]

L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, J. Opt. Soc. Am. A 17, 2165 (2000).
[CrossRef]

Dridi, K. H.

T. Sondergaard and K. H. Dridi, Phys. Rev. B 61, 15688 (2000).
[CrossRef]

Enoch, S.

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Gralak, B.

Kawakami, S.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

Kosaka, H.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

McPhedran, R. C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[CrossRef]

L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, J. Opt. Soc. Am. A 17, 2165 (2000).
[CrossRef]

Nakamura, M.

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

Nicorovici, N. A.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[CrossRef]

L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, J. Opt. Soc. Am. A 17, 2165 (2000).
[CrossRef]

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

Ochiai, T.

J. Bravo-Abad, T. Ochiai, and J. Sanchez-Dehesa, Phys. Rev. B 67, 115116 (2003).
[CrossRef]

Ohtaka, K.

K. Ohtaka, T. Ueta, and K. Amemiya, Phys. Rev. B 57, 2550 (1998).
[CrossRef]

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phys. Lett. 77, 3902 (2000).
[CrossRef]

Robinson, P. A.

Sanchez-Dehesa, J.

J. Bravo-Abad, T. Ochiai, and J. Sanchez-Dehesa, Phys. Rev. B 67, 115116 (2003).
[CrossRef]

Sato, T.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

Sondergaard, T.

T. Sondergaard and K. H. Dridi, Phys. Rev. B 61, 15688 (2000).
[CrossRef]

Soukoulis, C. M.

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

Tanaka, M.

R. W. Ziolkowski and M. Tanaka, Opt. Quantum Electron. 31, 843 (1999).
[CrossRef]

Tayeb, G.

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phys. Lett. 77, 3902 (2000).
[CrossRef]

Tomita, A.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

Ueta, T.

K. Ohtaka, T. Ueta, and K. Amemiya, Phys. Rev. B 57, 2550 (1998).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski and M. Tanaka, Opt. Quantum Electron. 31, 843 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phys. Lett. 77, 3902 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Opt. Soc. Am. A (2)

Opt. Quantum Electron. (1)

R. W. Ziolkowski and M. Tanaka, Opt. Quantum Electron. 31, 843 (1999).
[CrossRef]

Phys. Rev. B (7)

T. Sondergaard and K. H. Dridi, Phys. Rev. B 61, 15688 (2000).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

J. Bravo-Abad, T. Ochiai, and J. Sanchez-Dehesa, Phys. Rev. B 67, 115116 (2003).
[CrossRef]

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, Phys. Rev. B 62, 1477 (2000).
[CrossRef]

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

K. Ohtaka, T. Ueta, and K. Amemiya, Phys. Rev. B 57, 2550 (1998).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10 096 (1998).
[CrossRef]

Phys. Rev. E (1)

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of light incident onto a two-dimensional photonic crystal of square lattice circular dielectric rods in free space, with finite extent vertically (y direction) and infinite horizontally (x direction). The input and output interfaces are both normal to one of the square lattice diagonals.

Fig. 2
Fig. 2

(a) Equifrequency dispersion contours for TE modes in the photonic crystal (upper panel) and free space (lower panel) with normalized frequency ωd/c equivalent to 3.55. The crystal parameters are the same as in Fig. 1. (b) Photonic crystal equifrequency contours within the first Brillouin zone (BZ) at some other frequencies. The two vertical white lines pass through points 2-1/2π,0 and -2-1/2π,0.

Fig. 3
Fig. 3

Numerical simulation of the electric field pattern of the x component generated by a TE-polarized Gaussian beam, with an incident angle θinc of 40° and a normalized frequency ωd/c equivalent to 3.55, impinging upon the 40-layer photonic crystal stack from below.

Fig. 4
Fig. 4

(a) Illustration showing angle of incidence θinc and the two angles of refraction θp and θn. (b) Electric field intensity distribution of the incident Gaussian beam at the input interface (dotted curves) and the transmitted rays at the output interface (solid curves). Same parameters as in Fig. 3, except that three incident angles are considered: 35°, 40°, and 45°. Arrows pointing downward indicate the beam peak positions, and refraction angles θp and θn are estimated.

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