Abstract

We present a dual-negative refraction effect based on the overlapping bands in a two-dimensional triangular photonic crystal formed by holographic lithography. Under certain conditions, one incident plane wave launched into this photonic crystal can be dispersed into two negative refracted waves at the same frequency and the same perpendicular polarization state with different phase velocities and group velocities. We find that this dual-negative refraction behavior can be easily manipulated by adjusting the incident angle, the frequency of incident wave and the filling ratio of the PhC. This special effect can be applied to realize wave-front division and optical interference in optical holography. Based on this effect, a double focusing imaging phenomenon has been achieved by the PhC slab. These unique features may show great impacts on both fundamental physics and optical device applications.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
  3. V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
    [CrossRef]
  4. G. Sun, A. S. Jugessur, and A. G. Kirk, “Imaging properties of dielectric photonic crystal slabs for large object distances,” Opt. Express 14(15), 6755–6765 (2006).
    [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [CrossRef] [PubMed]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  7. P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86(20), 201108 (2005).
    [CrossRef]
  8. C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010

2009

2007

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

K. Ren, Z. Y. Li, X. B. Ren, S. Feng, B. Y. Cheng, and D. Z. Zhang, “Three-dimensional light focusing in inverse opal photonic crystals,” Phys. Rev. B 75(11), 115108 (2007).
[CrossRef]

2006

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73(16), 165310 (2006).
[CrossRef]

G. Sun, A. S. Jugessur, and A. G. Kirk, “Imaging properties of dielectric photonic crystal slabs for large object distances,” Opt. Express 14(15), 6755–6765 (2006).
[CrossRef] [PubMed]

2005

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “Refraction and rightness in photonic crystals,” Opt. Express 13(21), 8596–8605 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[CrossRef]

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
[CrossRef]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86(20), 201108 (2005).
[CrossRef]

2004

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Y. Luo, W. Zhang, Y. Huang, J. Zhao, and J. Peng, “Wide-angle beam splitting by use of positive-negative refraction in photonic crystals,” Opt. Lett. 29(24), 2920–2922 (2004).
[CrossRef]

2003

2001

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1999

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

1968

V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of sigma and mu,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Cai, L. Z.

Cai, W. S.

Chen, Y. F.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Cheng, B. Y.

K. Ren, Z. Y. Li, X. B. Ren, S. Feng, B. Y. Cheng, and D. Z. Zhang, “Three-dimensional light focusing in inverse opal photonic crystals,” Phys. Rev. B 75(11), 115108 (2007).
[CrossRef]

Chettiar, U. K.

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Dong, G. Y.

Drachev, V. P.

Feng, L.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Feng, S.

K. Ren, Z. Y. Li, X. B. Ren, S. Feng, B. Y. Cheng, and D. Z. Zhang, “Three-dimensional light focusing in inverse opal photonic crystals,” Phys. Rev. B 75(11), 115108 (2007).
[CrossRef]

Gajic, R.

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73(16), 165310 (2006).
[CrossRef]

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “Refraction and rightness in photonic crystals,” Opt. Express 13(21), 8596–8605 (2005).
[CrossRef] [PubMed]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Hingerl, K.

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73(16), 165310 (2006).
[CrossRef]

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “Refraction and rightness in photonic crystals,” Opt. Express 13(21), 8596–8605 (2005).
[CrossRef] [PubMed]

Huang, Y.

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Joannopoulos, J. D.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Jugessur, A. S.

Kang, X. L.

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Kildishev, A. V.

Kirk, A. G.

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Kuchar, F.

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73(16), 165310 (2006).
[CrossRef]

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “Refraction and rightness in photonic crystals,” Opt. Express 13(21), 8596–8605 (2005).
[CrossRef] [PubMed]

Li, G. J.

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Li, Y. P.

Li, Z. Y.

K. Ren, Z. Y. Li, X. B. Ren, S. Feng, B. Y. Cheng, and D. Z. Zhang, “Three-dimensional light focusing in inverse opal photonic crystals,” Phys. Rev. B 75(11), 115108 (2007).
[CrossRef]

Liu, Q.

Lu, M. H.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Lu, W. T.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86(20), 201108 (2005).
[CrossRef]

Luo, Y.

Mao, Y. W.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Meisels, R.

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73(16), 165310 (2006).
[CrossRef]

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, “Refraction and rightness in photonic crystals,” Opt. Express 13(21), 8596–8605 (2005).
[CrossRef] [PubMed]

Ming, N. B.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Nielsen, J. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Parimi, P. V.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86(20), 201108 (2005).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Peng, J.

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
[CrossRef]

Ren, K.

K. Ren, Z. Y. Li, X. B. Ren, S. Feng, B. Y. Cheng, and D. Z. Zhang, “Three-dimensional light focusing in inverse opal photonic crystals,” Phys. Rev. B 75(11), 115108 (2007).
[CrossRef]

Ren, X. B.

K. Ren, Z. Y. Li, X. B. Ren, S. Feng, B. Y. Cheng, and D. Z. Zhang, “Three-dimensional light focusing in inverse opal photonic crystals,” Phys. Rev. B 75(11), 115108 (2007).
[CrossRef]

Sarychev, A. K.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Soljacic, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Sridhar, S.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86(20), 201108 (2005).
[CrossRef]

Sun, G.

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Tandon, S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006).
[CrossRef] [PubMed]

Tanielian, M. H.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Thompson, M. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystal,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of sigma and mu,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Vier, D. C.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Vodo, P.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86(20), 201108 (2005).
[CrossRef]

Wang, Y. R.

Yang, X. L.

Yuan, H. K.

Zhang, C.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Zhang, D. Z.

K. Ren, Z. Y. Li, X. B. Ren, S. Feng, B. Y. Cheng, and D. Z. Zhang, “Three-dimensional light focusing in inverse opal photonic crystals,” Phys. Rev. B 75(11), 115108 (2007).
[CrossRef]

Zhang, W.

Zhao, J.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Y. Luo, W. Zhang, Y. Huang, J. Zhao, and J. Peng, “Wide-angle beam splitting by use of positive-negative refraction in photonic crystals,” Opt. Lett. 29(24), 2920–2922 (2004).
[CrossRef]

Zhu, S. N.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Zhu, Y. Y.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Zi, J.

M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Negative birefraction of acoustic waves in a sonic crystal,” Nat. Mater. 6(10), 744–748 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett.

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the 2D triangular PhC with hexagonal dielectric rods in air; (b) Lowest four bands of this PhC for TM polarization. The black line marks the normalized frequency a/λ = 0.32.

Fig. 2
Fig. 2

EFC plots of (a) TM2 and (b) TM3 bands in the PhC. (c) Wave vector diagram for TM2 and TM3 bands at the frequency of 0.32 with different incident angles of 10°, 20° and 30°.

Fig. 3
Fig. 3

Ray tracing of the point source at the frequency of 0.32 placed in front of the PhC slab.

Fig. 4
Fig. 4

The FDTD simulations of electric field distributions with different incident angles of (a) θi = 10°; (b) θi = 20°; (c) θi = 30° at the frequency of 0.32.

Fig. 5
Fig. 5

Electric field patterns of double focusing imaging for the PhC slab with (a) a/λ = 0.32, f = 82.2%, (b) a/λ = 0.28, f = 82.2%, (c) a/λ = 0.35, f = 59.1%.

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