Abstract

The single defect structure of a two-dimensional graded index photonic crystal (PC) is investigated. By introduction of an air hole located at center of the photonic crystal-based lenses, we can obtain an extremely small focusing spot, sited at full-width and half maximum (FWHM) as fine as λ/75, which is positioned at the subsurface and top surface of the PCs respectively. Computational calculations were performed on the basis of finite-different time–domain (FDTD) algorithm for the purpose of verifying the feasibility of our design. To study influence of the defect on nanofocusing property of the PC lenses, we set different length of the air holes at center of the PC lenses. The influence of wavelength and material on the nanofocusing performance of the PC lenses is discussed. New applications in optoelectronic devices, nanometrology, bioimaging, and biosensing from the graded index of PC lenses is possible.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (1)

2013 (4)

L. Jin, Q. Y. Zhu, and Y. Q. Fu, “Tunability of graded negative index-based photonic crystal lenses for fine focusing,” Chin. Phys. B 22(9), 094102 (2013).
[Crossref]

L. Jin, Q. Y. Zhu, Y. Q. Fu, and W. X. Yu, “Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations,” Chin. Phys. B 22(10), 104101 (2013).
[Crossref]

H. Zhang, J. Zhu, Z. Zhu, Y. Jin, Q. Li, and G. Jin, “Surface-plasmon-enhanced GaN-LED based on a multilayered M-shaped nano-grating,” Opt. Express 21(11), 13492–13501 (2013).
[Crossref] [PubMed]

H. S. Zhang, J. Zhu, Z. D. Zhu, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on the quasi-symmetrical planar waveguide structure,” Opt. Commun. 311, 311–316 (2013).
[Crossref]

2012 (4)

Q. Y. Zhu, Y. Q. Fu, D. Q. Hu, and Z. M. Zhang, “A novel optical beam splitter based on photonic crystal with hybrid lattices,” Chin. Phys. B 21(6), 064220 (2012).
[Crossref]

K. Ren and X. B. Ren, “Y-shaped beam splitter by graded structure design in a photonic crystal,” Chin. Sci. Bull. 57(11), 1241–1245 (2012).
[Crossref]

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10-11), 2638–2641 (2012).
[Crossref]

G. Vitrant, S. Zaiba, B. Y. Vineeth, T. Kouriba, O. Ziane, O. Stéphan, J. Bosson, and P. L. Baldeck, “Obstructive micro diffracting structures as an alternative to plasmonics nano slits for making efficient microlenses,” Opt. Express 20(24), 26542–26547 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (2)

2009 (1)

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High Efficiency of Graded Index Photonic Crystal as an Input Coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[Crossref]

2008 (2)

2007 (1)

2006 (1)

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[Crossref]

2005 (2)

2004 (3)

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[Crossref] [PubMed]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[Crossref]

2003 (1)

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

2002 (1)

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” Selected Topics in Quantum Electronics, IEEE Journal of 8(6), 1246–1257 (2002).
[Crossref]

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction-like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[Crossref]

1999 (3)

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

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” JOSA B 16(2), 275–285 (1999).
[Crossref]

1998 (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref] [PubMed]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Akmansoy, É.

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10-11), 2638–2641 (2012).
[Crossref]

Albert, J. P.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[Crossref]

Almeida, V. R.

Asatsuma, T.

Baba, T.

Baldeck, P. L.

Barrios, C. A.

Bosson, J.

Caglayan, H.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High Efficiency of Graded Index Photonic Crystal as an Input Coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[Crossref]

Cakmak, A. O.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High Efficiency of Graded Index Photonic Crystal as an Input Coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[Crossref]

Cassagne, D.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[Crossref]

E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30(17), 2278–2280 (2005).
[Crossref] [PubMed]

Centeno, E.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[Crossref]

E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30(17), 2278–2280 (2005).
[Crossref] [PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Chen, L. W.

H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” JOSA B 28(9), 2098–2104 (2011).
[Crossref]

Citrin, D. S.

Colak, E.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High Efficiency of Graded Index Photonic Crystal as an Input Coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[Crossref]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Fan, S.

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Fu, Y. Q.

L. Jin, Q. Y. Zhu, and Y. Q. Fu, “Tunability of graded negative index-based photonic crystal lenses for fine focusing,” Chin. Phys. B 22(9), 094102 (2013).
[Crossref]

L. Jin, Q. Y. Zhu, Y. Q. Fu, and W. X. Yu, “Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations,” Chin. Phys. B 22(10), 104101 (2013).
[Crossref]

Q. Y. Zhu, Y. Q. Fu, D. Q. Hu, and Z. M. Zhang, “A novel optical beam splitter based on photonic crystal with hybrid lattices,” Chin. Phys. B 21(6), 064220 (2012).
[Crossref]

Fujita, S.

Gajic, R.

Gaufillet, F.

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10-11), 2638–2641 (2012).
[Crossref]

Haus, H.

He, S. L.

Hingerl, K.

Hu, B.

Hu, D. Q.

Q. Y. Zhu, Y. Q. Fu, D. Q. Hu, and Z. M. Zhang, “A novel optical beam splitter based on photonic crystal with hybrid lattices,” Chin. Phys. B 21(6), 064220 (2012).
[Crossref]

Ippen, E. P.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Isic, G.

Jin, G.

Jin, G. F.

H. S. Zhang, J. Zhu, Z. D. Zhu, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on the quasi-symmetrical planar waveguide structure,” Opt. Commun. 311, 311–316 (2013).
[Crossref]

Jin, L.

L. Jin, Q. Y. Zhu, and Y. Q. Fu, “Tunability of graded negative index-based photonic crystal lenses for fine focusing,” Chin. Phys. B 22(9), 094102 (2013).
[Crossref]

L. Jin, Q. Y. Zhu, Y. Q. Fu, and W. X. Yu, “Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations,” Chin. Phys. B 22(10), 104101 (2013).
[Crossref]

Jin, Y.

Joannopoulos, J.

Joannopoulos, J. D.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Johnson, S. G.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Kawakami, S.

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

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Kawashima, T.

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

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Kosaka, H.

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

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Kouriba, T.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Kurt, H.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High Efficiency of Graded Index Photonic Crystal as an Input Coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[Crossref]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
[Crossref] [PubMed]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Li, Q.

Li, Q. Q.

H. S. Zhang, J. Zhu, Z. D. Zhu, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on the quasi-symmetrical planar waveguide structure,” Opt. Commun. 311, 311–316 (2013).
[Crossref]

Lidorikis, E.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Lipson, M.

Loncar, M.

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” Selected Topics in Quantum Electronics, IEEE Journal of 8(6), 1246–1257 (2002).
[Crossref]

Matsumoto, T.

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Mihalache, D.

Miret, J. J.

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction-like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[Crossref]

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

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Nozaki, K.

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[Crossref]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Ozbay, E.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High Efficiency of Graded Index Photonic Crystal as an Input Coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[Crossref]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” JOSA B 16(2), 275–285 (1999).
[Crossref]

Panoiu, N. C.

Qi, M.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Rakich, P. T.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Ren, K.

K. Ren and X. B. Ren, “Y-shaped beam splitter by graded structure design in a photonic crystal,” Chin. Sci. Bull. 57(11), 1241–1245 (2012).
[Crossref]

K. Ren and X. Ren, “Controlling light transport by using a graded photonic crystal,” Appl. Opt. 50(15), 2152–2157 (2011).
[Crossref] [PubMed]

Ren, X.

Ren, X. B.

K. Ren and X. B. Ren, “Y-shaped beam splitter by graded structure design in a photonic crystal,” Chin. Sci. Bull. 57(11), 1241–1245 (2012).
[Crossref]

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Sato, T.

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

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Scherer, A.

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” Selected Topics in Quantum Electronics, IEEE Journal of 8(6), 1246–1257 (2002).
[Crossref]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” JOSA B 16(2), 275–285 (1999).
[Crossref]

Shen, L.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

Smith, H. I.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Stéphan, O.

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

Tamamura, T.

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

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Tomita, A.

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

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Vasic, B.

Villeneuve, P.

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Vineeth, B. Y.

Vitrant, G.

Vuckovic, J.

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” JOSA B 16(2), 275–285 (1999).
[Crossref]

Wang, B.

Wang, H. W.

H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” JOSA B 28(9), 2098–2104 (2011).
[Crossref]

Witzens, J.

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” Selected Topics in Quantum Electronics, IEEE Journal of 8(6), 1246–1257 (2002).
[Crossref]

Xu, Q.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Ye, F.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

Yu, W. X.

L. Jin, Q. Y. Zhu, Y. Q. Fu, and W. X. Yu, “Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations,” Chin. Phys. B 22(10), 104101 (2013).
[Crossref]

Zaiba, S.

Zapata-Rodriguez, C. J.

Zhang, H.

Zhang, H. S.

H. S. Zhang, J. Zhu, Z. D. Zhu, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on the quasi-symmetrical planar waveguide structure,” Opt. Commun. 311, 311–316 (2013).
[Crossref]

Zhang, Z. M.

Q. Y. Zhu, Y. Q. Fu, D. Q. Hu, and Z. M. Zhang, “A novel optical beam splitter based on photonic crystal with hybrid lattices,” Chin. Phys. B 21(6), 064220 (2012).
[Crossref]

Zhu, J.

H. S. Zhang, J. Zhu, Z. D. Zhu, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on the quasi-symmetrical planar waveguide structure,” Opt. Commun. 311, 311–316 (2013).
[Crossref]

H. Zhang, J. Zhu, Z. Zhu, Y. Jin, Q. Li, and G. Jin, “Surface-plasmon-enhanced GaN-LED based on a multilayered M-shaped nano-grating,” Opt. Express 21(11), 13492–13501 (2013).
[Crossref] [PubMed]

Zhu, Q. Y.

L. Jin, Q. Y. Zhu, Y. Q. Fu, and W. X. Yu, “Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations,” Chin. Phys. B 22(10), 104101 (2013).
[Crossref]

L. Jin, Q. Y. Zhu, and Y. Q. Fu, “Tunability of graded negative index-based photonic crystal lenses for fine focusing,” Chin. Phys. B 22(9), 094102 (2013).
[Crossref]

Q. Y. Zhu, Y. Q. Fu, D. Q. Hu, and Z. M. Zhang, “A novel optical beam splitter based on photonic crystal with hybrid lattices,” Chin. Phys. B 21(6), 064220 (2012).
[Crossref]

Zhu, Z.

Zhu, Z. D.

H. S. Zhang, J. Zhu, Z. D. Zhu, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on the quasi-symmetrical planar waveguide structure,” Opt. Commun. 311, 311–316 (2013).
[Crossref]

Ziane, O.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[Crossref]

Chin. Phys. B (3)

Q. Y. Zhu, Y. Q. Fu, D. Q. Hu, and Z. M. Zhang, “A novel optical beam splitter based on photonic crystal with hybrid lattices,” Chin. Phys. B 21(6), 064220 (2012).
[Crossref]

L. Jin, Q. Y. Zhu, and Y. Q. Fu, “Tunability of graded negative index-based photonic crystal lenses for fine focusing,” Chin. Phys. B 22(9), 094102 (2013).
[Crossref]

L. Jin, Q. Y. Zhu, Y. Q. Fu, and W. X. Yu, “Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations,” Chin. Phys. B 22(10), 104101 (2013).
[Crossref]

Chin. Sci. Bull. (1)

K. Ren and X. B. Ren, “Y-shaped beam splitter by graded structure design in a photonic crystal,” Chin. Sci. Bull. 57(11), 1241–1245 (2012).
[Crossref]

J. Appl. Phys. (1)

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High Efficiency of Graded Index Photonic Crystal as an Input Coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[Crossref]

J. Opt. Soc. Am. B (3)

JOSA B (2)

H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” JOSA B 28(9), 2098–2104 (2011).
[Crossref]

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” JOSA B 16(2), 275–285 (1999).
[Crossref]

Nature (1)

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Opt. Commun. (2)

H. S. Zhang, J. Zhu, Z. D. Zhu, Q. Q. Li, and G. F. Jin, “Surface-plasmon-enhanced GaN-LED based on the quasi-symmetrical planar waveguide structure,” Opt. Commun. 311, 311–316 (2013).
[Crossref]

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10-11), 2638–2641 (2012).
[Crossref]

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. B (3)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction-like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[Crossref]

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58(16), R10096 (1998).
[Crossref]

Phys. Rev. Lett. (2)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Science (2)

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Selected Topics in Quantum Electronics, IEEE Journal of (1)

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” Selected Topics in Quantum Electronics, IEEE Journal of 8(6), 1246–1257 (2002).
[Crossref]

Other (3)

M. A. Verschuuren and H. A. V. Sprang, “Photonic crystal LED,” U.S. Patent 8,536–600. 2013–9-17.

D. G. Zhang, Y. Wang, T. Huang, and Z. B. Ouyang, “Low-loss Y-junction two-dimensional magneto-photonic crystals circulator using a ferrite cylinder,” Advanced Materials and Processes for RF and THz Applications (IMWS-AMP), 2015 IEEE MTT-S International Microwave Workshop Series on. IEEE, 2015: 1–3.
[Crossref]

L. F. Chen, C. K. Ong, C. P. Neo, V. V. Varadan, and K. Vijay, Varadan, Microwave Electronics. Measurement and Material Characterization (John Wiley and Sons, 2004), p.170.

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic diagram for the graded index PCs lenses. (b) Schematic of the PCs lenses perforated with graded-radius air-holes and single rectangular air-hole. The original coordinate point (0,0,0) is set at the center of the structure.
Fig. 2
Fig. 2 Intensity distributions along the transverse direction. The red line is the graded PCs, the blue line is the PCs only have single rectangular air-hole and the black line is the graded PCs with a rectangular air-hole with the ultra-fine focusing occurred at sub-surface of the PC lenses.
Fig. 3
Fig. 3 Intensity distributions in the x-z plane of the structure perforated with defects.
Fig. 4
Fig. 4 Intensity distributions along the transverse direction with the change of width (d) of the rectangular air-hole. The inset figure is zoom in of the central peak intensity of the curve.
Fig. 5
Fig. 5 Intensity distributions along the transverse direction with the change of length (l) of the rectangular air-hole. The inset figure is zoom in of the central peak intensity of the curve.
Fig. 6
Fig. 6 Intensity distributions along the transverse direction for the width of the rectangular air-hole 0.01 μm. The ultra-sharp focusing occurred at top surface of the PCs lenses.
Fig. 7
Fig. 7 Intensity distributions along the transverse direction with different substrate materials. The inset figure zoom in of the central peak intensity of the curve.
Fig. 8
Fig. 8 Intensity distribution along the propagation direction with different incident wavelength. The position of the lens is y = 0.

Equations (2)

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a b 1 ( λ 2a ) 2 = a1 b1 1 ( λ 2a ) 2
λ=2a1 ( b1 b ) 2 [ a 2 a1 a1 ]0.

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