Abstract

We investigate the beam propagation behavior in the photonic crystal (PhC) of the local super-collimation (LSC) regions both theoretically and numerically. A theory based on the cubic dispersion model in the LSC regions is established, which is a powerful tool to predict the beam evolution after a long propagation distance. The numerical experiments are also implemented, whose results agree well with those from our theory. Both the theoretical and simulation results show the new phenomenon of the asymmetric beam broadening for beams in the LSC regions, which is quite different from the traditional symmetric broadening. Physical reasons of such asymmetric broadening are explained by the cubic dispersion model and the solution to suppress the asymmetric broadening is proposed. Since the LSC beams could be widely used in photonic devices, such as hypersensitive spectrometers and demultiplexers, the deep insights of the beam propagation behavior in the LSC regions can help us to optimize our designs, such as choosing the proper beam width and the proper working range in the phase space.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

2018 (2)

J. Upham, B. Gao, L. O’Faolain, Z. Shi, S. A. Schulz, and R. W. Boyd, “Realization of a flat-band superprism on-chip from parallelogram lattice photonic crystals,” Opt. Lett. 43(20), 4981–4984 (2018).
[Crossref]

M. Gumus, I. H. Giden, O. Akcaalan, M. Turduev, and H. Kurt, “Enhanced superprism effect in symmetry reduced photonic crystals,” Appl. Phys. Lett. 113(13), 131103 (2018).
[Crossref]

2017 (2)

S. Gao, Y. Dou, Q. Li, and X. Jiang, “Tunable photonic crystal lens with high sensitivity of refractive index,” Opt. Express 25(6), 7112–7120 (2017).
[Crossref]

S. Pahlavan and V. Ahmadi, “Novel optical demultiplexer design using oblique boundary in hetero photonic crystals,” IEEE Photonics Technol. Lett. 29(6), 511–514 (2017).
[Crossref]

2016 (1)

X. Lin, H. Fang, L. Wang, G. P. Wang, and X. Jiang, “Transmissive refractive index sensing based on frequency-sensitive responses of two-dimensional photonic crystals,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (4)

I. H. Giden, M. Turduev, and H. Kurt, “Broadband super-collimation with low-symmetric photonic crystal,” Photon. Nanostruct. Fundam. Appl. 11(2), 132–138 (2013).
[Crossref]

W. Liang, X. Liu, and Y. Miao, “Large-angle beam splitter with sensitive adjustable power ratio based on superprism effect,” J. Phys. D: Appl. Phys. 46(49), 495109 (2013).
[Crossref]

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, “Super-collimation with high frequency sensitivity in 2d photonic crystals induced by saddle-type van hove singularities,” Opt. Express 21(25), 30140–30147 (2013).
[Crossref]

L. Hao, A. Wu, L. Wei, X. Lin, and F. Gan, “Millimeter-scale and large-angle self-collimation in a photonic crystal composed of silicon nanorods,” IEEE Photonics J. 5(2), 2201306 (2013).
[Crossref]

2012 (2)

2010 (2)

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

2009 (2)

2008 (1)

2007 (1)

T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91(9), 091117 (2007).
[Crossref]

2006 (3)

2005 (4)

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13(26), 10768–10776 (2005).
[Crossref]

B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Select. Areas Commun. 23(7), 1355–1364 (2005).
[Crossref]

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

B. Momeni and A. Adibi, “An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals,” J. Lightwave Technol. 23(3), 1522–1532 (2005).
[Crossref]

2004 (1)

2002 (1)

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
[Crossref]

2001 (1)

1999 (1)

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]

1998 (1)

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]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).

Adibi, A.

Ahmadi, V.

S. Pahlavan and V. Ahmadi, “Novel optical demultiplexer design using oblique boundary in hetero photonic crystals,” IEEE Photonics Technol. Lett. 29(6), 511–514 (2017).
[Crossref]

Akcaalan, O.

M. Gumus, I. H. Giden, O. Akcaalan, M. Turduev, and H. Kurt, “Enhanced superprism effect in symmetry reduced photonic crystals,” Appl. Phys. Lett. 113(13), 131103 (2018).
[Crossref]

Asatsuma, T.

T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91(9), 091117 (2007).
[Crossref]

Askari, M.

Baba, T.

T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91(9), 091117 (2007).
[Crossref]

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13(26), 10768–10776 (2005).
[Crossref]

T. Matsumoto and T. Baba, “Photonic crystal k-vector superprism,” J. Lightwave Technol. 22(3), 917–922 (2004).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
[Crossref]

Bassi, P.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Bernier, D.

Boyd, R. W.

Casale, M.

Cassan, E.

Chen, L.

Chen, W.

W. Liang, W. Chen, M. Yin, and C. Yin, “Highly efficient beam combiner based on the super-collimation effect in photonic crystals with elliptical rods,” J. Opt. 16(6), 065101 (2014).
[Crossref]

Chuang, Y. C.

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

Dong, J. W.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

Dou, Y.

Eggleton, B. J.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Fang, H.

X. Lin, H. Fang, L. Wang, G. P. Wang, and X. Jiang, “Transmissive refractive index sensing based on frequency-sensitive responses of two-dimensional photonic crystals,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Fei, Q.

Fujita, S.

Gan, F.

L. Hao, A. Wu, L. Wei, X. Lin, and F. Gan, “Millimeter-scale and large-angle self-collimation in a photonic crystal composed of silicon nanorods,” IEEE Photonics J. 5(2), 2201306 (2013).
[Crossref]

Gao, B.

Gao, S.

Giden, I. H.

M. Gumus, I. H. Giden, O. Akcaalan, M. Turduev, and H. Kurt, “Enhanced superprism effect in symmetry reduced photonic crystals,” Appl. Phys. Lett. 113(13), 131103 (2018).
[Crossref]

I. H. Giden, M. Turduev, and H. Kurt, “Broadband super-collimation with low-symmetric photonic crystal,” Photon. Nanostruct. Fundam. Appl. 11(2), 132–138 (2013).
[Crossref]

Grillet, C.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Gumus, M.

M. Gumus, I. H. Giden, O. Akcaalan, M. Turduev, and H. Kurt, “Enhanced superprism effect in symmetry reduced photonic crystals,” Appl. Phys. Lett. 113(13), 131103 (2018).
[Crossref]

Hamam, R. E.

Hao, L.

L. Hao, A. Wu, L. Wei, X. Lin, and F. Gan, “Millimeter-scale and large-angle self-collimation in a photonic crystal composed of silicon nanorods,” IEEE Photonics J. 5(2), 2201306 (2013).
[Crossref]

Hosseini, E. S.

Huang, J.

Ibanescu, M.

R. E. Hamam, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Broadband super-collimation in a hybrid photonic crystal structure,” Opt. Express 17(10), 8109–8118 (2009).
[Crossref]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

Jiang, X.

Joannopoulos, J. D.

R. E. Hamam, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Broadband super-collimation in a hybrid photonic crystal structure,” Opt. Express 17(10), 8109–8118 (2009).
[Crossref]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

Johnson, S. G.

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]

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

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]

Kurt, H.

M. Gumus, I. H. Giden, O. Akcaalan, M. Turduev, and H. Kurt, “Enhanced superprism effect in symmetry reduced photonic crystals,” Appl. Phys. Lett. 113(13), 131103 (2018).
[Crossref]

I. H. Giden, M. Turduev, and H. Kurt, “Broadband super-collimation with low-symmetric photonic crystal,” Photon. Nanostruct. Fundam. Appl. 11(2), 132–138 (2013).
[Crossref]

Leng, F. C.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

Leung, K. M.

K. M. Leung, Plane-Wave Calculation of Photonic Band Structure (Springer, 1993).

Li, Q.

Li, W.

Liang, W.

W. Liang, W. Chen, M. Yin, and C. Yin, “Highly efficient beam combiner based on the super-collimation effect in photonic crystals with elliptical rods,” J. Opt. 16(6), 065101 (2014).
[Crossref]

W. Liang, X. Liu, and Y. Miao, “Large-angle beam splitter with sensitive adjustable power ratio based on superprism effect,” J. Phys. D: Appl. Phys. 46(49), 495109 (2013).
[Crossref]

Liang, W. Y.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

Lin, G.

Lin, X.

Liu, J.

Liu, X.

W. Liang, X. Liu, and Y. Miao, “Large-angle beam splitter with sensitive adjustable power ratio based on superprism effect,” J. Phys. D: Appl. Phys. 46(49), 495109 (2013).
[Crossref]

Lupu, A.

Marris-Morini, D.

Martijn de Sterke, C.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Matsumoto, T.

T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91(9), 091117 (2007).
[Crossref]

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13(26), 10768–10776 (2005).
[Crossref]

T. Matsumoto and T. Baba, “Photonic crystal k-vector superprism,” J. Lightwave Technol. 22(3), 917–922 (2004).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
[Crossref]

McPhedran, R. C.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

Miao, Y.

W. Liang, X. Liu, and Y. Miao, “Large-angle beam splitter with sensitive adjustable power ratio based on superprism effect,” J. Phys. D: Appl. Phys. 46(49), 495109 (2013).
[Crossref]

Mohammadi, S.

Momeni, B.

Norton, A.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Notomi, M.

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]

O’Faolain, L.

Pahlavan, S.

S. Pahlavan and V. Ahmadi, “Novel optical demultiplexer design using oblique boundary in hetero photonic crystals,” IEEE Photonics Technol. Lett. 29(6), 511–514 (2017).
[Crossref]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

Rakhshandehroo, M.

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

Roux, X. L.

Ru, G.

Sakoda, K.

K. Sakoda, Optical properties of photonic crystals (Springer, 2005).

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]

Schulz, S. A.

Shi, Z.

Soljacic, M.

Soltani, M.

Steel, M. J.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Suleski, T. J.

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

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]

Tandon, S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

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]

Turduev, M.

M. Gumus, I. H. Giden, O. Akcaalan, M. Turduev, and H. Kurt, “Enhanced superprism effect in symmetry reduced photonic crystals,” Appl. Phys. Lett. 113(13), 131103 (2018).
[Crossref]

I. H. Giden, M. Turduev, and H. Kurt, “Broadband super-collimation with low-symmetric photonic crystal,” Photon. Nanostruct. Fundam. Appl. 11(2), 132–138 (2013).
[Crossref]

Upham, J.

Vivien, L.

Wang, G. P.

X. Lin, H. Fang, L. Wang, G. P. Wang, and X. Jiang, “Transmissive refractive index sensing based on frequency-sensitive responses of two-dimensional photonic crystals,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Wang, H. Z.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

Wang, L.

X. Lin, H. Fang, L. Wang, G. P. Wang, and X. Jiang, “Transmissive refractive index sensing based on frequency-sensitive responses of two-dimensional photonic crystals,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Wang, T. B.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

Wei, L.

L. Hao, A. Wu, L. Wei, X. Lin, and F. Gan, “Millimeter-scale and large-angle self-collimation in a photonic crystal composed of silicon nanorods,” IEEE Photonics J. 5(2), 2201306 (2013).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

Wu, A.

L. Hao, A. Wu, L. Wei, X. Lin, and F. Gan, “Millimeter-scale and large-angle self-collimation in a photonic crystal composed of silicon nanorods,” IEEE Photonics J. 5(2), 2201306 (2013).
[Crossref]

Yao, K.

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).

Yin, C.

W. Liang, W. Chen, M. Yin, and C. Yin, “Highly efficient beam combiner based on the super-collimation effect in photonic crystals with elliptical rods,” J. Opt. 16(6), 065101 (2014).
[Crossref]

Yin, C. P.

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

Yin, M.

W. Liang, W. Chen, M. Yin, and C. Yin, “Highly efficient beam combiner based on the super-collimation effect in photonic crystals with elliptical rods,” J. Opt. 16(6), 065101 (2014).
[Crossref]

Zhang, X.

Zheng, Y.

Zhi-Yuan, L.

Zoli, R.

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

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]

T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91(9), 091117 (2007).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81(13), 2325–2327 (2002).
[Crossref]

M. Gumus, I. H. Giden, O. Akcaalan, M. Turduev, and H. Kurt, “Enhanced superprism effect in symmetry reduced photonic crystals,” Appl. Phys. Lett. 113(13), 131103 (2018).
[Crossref]

IEEE J. Select. Areas Commun. (1)

B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Select. Areas Commun. 23(7), 1355–1364 (2005).
[Crossref]

IEEE Photonics J. (2)

L. Hao, A. Wu, L. Wei, X. Lin, and F. Gan, “Millimeter-scale and large-angle self-collimation in a photonic crystal composed of silicon nanorods,” IEEE Photonics J. 5(2), 2201306 (2013).
[Crossref]

X. Lin, H. Fang, L. Wang, G. P. Wang, and X. Jiang, “Transmissive refractive index sensing based on frequency-sensitive responses of two-dimensional photonic crystals,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (1)

S. Pahlavan and V. Ahmadi, “Novel optical demultiplexer design using oblique boundary in hetero photonic crystals,” IEEE Photonics Technol. Lett. 29(6), 511–514 (2017).
[Crossref]

IEEE Trans. Antennas Propag. (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).

J. Lightwave Technol. (2)

J. Opt. (2)

Y. C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

W. Liang, W. Chen, M. Yin, and C. Yin, “Highly efficient beam combiner based on the super-collimation effect in photonic crystals with elliptical rods,” J. Opt. 16(6), 065101 (2014).
[Crossref]

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

J. Phys. D: Appl. Phys. (2)

W. Y. Liang, T. B. Wang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, “Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods,” J. Phys. D: Appl. Phys. 43(7), 075103 (2010).
[Crossref]

W. Liang, X. Liu, and Y. Miao, “Large-angle beam splitter with sensitive adjustable power ratio based on superprism effect,” J. Phys. D: Appl. Phys. 46(49), 495109 (2013).
[Crossref]

Nat. Mater. (1)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, 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]

Opt. Express (10)

R. E. Hamam, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Broadband super-collimation in a hybrid photonic crystal structure,” Opt. Express 17(10), 8109–8118 (2009).
[Crossref]

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14(6), 2413–2422 (2006).
[Crossref]

B. Momeni, E. S. Hosseini, and A. Adibi, “Planar photonic crystal microspectrometers in silicon-nitride for the visible range,” Opt. Express 17(19), 17060–17069 (2009).
[Crossref]

T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13(26), 10768–10776 (2005).
[Crossref]

D. Bernier, X. L. Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, “Compact, low cross-talk cwdm demultiplexer using photonic crystal superprism,” Opt. Express 16(22), 17209–17214 (2008).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref]

G. Ru, Y. Zheng, J. Liu, and X. Jiang, “Hyper collimation ability of two-dimensional photonic crystals,” Opt. Express 27(9), 11968–11978 (2019).
[Crossref]

B. Gao, Z. Shi, and R. W. Boyd, “Design of flat-band superprism structures for on-chip spectroscopy,” Opt. Express 23(5), 6491–6496 (2015).
[Crossref]

X. Lin, X. Zhang, L. Chen, M. Soljačić, and X. Jiang, “Super-collimation with high frequency sensitivity in 2d photonic crystals induced by saddle-type van hove singularities,” Opt. Express 21(25), 30140–30147 (2013).
[Crossref]

S. Gao, Y. Dou, Q. Li, and X. Jiang, “Tunable photonic crystal lens with high sensitivity of refractive index,” Opt. Express 25(6), 7112–7120 (2017).
[Crossref]

Opt. Lett. (3)

Photon. Nanostruct. Fundam. Appl. (1)

I. H. Giden, M. Turduev, and H. Kurt, “Broadband super-collimation with low-symmetric photonic crystal,” Photon. Nanostruct. Fundam. Appl. 11(2), 132–138 (2013).
[Crossref]

Phys. Rev. B (1)

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. E (1)

M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, “Analytic properties of photonic crystal superprism parameters,” Phys. Rev. E 71(5), 056608 (2005).
[Crossref]

Other (4)

K. M. Leung, Plane-Wave Calculation of Photonic Band Structure (Springer, 1993).

“Eastwave v6.0,” DONGJUN Information Technology Co., Ltd., Shanghai, China. http://www.eastwave.com.cn .

K. Sakoda, Optical properties of photonic crystals (Springer, 2005).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

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Figures (5)

Fig. 1.
Fig. 1. (a) The EFCs of the second band, $H_z$-polarization of the PhC and the corresponding $r$ factor color map in logarithmic scale in the $\vec k$- space. Four colored EFCs correspond to normalized frequencies $0.379$, $0.381$, $0.382$ and $0.3857$. The LSC regions refer to the regions where the $r$ parameter is particularly large. (b) The red EFC in (a) with normalized frequency $0.379$ is extracted as an example and the inflection point on the EFC is labelled. Schematically, the directions and lengths of arrows indicate the group velocity directions of modes and the relative intensities of modes which are excited by the incident beam. (c) The schematic figure for the system of this work. Supposing a Gaussian beam with incident angle $\theta _{in}$, beam waist width $W_0$ and frequency $\omega$ is incident to the interface between vacuum and the PhC, the properties of refracted LSC beams inside the PhC are studied. The refraction angle $\theta _{PC}$ of LSC beams is determined by $k_{y0} = k_{in} sin(\theta _{in})$, where $k_{in}$ is the wave vector showing the direction of the incident Gaussian beam and $k_{y0}$ is the $y$-direction wave vector of the central mode of the incident Gaussian beam. (d) The structure of the rod-in-air type two-dimensional (2D) PhC. Rods are arranged in a rectangular lattice, where $(a,\;b)$ are the lattice constants of the PhC in $(x,\;y)$ directions, respectively. $(K_a,K_b)$ are the reciprocal lattice vectors.
Fig. 2.
Fig. 2. The fitting EFC sections (the black lines) based on our cubic dispersion model for the modes which are excited by incident beams with different beam waist widths which are (a) $W_0=8a$, (b) $W_0=13a$, (c) $W_0=20a$ and (d) $W_0=30a$, respectively. The red line in (a)–(d) is the EFC with the normalized frequency $0.379$ shown in Fig. 1(a). (e) The square fitting errors $(\Delta k_x)^2$ of the Eq. (1) deviating from the original EFC sections for the four cases.
Fig. 3.
Fig. 3. The asymmetric broadening of LSC beams inside the PhC when the Gaussian beams with different beam widths are incident. The size of the PhC is $900a\times 242b$. (a)–(c) The normalized intensity distributions $|H_z(x,\;y)|^2$ in steady-state when incident waist widths are (a) $W_0=8a$, (b) $W_0=13a$ and (c) $W_0=20a$, respectively. (d)–(f) The normalized intensity distributions $|H_z(x=x_1,\;y)|^2$ along $y$-axis for different incident beam widths at the propagation distance of $x_1=360a$. (g)–(i) The normalized intensity distributions $|H_z(x=x_2,\;y)|^2$ along $y$-axis for different incident beam widths at the propagation distance of $x_2=720a$. Both distances are indicated by white dashed lines in (a)–(c), respectively. In (d)–(i), the blue lines are the numerical results from FDTD simulations and the red envelopes are obtained by our theory from the cubic dispersion model. (j) The rotated EFC near the inflection point and the arrows to show the group velocity directions of modes near the inflection point. (k) The normalized intensity distributions $|H_z(x,\;y)|^2$ in steady-state with the incident beam waist width $20a$ when modes away from the inflection point of the EFC $f=0.379 c/a$ are excited.
Fig. 4.
Fig. 4. (a)–(d) The evolution of beam intensity envelopes $|H_z(x=x_i,\;y)|^2$ along the $y$-axis at different propagation distances $x$ from $0$ to $10000a$ with an interval step as $2000a$, for the cases with the incident beam waist widths (a) $W_0=8a$, (b) $W_0=13a$, (c) $W_0=20a$ and (d) $W_0=30a$. (e) The energy percentage of all "shadow beams" and (f) The half width of the "main beam" versus propagation distance $x$ for the cases with incident waist widths $W_0=8a$ (violet), $W_0=13a$ (green), $W_0=20a$ (yellow) and $W_0=30a$ (grey), respectively. The inset in (f) is the zoomed-in panel showing the cross points of the curves at around $4500a$ and $5300a$. And the yellow dotted line in (f) is the evolution of the half beam width when the modes away from the inflection point are excited when $W_0=20a$. In (e) and (f), theoretical results from $x=0$ to $x=10000a$ with an interval step as $200a$ are presented by curves and labelled as "T". And simulation results from $x=0$ to $x=800a$ with an interval step as $200a$ are presented by asterisks and labelled as "S".
Fig. 5.
Fig. 5. (a)–(c) The normalized beam intensity distributions $|H_z(x=x_2,\;y)|^2$ along the $y$-axis at the propagation distance $x_2=720a$ for different frequencies (a) $f=0.379 c/a$, (b) $f=0.381 c/a$ and (c) $f=0.382 c/a$. The FDTD simulation results are shown in blue lines and the theoretical envelope results are shown in red lines. (d) The half width of the "main beam" versus propagation distance $x$ for the cases with incident frequencies $f=0.379 c/a$ (red), $f=0.381 c/a$ (dark blue) and $f=0.382 c/a$ (light blue), respectively. Theoretical results from $x=0$ to $x=10000a$ with an interval step as $200a$ are presented by curves and labelled as "T". And simulation results from $x=0$ to $x=800a$ with an interval step as $200a$ are presented by asterisks and labelled as "S". (e) To compare the EFC sections near the inflection points of the three frequencies, we rotate and shift the EFC sections of the three frequencies and set them together with rules (i) the inflection points of all EFC sections at the origin and (ii) the EFC tangential directions at the inflection points in the $k_y'$ direction.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

k x ( k y ) = γ + β k y + α ( k y k y 0 ) 3 ,
A ( k y ) | x = x 1 = A ( k y ) | x = 0 × exp ( i k x ( k y ) x 1 ) ,
H z ( x , y ) = h z 0 W 0 2 π d k y [ exp ( W 0 2 ( k y k y 0 ) 2 4 + i k x x + i k y y ) ] .

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