Abstract

We design a photonic crystal (PhC) lens whose focal length is highly tunable based on the frequency sensitive super-collimation (FSSC) phenomenon. Theoretically, an analytic expression of the focal length in PhCs is derived. The diffraction could be dramatically changed by modest change in refractive index of the dielectric rods in PhCs, because the sensitivity of the equi-frequency-contours around FSSC to refractive index is several orders larger than that in common bulk material. Numerically, we demonstrate that focal length can be nearly one order larger with only 0.2% refractive index change, from 28a (a is lattice constant) to 240a. With its micro-size, high sensitivity and feasibility by on-chip technology, such tunable lens has great potentials in modern optical systems.

© 2017 Optical Society of America

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References

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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]
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    [Crossref] [PubMed]
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    [Crossref]
  18. D. Hohlfeld and H. Zappe, “An all-dielectric tunable optical filter based on the thermo-optic effect,” J. Opt. A 6(6), 504–511 (2004).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  24. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
    [Crossref] [PubMed]
  25. J. F. Shackelford, “CRC materials science and engineering handbook,” Chem. Eng. 11, 41 (1999).
  26. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
    [Crossref]

2016 (1)

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

2014 (1)

2013 (1)

2012 (1)

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

2011 (1)

Y. Cui, V. A. Tamma, J. B. Lee, and W. Park, “Mechanically tunable negative-index photonic crystal lens,” IEEE Photonics J. 2(6), 1003–1012 (2011).
[Crossref]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

2008 (2)

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

2007 (1)

K. Ren, Z. Y. Li, X. Ren, B. Cheng, and D. Zhang, “Tunable negative refraction by electro-optical control in two-dimensional photonic crystal,” Appl. Phys., A Mater. Sci. Process. 87(2), 181–185 (2007).
[Crossref]

2006 (2)

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]

Q. Wu, E. Schonbrun, and W. Park, “Tunable superlensing by a mechanically controlled photonic crystal,” J. Opt. Soc. Am. B 23(3), 479–484 (2006).
[Crossref]

2005 (2)

M. Tinker and J. B. Lee, “Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency,” Opt. Express 13(18), 7174–7188 (2005).
[Crossref] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

2004 (2)

D. Hohlfeld and H. Zappe, “An all-dielectric tunable optical filter based on the thermo-optic effect,” J. Opt. A 6(6), 504–511 (2004).
[Crossref]

W. Park and J. B. Lee, “Mechanically tunable photonic crystal structure,” Appl. Phys. Lett. 85(21), 4845–4847 (2004).
[Crossref]

2002 (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[Crossref]

2001 (2)

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref] [PubMed]

2000 (1)

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88(12), 7115–7119 (2000).
[Crossref]

1999 (3)

K. Busch and S. John, “Liquid crystal photonic band gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83(5), 967–970 (1999).
[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]

J. F. Shackelford, “CRC materials science and engineering handbook,” Chem. Eng. 11, 41 (1999).

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]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref] [PubMed]

Arlandis, J.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Busch, K.

K. Busch and S. John, “Liquid crystal photonic band gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83(5), 967–970 (1999).
[Crossref]

Campos, J.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Centeno, E.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Chen, L.

Cheng, B.

K. Ren, Z. Y. Li, X. Ren, B. Cheng, and D. Zhang, “Tunable negative refraction by electro-optical control in two-dimensional photonic crystal,” Appl. Phys., A Mater. Sci. Process. 87(2), 181–185 (2007).
[Crossref]

Cocorullo, G.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88(12), 7115–7119 (2000).
[Crossref]

Cui, Y.

Y. Cui, V. A. Tamma, J. B. Lee, and W. Park, “Mechanically tunable negative-index photonic crystal lens,” IEEE Photonics J. 2(6), 1003–1012 (2011).
[Crossref]

Cuypers, D.

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

Dahlem, M.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

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]

De Smet, H.

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

De Smet, J.

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

Della Corte, F. G.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88(12), 7115–7119 (2000).
[Crossref]

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref] [PubMed]

Esposito Montefusco, M.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88(12), 7115–7119 (2000).
[Crossref]

Gauthier-Lafaye, O.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

Hall, K.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

Hohlfeld, D.

D. Hohlfeld and H. Zappe, “An all-dielectric tunable optical filter based on the thermo-optic effect,” J. Opt. A 6(6), 504–511 (2004).
[Crossref]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

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.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

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]

Jiang, X.

Joannopoulos, J.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

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]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[Crossref]

John, S.

K. Busch and S. John, “Liquid crystal photonic band gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83(5), 967–970 (1999).
[Crossref]

Johnson, S.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[Crossref]

Joshi, P.

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

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]

Kesler, M.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

Kolodziejski, L.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

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 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]

Kurs, A.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

Lee, J. B.

Y. Cui, V. A. Tamma, J. B. Lee, and W. Park, “Mechanically tunable negative-index photonic crystal lens,” IEEE Photonics J. 2(6), 1003–1012 (2011).
[Crossref]

M. Tinker and J. B. Lee, “Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency,” Opt. Express 13(18), 7174–7188 (2005).
[Crossref] [PubMed]

W. Park and J. B. Lee, “Mechanically tunable photonic crystal structure,” Appl. Phys. Lett. 85(21), 4845–4847 (2004).
[Crossref]

Li, W.

Li, Z. Y.

K. Ren, Z. Y. Li, X. Ren, B. Cheng, and D. Zhang, “Tunable negative refraction by electro-optical control in two-dimensional photonic crystal,” Appl. Phys., A Mater. Sci. Process. 87(2), 181–185 (2007).
[Crossref]

Lin, X.

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[Crossref]

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

Monmayrant, A.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref] [PubMed]

Moreau, A.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Moretti, L.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88(12), 7115–7119 (2000).
[Crossref]

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

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]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Park, W.

Y. Cui, V. A. Tamma, J. B. Lee, and W. Park, “Mechanically tunable negative-index photonic crystal lens,” IEEE Photonics J. 2(6), 1003–1012 (2011).
[Crossref]

Q. Wu, E. Schonbrun, and W. Park, “Tunable superlensing by a mechanically controlled photonic crystal,” J. Opt. Soc. Am. B 23(3), 479–484 (2006).
[Crossref]

W. Park and J. B. Lee, “Mechanically tunable photonic crystal structure,” Appl. Phys. Lett. 85(21), 4845–4847 (2004).
[Crossref]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[Crossref]

Petrich, G.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

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]

Pollès, R.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[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]

Ren, K.

K. Ren, Z. Y. Li, X. Ren, B. Cheng, and D. Zhang, “Tunable negative refraction by electro-optical control in two-dimensional photonic crystal,” Appl. Phys., A Mater. Sci. Process. 87(2), 181–185 (2007).
[Crossref]

Ren, X.

K. Ren, Z. Y. Li, X. Ren, B. Cheng, and D. Zhang, “Tunable negative refraction by electro-optical control in two-dimensional photonic crystal,” Appl. Phys., A Mater. Sci. Process. 87(2), 181–185 (2007).
[Crossref]

Rendina, I.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88(12), 7115–7119 (2000).
[Crossref]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

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]

Schonbrun, E.

Shackelford, J. F.

J. F. Shackelford, “CRC materials science and engineering handbook,” Chem. Eng. 11, 41 (1999).

Shang, X.

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

Shih, T. M.

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref] [PubMed]

Soljacic, M.

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] [PubMed]

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

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]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[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]

Tamma, V. A.

Y. Cui, V. A. Tamma, J. B. Lee, and W. Park, “Mechanically tunable negative-index photonic crystal lens,” IEEE Photonics J. 2(6), 1003–1012 (2011).
[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]

Tinker, M.

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]

Trinidad, A. M.

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

Wu, Q.

Zappe, H.

D. Hohlfeld and H. Zappe, “An all-dielectric tunable optical filter based on the thermo-optic effect,” J. Opt. A 6(6), 504–511 (2004).
[Crossref]

Zhang, D.

K. Ren, Z. Y. Li, X. Ren, B. Cheng, and D. Zhang, “Tunable negative refraction by electro-optical control in two-dimensional photonic crystal,” Appl. Phys., A Mater. Sci. Process. 87(2), 181–185 (2007).
[Crossref]

Zhang, X.

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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (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]

T. M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljačić, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93(13), 131111 (2008).
[Crossref]

W. Park and J. B. Lee, “Mechanically tunable photonic crystal structure,” Appl. Phys. Lett. 85(21), 4845–4847 (2004).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (1)

K. Ren, Z. Y. Li, X. Ren, B. Cheng, and D. Zhang, “Tunable negative refraction by electro-optical control in two-dimensional photonic crystal,” Appl. Phys., A Mater. Sci. Process. 87(2), 181–185 (2007).
[Crossref]

Chem. Eng. (1)

J. F. Shackelford, “CRC materials science and engineering handbook,” Chem. Eng. 11, 41 (1999).

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method ☆,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

IEEE Photonics J. (2)

Y. Cui, V. A. Tamma, J. B. Lee, and W. Park, “Mechanically tunable negative-index photonic crystal lens,” IEEE Photonics J. 2(6), 1003–1012 (2011).
[Crossref]

X. Shang, A. M. Trinidad, P. Joshi, J. De Smet, D. Cuypers, and H. De Smet, “Tunable optical beam deflection via liquid crystal gradient refractive index generated by highly resistive polymer film,” IEEE Photonics J. 8(3), 1 (2016).
[Crossref]

J. Appl. Phys. (1)

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88(12), 7115–7119 (2000).
[Crossref]

J. Opt. A (1)

D. Hohlfeld and H. Zappe, “An all-dielectric tunable optical filter based on the thermo-optic effect,” J. Opt. A 6(6), 504–511 (2004).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Mater. (1)

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]

Nat. Photonics (1)

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (2)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[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. E Stat. Nonlin. Soft Matter Phys. (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 Stat. Nonlin. Soft Matter Phys. 71(5), 056608 (2005).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

K. Busch and S. John, “Liquid crystal photonic band gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83(5), 967–970 (1999).
[Crossref]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref] [PubMed]

Other (3)

H. Fang, X. Lin, Y. Long, S. Gao, and X. Jiang, ” Experimental demonstration of super-collimation with high frequency sensitivity in a photonics crystal slab,” to be published.

J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

K. Sakoda, Optical Properties of Photonic Crystals, 2nd ed. (Springer, 2005).

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Figures (6)

Fig. 1
Fig. 1

(a) EFCs of the 2D rectangle lattice PhC in the second band with H polarization: the refractive index n = 3.4, the radius of rods r = 0.3a and the lattice aspect ratio β = b/a = 2.0; (b) the relationship between κ 0 and the frequency ω in PhC, air and silicon, respectively.

Fig. 2
Fig. 2

(a) The SC index sensitivity for silicon rods 2D PhCs with different radii r and aspect ratio β. The unit of η is a/2π . The SC frequency is degenerate on the left side of the dash line and nondegenerate on the right side. (b) log 10 κ 0 ω | ω SC for silicon rods 2D PhCs with different radii r and aspect ratio β; (c) log 10 | ω n | ω SC | for silicon rods 2D PhCs with different radii r and aspect ratio β .(d) and (e) The EFCs corresponding to the two points:①r = 0.34a,β = 1.5; ②r = 0.31a,β = 1.7.

Fig. 3
Fig. 3

(a) The SC index sensitivity for germanium rods 2D PhCs with different radius r and aspect ratio β and the unit of η is a/2π . The SC frequency is degenerate on the left side of the dash line and nondegenerate on the right side. (b) The EFCs corresponding to the point ①:r = 0.27a, β = 1.2.

Fig. 4
Fig. 4

(a)The schematic diagram of FDTD simulation; (b)-(d) the monochromatic beams propagating in three different PhCs whose refractive indices of the cylinders are (b) n = 3.988; (c) n = 3.992; (d) n = 3.996, respectively.

Fig. 5
Fig. 5

The envelope of Hz distribution along y axes at (a) x = 28a; (b) x = 58a.

Fig. 6
Fig. 6

The tunable focal length. The stars are the results of the FDTD simulation and the solid line are the result of PWEM theory in section 2 while red and blue corresponding to ω 1 =0.363 2πc a and ω 2 =0.3642 2πc a , respectively.

Equations (6)

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

H z (0,y)= H z0 exp( i2π y 2 Ra y 2 W 0 2 ),
H z ( k y )=F{ H z (y)}= H z0 2( 2πi Ra + 1 W 0 2 ) exp( Ra W 0 2 4(Ra2πi W 0 2 ) k y 2 ).
H z (x,y)= F 1 { H z ( k y )exp(iϕ) },
ϕ= k x x+ k y y=( k x0 + κ 0 2 k y 2 )x+ k y y.
W(x)= (4 κ 0 2 ( W 0 4 + (Ra/2π) 2 x 2 4 κ 0 (Ra/2π) W 0 4 x 0 + (Ra/2π) 2 W 0 4 ) (Ra/2π) W 0 .
η=| κ 0 n | ω ω SC |=| κ 0 ω | ω ω SC × ω n | ω SC |.

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