Abstract

We propose a two dimensional (2D) photonic crystal (PhC) structure that supports super-collimation over a large frequency range (over 4 times that of a traditional square lattice of holes). We theoretically and numerically investigate the collimation mechanism in our 2D structure, in comparison to that of two other frequently used related PhC structures. We also point out the potential importance of our proposed structure in the design of super-collimation-based devices for both monochromatic and polychromatic light.

© 2009 Optical Society of America

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, second edition (Princeton University Press, 2008).
  2. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
    [Crossref]
  3. P. St. J. Russella, S. Tredwella, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
    [Crossref]
  4. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phy. A: Materials Science & Processing 68, 25–28 (1999).
    [Crossref]
  5. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
    [Crossref]
  6. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
    [Crossref]
  7. E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  8. C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
    [Crossref]
  9. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
    [Crossref]
  10. M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
    [Crossref]
  11. M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Appl. Phys. Lett. 86, 171101 (2005).
    [Crossref]
  12. D. L. C. Chan, M. Soljacčić, and J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs”, Opt. Express 14, 8785 (2006).
    [Crossref] [PubMed]
  13. 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, 1212–1214 (1999).
    [Crossref]
  14. L. Wu, M. Mazilu, and T. F. Krauss, “Beam Steering in Planar-Photonic Crystals:From Superprism to Supercollimator,” J. Lightwave Technol. 21, 561–566 (2003).
    [Crossref]
  15. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).
  16. J. Shin and S. Fan, “Conditions for self-collimation in three-dimensional photonic crystals,” Opt. Lett. 30, 2397–2399 (2005).
    [Crossref] [PubMed]
  17. P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
    [Crossref]
  18. T.-M. Shih, A. Kurs, M. Dahlem, G. Petrich, M. Soljacic, E. Ippen, L. Kolodziejski, K. Hall, and M. Kesler, “Supercollimation in photonic crystals composed of silicon rods,” Appl. Phys. Lett. 93, 131111 (2008).
    [Crossref]
  19. D. Chigrin, S. Enoch, C. S. Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003).
    [Crossref] [PubMed]
  20. Ashcroft & Mermin, Solid State Physics (Saunders College, 1976).
  21. M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
    [Crossref]
  22. As explained in [21], one could embed a slab of our proposed 2D PhC into a 3D PhC having a complete photonic bandgap, and design things in such a way that the extended frequency range supporting supercollimation falls inside the complete bandgap of the 3D PhC. This would prevent radiation losses from the ‘slab version’ of our proposed 2D PhC structure.
  23. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
    [Crossref] [PubMed]
  24. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref] [PubMed]
  25. T. Rowan, “Functional Stability Analysis of Numerical Algorithms,” Ph.D. thesis, Department of Computer Science, University of Texas at Austin, (1990).
  26. C. Luo, M. Soljacic, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29, 745747 (2004).
    [Crossref]

2008 (1)

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

2006 (2)

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

D. L. C. Chan, M. Soljacčić, and J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs”, Opt. Express 14, 8785 (2006).
[Crossref] [PubMed]

2005 (2)

J. Shin and S. Fan, “Conditions for self-collimation in three-dimensional photonic crystals,” Opt. Lett. 30, 2397–2399 (2005).
[Crossref] [PubMed]

M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Appl. Phys. Lett. 86, 171101 (2005).
[Crossref]

2004 (3)

C. Luo, M. Soljacic, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29, 745747 (2004).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[Crossref]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

2003 (3)

2002 (1)

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

2001 (2)

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[Crossref]

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

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, 1212–1214 (1999).
[Crossref]

P. St. J. Russella, S. Tredwella, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[Crossref]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phy. A: Materials Science & Processing 68, 25–28 (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, R10096–R10099 (1998).
[Crossref]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[Crossref]

1997 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[Crossref]

1994 (1)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

1987 (1)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Alerhand, O. L.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

Chan, D. L. C.

Chen, C.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

Chigrin, D.

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phy. A: Materials Science & Processing 68, 25–28 (1999).
[Crossref]

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[Crossref] [PubMed]

Dahlem, M.

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

Dahlem, M. S

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Devenyi, A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

Enoch, S.

Fan, S.

J. Shin and S. Fan, “Conditions for self-collimation in three-dimensional photonic crystals,” Opt. Lett. 30, 2397–2399 (2005).
[Crossref] [PubMed]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[Crossref]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[Crossref]

Fink, Y.

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phy. A: Materials Science & Processing 68, 25–28 (1999).
[Crossref]

Hall, K.

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

Hau, L. V.

M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Appl. Phys. Lett. 86, 171101 (2005).
[Crossref]

Ibanescu, M.

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Ippen, E.

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

Ippen, Erich P.

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Joannopoulos, J. D.

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

D. L. C. Chan, M. Soljacčić, and J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs”, Opt. Express 14, 8785 (2006).
[Crossref] [PubMed]

M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Appl. Phys. Lett. 86, 171101 (2005).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[Crossref]

C. Luo, M. Soljacic, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29, 745747 (2004).
[Crossref]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[Crossref]

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

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[Crossref]

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

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

Johnson, S. G.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

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

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[Crossref]

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

Kash, K.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[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, 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, R10096–R10099 (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, 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, R10096–R10099 (1998).
[Crossref]

Kesler, M.

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

Kolodziejski, L.

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

Kolodziejski, Leslie A.

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 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, 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, R10096–R10099 (1998).
[Crossref]

Krauss, T. F.

Kurs, A.

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

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phy. A: Materials Science & Processing 68, 25–28 (1999).
[Crossref]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[Crossref] [PubMed]

Lidorikis, E.

M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Appl. Phys. Lett. 86, 171101 (2005).
[Crossref]

Luo, C.

C. Luo, M. Soljacic, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29, 745747 (2004).
[Crossref]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

Mazilu, M.

Meade, R. D.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

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

Murakowski, J.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

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, 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, R10096–R10099 (1998).
[Crossref]

Petrich, G.

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

Petrich, G. S.

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[Crossref]

Prather, D. W.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

Pustai, D. M.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

Rakich, P. T.

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Roberts, P. J.

P. St. J. Russella, S. Tredwella, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[Crossref]

Rowan, T.

T. Rowan, “Functional Stability Analysis of Numerical Algorithms,” Ph.D. thesis, Department of Computer Science, University of Texas at Austin, (1990).

Russella, P. St. J.

P. St. J. Russella, S. Tredwella, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[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, 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, R10096–R10099 (1998).
[Crossref]

Schneider, G. J.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

Schubert, E. F.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[Crossref]

Sharkawy, A.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

Shi, S.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

Shih, T.-M.

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

Shin, J.

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[Crossref] [PubMed]

Smith, D. A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

Soljaccic, M.

Soljacic, M.

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

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Appl. Phys. Lett. 86, 171101 (2005).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[Crossref]

C. Luo, M. Soljacic, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Opt. Lett. 29, 745747 (2004).
[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, 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, R10096–R10099 (1998).
[Crossref]

Tandon, S.

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

Tayeb, G.

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, 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, R10096–R10099 (1998).
[Crossref]

Torres, C. S.

Tredwella, S.

P. St. J. Russella, S. Tredwella, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[Crossref]

Venkataraman, S.

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Express 29, 50–52 (2004).

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[Crossref]

Winn, J. N.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[Crossref]

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

Wu, L.

Yablonovitch, E.

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phy. A: Materials Science & Processing 68, 25–28 (1999).
[Crossref]

Appl. Phy. A: Materials Science & Processing (1)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phy. A: Materials Science & Processing 68, 25–28 (1999).
[Crossref]

Appl. Phys. Lett. (4)

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Appl. Phys. Lett. 86, 171101 (2005).
[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, 1212–1214 (1999).
[Crossref]

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

J. Appl. Phys. (1)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavlties,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

J. Lightwave Technol. (1)

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[Crossref] [PubMed]

Nature Mater. (2)

P. T. Rakich, M. S Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, Leslie A. Kolodziejski, and Erich P. Ippen, “Achieving centimetre scale super collimation in a large area 2D photonic crystal,” Nature Mater. 5, 93–96 (2006).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[Crossref]

Opt. Commun. (1)

P. St. J. Russella, S. Tredwella, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (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, R10096–R10099 (1998).
[Crossref]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[Crossref]

Phys. Rev. Lett. (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[Crossref]

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Other (4)

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

As explained in [21], one could embed a slab of our proposed 2D PhC into a 3D PhC having a complete photonic bandgap, and design things in such a way that the extended frequency range supporting supercollimation falls inside the complete bandgap of the 3D PhC. This would prevent radiation losses from the ‘slab version’ of our proposed 2D PhC structure.

Ashcroft & Mermin, Solid State Physics (Saunders College, 1976).

T. Rowan, “Functional Stability Analysis of Numerical Algorithms,” Ph.D. thesis, Department of Computer Science, University of Texas at Austin, (1990).

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Figures (3)

Fig. 1.
Fig. 1.

Two “often-used” low-diffraction structures. (a) Profile of the refractive index of a 2D holes-in-dielectric structure, with the dielectric having n = 3.5, and the holes having radius r = 0.421a′, where a′ is the nearest-neighbor center-to-center separation between holes (the square lattice spacing). Note that the holes form a square lattice. (b) Color contour plot of the frequency of the first TE band for the structure shown in Fig. 1(a). (c) Profile of the refractive index for a waveguide array structure, with the waveguide having refractive index n = 3.5. (d) Projected band diagram of the first TM band for the waveguide array with t = 0.2a. (e) Color contour plot of the frequency of the first TM band for the waveguide array with t = 0.2a.

Fig. 2.
Fig. 2.

Proposed 2D PhC structure (a) Schematic of the refractive index: the rods, of radius r, and waveguides, of thickness t, (shown in green) both have n = 3.5, and are surrounded by air (n = 1). The rods form a square lattice, with lattice constant a, and the waveguides are halfway (on the y-axis) between the rods. (b) Projected band diagram of lowest four TM bands for r = 0.16; and t = 0.2a. (c) Color contour plot of the frequency of the fourth TM band.

Fig. 3.
Fig. 3.

Intensity profile of the propagating beam (of angular frequency 0.495 (2πc/a), and physical width corresponding to σky = 0.12(2π/a)) as a function of y(a), at x = 0 (in blue) and at i = 500a (in red), in (a) Our proposed PhC structure shown in Fig. 2, (b) The 2D holes structure shown in Fig. 1(a), but with lattice constant a′ = (0.2124/0.495)a, where a is the lattice constant in our proposed structure and in the waveguide array structures, (c) The waveguide array structure with t = 0.2a. Note that the spikes in (a) and (c) correspond to the positions of the “waveguide” strips.

Equations (3)

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

ω4TM(kx,ky)=ω4TM(kx,0)+α4TM(kx)·(ky)2+β4TM(kx)·(ky)4+
Ez(x,y,t)=eiωt kyvaluesonCFCoffreq.ω d ky e(ky)2/2(σky)2 E(kx,ky)n=4(x,y)eiωt A (x,y)
ω1TE(kx,ky)=ω1TE(kx,0)+α1TE(kx)·(ky)2+β1TE(kx)·(ky)4+

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