Abstract

We propose a simple, fast, and accurate method to design complex layered photonic crystal structures that exhibit mesoscopic self-collimation. We apply this method to the control of the overall reflectivity of such structures, and we numerically demonstrate high-transmissivity (>99%) self-collimating waveguides and high-reflectivity (>99%) self-collimating Bragg mirrors.

© 2014 Optical Society of America

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  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, 1212–1214 (1999).
    [CrossRef]
  2. D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
    [CrossRef]
  3. R. C. Rumpf and J. J. Pazos, “Optimization of planar self-collimating photonic crystals,” J. Opt. Soc. Am. A 30, 1297–1304 (2013).
    [CrossRef]
  4. 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, 037401 (2012).
    [CrossRef]
  5. T. Matsumoto, K.-S. Eom, and T. Baba, “Focusing of light by negative refraction in a photonic crystal slab superlens on silicon-on-insulator substrate,” Opt. Lett. 31, 2786–2788 (2006).
    [CrossRef]
  6. T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005).
    [CrossRef]
  7. 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, 93–96 (2006).
    [CrossRef]
  8. V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
    [CrossRef]
  9. Y.-C. Chuang and T. J. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12, 035102 (2010).
    [CrossRef]
  10. X. Shen, T.-J. Cui, and J. Ye., “Anti-reflection for self-collimated beams using graded index coupler,” in Symposium on Photonics and Optoelectronics (SOPO) (IEEE, 2011), pp. 1–4.
  11. 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]
  12. 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,” Comp. Phys. Commun. 181, 687–702 (2010).
    [CrossRef]

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, 037401 (2012).
[CrossRef]

2010 (2)

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

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,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

2009 (1)

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

2007 (1)

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

2006 (2)

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, 93–96 (2006).
[CrossRef]

T. Matsumoto, K.-S. Eom, and T. Baba, “Focusing of light by negative refraction in a photonic crystal slab superlens on silicon-on-insulator substrate,” Opt. Lett. 31, 2786–2788 (2006).
[CrossRef]

2005 (1)

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, 1212–1214 (1999).
[CrossRef]

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, 037401 (2012).
[CrossRef]

Baba, T.

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,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Cabrini, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[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, 037401 (2012).
[CrossRef]

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, 037401 (2012).
[CrossRef]

Chang, A. S. P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Chen, C.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[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, 035102 (2010).
[CrossRef]

Cui, T.-J.

X. Shen, T.-J. Cui, and J. Ye., “Anti-reflection for self-collimated beams using graded index coupler,” in Symposium on Photonics and Optoelectronics (SOPO) (IEEE, 2011), pp. 1–4.

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, 93–96 (2006).
[CrossRef]

Dardano, P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Dhuey, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Eom, K.-S.

Fujita, S.

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, 037401 (2012).
[CrossRef]

Harteneck, B.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[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,” Comp. Phys. Commun. 181, 687–702 (2010).
[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, 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, 93–96 (2006).
[CrossRef]

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,” Comp. Phys. Commun. 181, 687–702 (2010).
[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, 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, 173–190 (2001).
[CrossRef]

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,” Comp. Phys. Commun. 181, 687–702 (2010).
[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]

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]

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]

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, 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]

Martin, R.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

Matsumoto, T.

Miao, B. L.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

Mocella, V.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

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, 037401 (2012).
[CrossRef]

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, 037401 (2012).
[CrossRef]

Moretti, L.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

Murakowski, J.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[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, 1212–1214 (1999).
[CrossRef]

Olynick, D.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[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,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Pazos, J. J.

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, 93–96 (2006).
[CrossRef]

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, 037401 (2012).
[CrossRef]

Prather, D. W.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

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, 93–96 (2006).
[CrossRef]

Rendina, I.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[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,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Rumpf, R. C.

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]

Schneider, G. J.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

Sharkawy, A.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

Shen, X.

X. Shen, T.-J. Cui, and J. Ye., “Anti-reflection for self-collimated beams using graded index coupler,” in Symposium on Photonics and Optoelectronics (SOPO) (IEEE, 2011), pp. 1–4.

Shi, S.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[CrossRef]

Soljacic, M.

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, 93–96 (2006).
[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, 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, 1212–1214 (1999).
[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, 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, 1212–1214 (1999).
[CrossRef]

Ye., J.

X. Shen, T.-J. Cui, and J. Ye., “Anti-reflection for self-collimated beams using graded index coupler,” in Symposium on Photonics and Optoelectronics (SOPO) (IEEE, 2011), pp. 1–4.

Appl. Phys. Lett. (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, 1212–1214 (1999).
[CrossRef]

Comp. 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,” Comp. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

J. Opt. (1)

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

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

J. Phys. D (1)

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635–2651 (2007).
[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, 93–96 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902 (2009).
[CrossRef]

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, 037401 (2012).
[CrossRef]

Other (1)

X. Shen, T.-J. Cui, and J. Ye., “Anti-reflection for self-collimated beams using graded index coupler,” in Symposium on Photonics and Optoelectronics (SOPO) (IEEE, 2011), pp. 1–4.

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Figures (6)

Fig. 1.
Fig. 1.

Principle mesoscopic self-collimation: slabs of high-index material (refractive index nbulk) alternate with slabs of PhC that compensate lateral spreading of the beam.

Fig. 2.
Fig. 2.

(a) Phase n and (b) curvature nc indices for a square-lattice PhC [see inset in (a)].

Fig. 3.
Fig. 3.

FDTD pulsed simulations (AR): (a) source (gray), transmission (green) and reflection (red) intensities and (b) waist of the source (gray) and of the transmitted beam (green) as a function of the frequency.

Fig. 4.
Fig. 4.

FDTD CW simulations at the optimum frequency uA1 for the AR design. (a) Energy profile of the gaussian beam. (b) Evolution with the propagation of the waist with (green) and without (black) the structure. (c) Transverse profile of the source (gray), the transmitted (green) and reflected beams (red).

Fig. 5.
Fig. 5.

FDTD pulsed simulations (HR). (a) Source (gray), transmission (green), and reflection (red) spectra. (b) Waist evolution with frequency for the source (gray) and reflected beam (red).

Fig. 6.
Fig. 6.

FDTD CW simulations for the HR design. (a) Energy profile of the continuous Gaussian beam at a frequency uH1. (b) Transverse profile of the source (gray), the transmitted (green), and reflected beams (red). (c) Evolution with distance inside the structure of the total energy (gray) and the total energy smoothed over one period of the structure (black).

Equations (2)

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d1nc(u)+d2nbulk=0,
d1×n(u)=mλ/4=ma/(4u)d2×nbulk=pλ/4=pa/(4u),

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