Abstract

We report the propagation of self-collimated ultrashort Gaussian pulses in a hybrid photonic crystal structure, in which broadband super-collimation was proposed recently. To choose their center frequencies, we compute group velocity dispersion and third-order dispersion as a function of frequency. Using the finite-difference time-domain method, we simulate the propagation of the pulses at two frequencies, one for zero group-velocity-dispersion and the other for optimized super-collimation. It is shown that the pulses nearly retain their transverse and longitudinal shapes during propagation over a long distance, and that third-order dispersion affects the pulse shape at zero group-velocity-dispersion frequency.

© 2011 OSA

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    [CrossRef]
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  4. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. Y. Loiko, R. Herrero, and K. Staliunas, “Ultrashort light pulses in photonic crystals in subdiffractive regimes,” J. Opt. Soc. Am. B 24, 1639–1645 (2007).
    [CrossRef]
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    [CrossRef]
  25. C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
    [CrossRef]
  26. 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]
  27. 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, 687–702 (2010).
    [CrossRef]

2010 (3)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (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,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

2009 (2)

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, 8109–8118 (2009).
[CrossRef] [PubMed]

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] [PubMed]

2008 (1)

C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
[CrossRef]

2007 (3)

Y. Loiko, R. Herrero, and K. Staliunas, “Ultrashort light pulses in photonic crystals in subdiffractive regimes,” J. Opt. Soc. Am. B 24, 1639–1645 (2007).
[CrossRef]

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

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

2006 (4)

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

A. Kim, K. B. Chung, and J. W. Wu, “Control of self-collimated Bloch waves by partially flat equifrequency contours in photonic crystals,” Appl. Phys. Lett. 89, 251120 (2006).
[CrossRef]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

2005 (3)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

S. Longhi, “Localized and nonspreading spatiotemporal Wannier wave packets in photonic crystals,” Phys. Rev. E 71, 016603 (2005).
[CrossRef]

O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. 30, 2611–2613 (2005).
[CrossRef] [PubMed]

2004 (3)

S. Longhi and D. Janner, “X-shaped waves in photonic crystals,” Phys. Rev. B 70, 235123 (2004).
[CrossRef]

D. N. Christodoulides, N. K. Efremidis, P. D. Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett. 29, 1446–1448 (2004).
[CrossRef] [PubMed]

S. Longhi, D. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclass. Opt. 6, 477 (2004).
[CrossRef]

2003 (2)

D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

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]

1997 (1)

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[CrossRef]

1992 (1)

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19–31 (1992).
[CrossRef]

1990 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[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, 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] [PubMed]

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] [PubMed]

Chen, C.

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

Chigrin, D. N.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

Chung, K. B.

A. Kim, K. B. Chung, and J. W. Wu, “Control of self-collimated Bloch waves by partially flat equifrequency contours in photonic crystals,” Appl. Phys. Lett. 89, 251120 (2006).
[CrossRef]

Cojocaru, C.

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Colman, P.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Combrié, S.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Conti, C.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

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] [PubMed]

De Rossi, A.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[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] [PubMed]

Di Trapani, P.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Efremidis, N. K.

Enoch, S.

Faccio, D.

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

Gong, Q.

C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
[CrossRef]

Greenleaf, J. F.

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19–31 (1992).
[CrossRef]

Hamam, R. E.

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] [PubMed]

Herrero, R.

Y. Loiko, R. Herrero, and K. Staliunas, “Ultrashort light pulses in photonic crystals in subdiffractive regimes,” J. Opt. Soc. Am. B 24, 1639–1645 (2007).
[CrossRef]

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Husko, C.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[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, 687–702 (2010).
[CrossRef]

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, 8109–8118 (2009).
[CrossRef] [PubMed]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

Janner, D.

S. Longhi and D. Janner, “X-shaped waves in photonic crystals,” Phys. Rev. B 70, 235123 (2004).
[CrossRef]

S. Longhi, D. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclass. Opt. 6, 477 (2004).
[CrossRef]

Jedrkiewicz, O.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Jiang, X.

C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
[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,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

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, 8109–8118 (2009).
[CrossRef] [PubMed]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

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]

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, 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]

Kim, A.

A. Kim, K. B. Chung, and J. W. Wu, “Control of self-collimated Bloch waves by partially flat equifrequency contours in photonic crystals,” Appl. Phys. Lett. 89, 251120 (2006).
[CrossRef]

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [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, 1212–1214 (1999).
[CrossRef]

Laporta, P.

S. Longhi, D. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclass. Opt. 6, 477 (2004).
[CrossRef]

Loiko, Y.

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

Y. Loiko, R. Herrero, and K. Staliunas, “Ultrashort light pulses in photonic crystals in subdiffractive regimes,” J. Opt. Soc. Am. B 24, 1639–1645 (2007).
[CrossRef]

Longhi, S.

S. Longhi, “Localized and nonspreading spatiotemporal Wannier wave packets in photonic crystals,” Phys. Rev. E 71, 016603 (2005).
[CrossRef]

S. Longhi and D. Janner, “X-shaped waves in photonic crystals,” Phys. Rev. B 70, 235123 (2004).
[CrossRef]

S. Longhi, D. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclass. Opt. 6, 477 (2004).
[CrossRef]

Lu, J.-Y.

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19–31 (1992).
[CrossRef]

Malomed, B. A.

Manela, O.

Martin, R.

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

Miao, B.

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

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Mihalache, D.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[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] [PubMed]

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] [PubMed]

Murakowski, J.

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

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, 687–702 (2010).
[CrossRef]

Pertsch, T.

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Prather, D. W.

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

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

Reivelt, K.

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[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] [PubMed]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[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, 687–702 (2010).
[CrossRef]

Saari, P.

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[CrossRef]

Sagnes, I.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (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, 1212–1214 (1999).
[CrossRef]

Schneider, G. J.

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

Segev, M.

Serrat, C.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Sharkawy, A.

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

Shi, S.

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

Silberberg, Y.

Sirutkaitis, V.

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

Soljacic, 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, 8109–8118 (2009).
[CrossRef] [PubMed]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

Sotomayor Torres, C. M.

Staliunas, K.

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

Y. Loiko, R. Herrero, and K. Staliunas, “Ultrashort light pulses in photonic crystals in subdiffractive regimes,” J. Opt. Soc. Am. B 24, 1639–1645 (2007).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[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. Soljačić, 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] [PubMed]

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]

Torner, L.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

Trapani, P. D.

Trillo, S.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Trull, J.

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

Wong, C. W.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Wu, J. W.

A. Kim, K. B. Chung, and J. W. Wu, “Control of self-collimated Bloch waves by partially flat equifrequency contours in photonic crystals,” Appl. Phys. Lett. 89, 251120 (2006).
[CrossRef]

Yao, P.

C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
[CrossRef]

Zhao, D.

C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
[CrossRef]

Zhou, C.

C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
[CrossRef]

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, 1212–1214 (1999).
[CrossRef]

A. Kim, K. B. Chung, and J. W. Wu, “Control of self-collimated Bloch waves by partially flat equifrequency contours in photonic crystals,” Appl. Phys. Lett. 89, 251120 (2006).
[CrossRef]

C. Zhou, Q. Gong, P. Yao, D. Zhao, and X. Jiang, “Bulletlike light pulses in photonic crystals,” Appl. Phys. Lett. 93, 061103 (2008).
[CrossRef]

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, 687–702 (2010).
[CrossRef]

IEEE Trans. Ultrason. Ferroelec. Freq. Contr. (1)

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19–31 (1992).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (2)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

S. Longhi, D. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B: Quantum Semiclass. Opt. 6, 477 (2004).
[CrossRef]

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

J. Phys. D: Appl. Phys. (1)

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

Nat. Mater. (1)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, 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] [PubMed]

Nat. Photonics (2)

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

Opt. Commun. (1)

Y. Loiko, K. Staliunas, R. Herrero, C. Cojocaru, J. Trull, V. Sirutkaitis, D. Faccio, and T. Pertsch, “Towards observation of sub-diffractive pulse propagation in photonic crystals,” Opt. Commun. 279, 377–383 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. B (1)

S. Longhi and D. Janner, “X-shaped waves in photonic crystals,” Phys. Rev. B 70, 235123 (2004).
[CrossRef]

Phys. Rev. E (3)

S. Longhi, “Localized and nonspreading spatiotemporal Wannier wave packets in photonic crystals,” Phys. Rev. E 71, 016603 (2005).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

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] [PubMed]

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the refractive index distribution of a hybrid photonic crystal structure containing rods of radius r = 0.16a and waveguides of thickness t = 0.2a, both with refractive index n = 3.5 surrounded by air of n = 1. The red square is a unit cell of lattice constant a. Waves propagate along the positive x direction. (b) Equi-frequency contour plot for the fourth TM band. The numbers on the curves represent frequencies in units of 2πc/a with c being the speed of light in air.

Fig. 2
Fig. 2

Group velocity dispersion and third-order dispersion as a function of frequency.

Fig. 3
Fig. 3

Electric field distributions in portions of the computational domain at fixed instances of time (red for positive and blue for negative values): (a) and (b) for ω 0 = 0.473(2πc/a); (c) and (d) for ω 0 = 0.495(2πc/a).

Fig. 4
Fig. 4

Variation of (a) width and (b) length with propagation distance. The black curves are for ω 0 = 0.473(2πc/a), and the blue ones for ω 0 = 0.495(2πc/a)

Fig. 5
Fig. 5

Transverse field profiles for: (a) Fig. 3(a) (red dotted line) and Fig. 3(b) (green solid line); (b) Fig. 3(c) (red dotted line) and Fig. 3(d) (blue solid line).

Fig. 6
Fig. 6

Longitudinal field profiles for: (a) Fig. 3(b) and (b) Fig. 3(d).

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