Abstract

We show that in plasmonic or metamaterial slab waveguides, it is possible to generate slow non-dispersing wavepackets which undergo neither spatial diffraction nor temporal spreading with no nonlinear effects by forming a type of hybrid wavepacket between slow-light waveguide modes and diffraction-free Airy wavepackets. Three mechanisms are involved in their slowness: the slow-light feature of waveguide modes, the initial launching speed of hybrid wavepackets, and their acceleration along the time domain in a moving frame.

© 2011 Optical Society of America

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  1. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
  2. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
    [CrossRef]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [CrossRef]
  4. G. A. Siviloglou, and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [CrossRef] [PubMed]
  5. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [CrossRef]
  6. H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
    [CrossRef] [PubMed]
  7. P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
    [CrossRef] [PubMed]
  8. M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
    [CrossRef]
  9. A. Salandrino, and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
    [CrossRef] [PubMed]
  10. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
    [CrossRef]
  11. C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
    [CrossRef] [PubMed]
  12. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
    [CrossRef] [PubMed]
  13. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
    [CrossRef] [PubMed]
  14. K.-Y. Kim, “Tunneling-induced temporary light trapping in negative-index-clad slab waveguide,” Jpn. J. Appl. Phys. 47(6), 4843–4845 (2008).
    [CrossRef]
  15. J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
    [CrossRef] [PubMed]
  16. W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
    [CrossRef]
  17. V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010).
    [CrossRef]
  18. A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
    [CrossRef] [PubMed]
  19. K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009).
    [CrossRef]
  20. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, 2001).
  21. I. M. Besieris, and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046605 (2008).
    [CrossRef]
  22. Although we have mainly discussed the slow non-dispersing wavepackets based on metamaterial waveguides, they can also be constructed via the association with other types of slow-light modes such as those in photonic crystal waveguides. Actually, they can be preferred in practice because the propagation loss of slow wavepackets can be significantly reduced. For a comprehensive review, see T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
    [CrossRef]
  23. The speed of the center-of-mass position of the hybrid wavepacket remains invariant. Refer to [3] and M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979) for more details.
    [CrossRef]
  24. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
    [CrossRef] [PubMed]

2010

A. Salandrino, and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[CrossRef] [PubMed]

H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
[CrossRef] [PubMed]

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
[CrossRef] [PubMed]

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
[CrossRef]

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
[CrossRef] [PubMed]

2009

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009).
[CrossRef]

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

2008

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

I. M. Besieris, and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046605 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[CrossRef] [PubMed]

K.-Y. Kim, “Tunneling-induced temporary light trapping in negative-index-clad slab waveguide,” Jpn. J. Appl. Phys. 47(6), 4843–4845 (2008).
[CrossRef]

2007

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef]

G. A. Siviloglou, and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[CrossRef] [PubMed]

2004

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[CrossRef] [PubMed]

2000

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
[CrossRef]

1987

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Asorey, M.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
[CrossRef]

Banyal, R. K.

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
[CrossRef]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

Besieris, I. M.

I. M. Besieris, and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046605 (2008).
[CrossRef]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef]

Casse, B. D. F.

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
[CrossRef]

Chávez-Cerda, S.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
[CrossRef]

Cheng, H.

H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
[CrossRef] [PubMed]

Choi, D.

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[CrossRef] [PubMed]

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(2), 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

A. Salandrino, and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef]

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
[CrossRef] [PubMed]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Facchi, P.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
[CrossRef]

Gramotnev, D. K.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
[CrossRef] [PubMed]

Gutiérrez-Vega, J. C.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
[CrossRef]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Huang, Y. J.

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
[CrossRef]

Hwang, C.-Y.

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[CrossRef] [PubMed]

Iturbe-Castillo, M. D.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000).
[CrossRef]

Kildishev, A. V.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010).
[CrossRef]

Kim, K.-Y.

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
[CrossRef] [PubMed]

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[CrossRef] [PubMed]

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009).
[CrossRef]

K.-Y. Kim, “Tunneling-induced temporary light trapping in negative-index-clad slab waveguide,” Jpn. J. Appl. Phys. 47(6), 4843–4845 (2008).
[CrossRef]

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
[CrossRef] [PubMed]

Koleskik, M.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Lee, B.

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
[CrossRef] [PubMed]

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
[CrossRef] [PubMed]

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009).
[CrossRef]

Lee, I.-M.

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
[CrossRef] [PubMed]

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009).
[CrossRef]

Lee, S.-Y.

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
[CrossRef] [PubMed]

Lu, W. T.

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
[CrossRef]

Man’ko, V. I.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
[CrossRef]

Marmo, G.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
[CrossRef]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Moloney, J. V.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Na, H.

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
[CrossRef] [PubMed]

Park, J.

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
[CrossRef] [PubMed]

Pascazio, S.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (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(2), 103–106 (2010).
[CrossRef]

Salandrino, A.

A. Salandrino, and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

Shaarawi, A. M.

I. M. Besieris, and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046605 (2008).
[CrossRef]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
[CrossRef] [PubMed]

Shalaev, V. M.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010).
[CrossRef]

Siviloglou, G. A.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
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G. A. Siviloglou, and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[CrossRef] [PubMed]

Smolyaninov, I. I.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010).
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Smolyaninova, V. N.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010).
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W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
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Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
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Sudarshan, E. C. G.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
[CrossRef]

Tian, J.

H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
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Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

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(2), 103–106 (2010).
[CrossRef]

Zang, W.

H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
[CrossRef] [PubMed]

Zharov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
[CrossRef] [PubMed]

Zhou, W.

H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett.

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
[CrossRef]

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010).
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K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009).
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A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
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J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
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Nature

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Opt. Express

H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010).
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C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010).
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J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010).
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G. A. Siviloglou, and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[CrossRef] [PubMed]

Phys. Rev. A

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[CrossRef] [PubMed]

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010).
[CrossRef] [PubMed]

Science

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Other

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Although we have mainly discussed the slow non-dispersing wavepackets based on metamaterial waveguides, they can also be constructed via the association with other types of slow-light modes such as those in photonic crystal waveguides. Actually, they can be preferred in practice because the propagation loss of slow wavepackets can be significantly reduced. For a comprehensive review, see T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

The speed of the center-of-mass position of the hybrid wavepacket remains invariant. Refer to [3] and M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979) for more details.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Effective indexes (neff) (a), group velocities (vg) (b), and group velocity dispersions (β2) (c) of TM-polarized dual modes in a negative-index-core waveguide. The solid blue and green dotted lines correspond to the backward and forward modes, respectively, and their exemplary transverse profiles are shown in (a). At f0 = 193.414 THz, we can obtain slow-light modes: a backward mode having neff = −1.8642, vg = c/92.8, β2 = 6.358 × 10−19, and a forward one with neff = 1.7908, vg = c/88.6, β2 = 6.339×10−19. They also have β3 = ∂β2/∂ω = 4.143 × 10−30 and 4.488 × 10−30, respectively.

Fig. 2
Fig. 2

Concept of a slow non-dispersing wavepacket. g(y) denotes the transverse profile of dual slow-light modes at the carrier frequency ω0. (a) and (b) Initial fields for the launching of slow non-dispersing wavepackets associated with backward and forward slow-light modes, respectively.

Fig. 3
Fig. 3

Intensity profiles of slow non-dispersing wavepackets through the waveguide analyzed in Fig. 1. (a)–(c) Propagating profiles of a slow non-dispersing wavepacket associated with the backward mode. (d)–(f) The same as (a)–(c) associated with the forward one. The average speeds of non-dispersing wavepackets in their peak positions are reduced by as much as 0.0045c0 and 0.0040c0, respectively, although vg of the slow-light modes is about 0.011c0 where c0 is the speed of light in a vacuum. Two additional factors contribute to this slowdown: one being the initial launching speed of hybrid wavepackets and the other their acceleration along the time domain in a moving frame (see Fig. 5 for details).

Fig. 4
Fig. 4

(a), (b) Propagating profiles (at z = 0, 10λ0, 20λ0, 30λ0, 40λ0, 50λ0) of temporal Airy wavepackets AT (τ,z) associated with backward and forward slow-light modes, respectively. Note that the transverse direction indicates time in a moving frame (τ) and the acceleration along τ can be interpreted as a slowdown of the local intensity peak of the wavepacket. (c), (d) The same as (a) and (b) for spatial Airy beams AS(x, z) (at z = 0, 10λ0, 30λ0, 50λ0)), in which the acceleration indicates a spatial shift in the local intensity peak of the beam. (e) Spatial trajectories of the slow non-dispersing wavepackets.

Fig. 5
Fig. 5

Further slowdown of vpeak of slow non-dispersing wavepackets (i) by modulating the initial launching speeds of hybrid wavepackets (compare the cases of aT = 0 and aT = 1) and (ii) due to their acceleration as they propagate through the waveguide. Solid blue and green dotted lines correspond to hybrid wavepackets associated with the backward and forward modes, respectively.

Equations (13)

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ϕ = A T ( t , z ) A S ( x , z ) g ( y ) exp [ j ( β 0 z ω 0 t ) ] ,
2 g y 2 + [ ω 0 2 c 2 ɛ ( y ) μ ( y ) β 2 ] g = 0 ,
j A S z + 1 2 β 0 2 A S x 2 = 0 ,
j A T z β 2 2 2 A T τ 2 + j B 3 3 A T τ 3 = 0 ,
A S ( x , z ) = A i [ x x 0 ( z 2 β 0 x 0 2 ) 2 + j a S z β 0 x 0 2 ] × exp [ j ( x + a S 2 x 0 2 x 0 z β 0 x 0 2 1 12 ( z β 0 x 0 2 ) 3 ) ] × exp [ a S x x 0 a S 2 ( z β 0 x 0 2 ) 2 ] ,
A T ( τ , z ) = 1 ( 1 + b Z ) 1 / 3 × A i [ ( T Z 2 / 4 j a T Z ) + b Z ( T a T 2 ) ( 1 + b Z ) 4 / 3 ] × exp [ 6 a T ( 2 T Z 2 ) + j Z ( 6 a T 2 6 T + Z 2 ) 12 ( 1 + b Z ) 2 ] × exp [ b 4 Z a T ( a T 2 + 3 T + a T 2 b Z ) + j 6 Z 2 ( a T 2 T ) 12 ( 1 + b Z ) 2 ] ,
τ = t z v g = α v g z + 1 2 ( β 2 2 2 τ 0 3 ) z 2 1 + B z τ 0 3 ,
z = C ( B t τ 0 3 1 + α v g ) + C 2 ( B t τ 0 3 1 + α v g ) 2 + 2 C t ,
v peak ( t ) = B C τ 0 3 + B C τ 0 3 ( B t τ 0 3 1 + α v g + τ 0 3 B C ) ( B t τ 0 3 1 + α v g + τ 0 3 B C ) 2 + τ 0 3 B C ( 2 1 + α v g τ 0 3 B C ) = B C τ 0 3 [ 1 + s g n ( B t τ 0 3 1 + α v g + τ 0 3 B C ) 1 + τ 0 3 B C ( 2 1 + α v g τ 0 3 B C ) ( B t τ 0 3 1 + α v g + τ 0 3 B C ) 2 ] ,
x = ( a S β x 0 ) z + 1 2 ( 1 2 β 2 x 0 3 ) z 2 θ x z z + 1 2 a x z 2 ,
v peak ( t ) = B C τ 0 3 [ 1 + sgn ( ζ ( t ) ) 1 + 1 ζ 2 ( t ) τ 0 3 B C ( 2 1 + α v g τ 0 3 B C ) ] .
z = 2 τ 0 3 β 2 2 [ 1 + α v g + ( 1 + α v g ) 2 + β 2 2 t τ 0 3 ] ,
v peak ( t ) = [ ( 1 + α v g ) 2 + β 2 2 t τ 0 3 ] 1 / 2 ,

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