Abstract

We experimentally study the fields close to an interface between two photonic crystal waveguides that have different dispersion properties. After the transition from a waveguide in which the group velocity of light is vgc/10 to a waveguide in which it is vgc/100, we observe a gradual increase in the field intensity and the lateral spreading of the mode. We attribute this evolution to the existence of a weakly evanescent mode that exponentially decays away from the interface. We compare this to the situation where the transition between the waveguides only leads to a minor change in group velocity and show that, in that case, the evolution is absent. Furthermore, we apply novel numerical mode extraction techniques to confirm experimental results.

© 2011 Optical Society of America

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  1. T. F. Krauss, Nat. Photon. 2, 448 (2008).
    [CrossRef]
  2. T. Baba, Nat. Photon. 2, 465 (2008).
    [CrossRef]
  3. J. Li, T. P. White, L. O. Faolain, A. Gomez-Iglesias, and T. F. Krauss, Opt. Express 16, 6227 (2008).
    [CrossRef] [PubMed]
  4. T. Baba, T. Kawasaki, H. Sasaki, J. Adachi, and D. Mori, Opt. Express 16, 9245 (2008).
    [CrossRef] [PubMed]
  5. T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
    [CrossRef]
  6. Y. A. Vlasov and S. J. McNab, Opt. Lett. 31, 50 (2006).
    [CrossRef] [PubMed]
  7. J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, Opt. Lett. 32, 2638 (2007).
    [CrossRef] [PubMed]
  8. T. P. White, L. C. Botten, C. M. de Sterke, K. B. Dossou, and R. C. McPhedran, Opt. Lett. 33, 2644 (2008).
    [CrossRef] [PubMed]
  9. J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, Phys. Rev. E 71, 036612 (2005).
    [CrossRef]
  10. L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. E 70, 056606 (2004).
    [CrossRef]
  11. S. Ha, A. A. Sukhorukov, K. B. Dossou, L. C. Botten, C. M. de Sterke, and Y. S. Kivshar, Opt. Lett. 34, 3776 (2009).
    [CrossRef] [PubMed]
  12. A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
    [CrossRef]
  13. M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
    [CrossRef] [PubMed]
  14. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
    [CrossRef] [PubMed]
  15. S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenović, L. Kuipers, D. M. Beggs, and T. F. Krauss, Opt. Express 18, 14654 (2010).
    [CrossRef] [PubMed]
  16. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
    [CrossRef] [PubMed]

2010

2009

S. Ha, A. A. Sukhorukov, K. B. Dossou, L. C. Botten, C. M. de Sterke, and Y. S. Kivshar, Opt. Lett. 34, 3776 (2009).
[CrossRef] [PubMed]

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

2008

2007

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, Opt. Lett. 32, 2638 (2007).
[CrossRef] [PubMed]

A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

2006

2005

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, Phys. Rev. E 71, 036612 (2005).
[CrossRef]

2004

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. E 70, 056606 (2004).
[CrossRef]

Adachi, J.

Asatryan, A. A.

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. E 70, 056606 (2004).
[CrossRef]

Baba, T.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

T. Baba, Nat. Photon. 2, 465 (2008).
[CrossRef]

T. Baba, T. Kawasaki, H. Sasaki, J. Adachi, and D. Mori, Opt. Express 16, 9245 (2008).
[CrossRef] [PubMed]

Ballato, A.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, Phys. Rev. E 71, 036612 (2005).
[CrossRef]

Ballato, J.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, Phys. Rev. E 71, 036612 (2005).
[CrossRef]

Beggs, D. M.

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenović, L. Kuipers, D. M. Beggs, and T. F. Krauss, Opt. Express 18, 14654 (2010).
[CrossRef] [PubMed]

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

Botten, L. C.

Burresi, M.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

de Sterke, C. M.

Dossou, K. B.

Engelen, R. J. P.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

Faolain, L. O.

Figotin, A.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, Phys. Rev. E 71, 036612 (2005).
[CrossRef]

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

Gomez-Iglesias, A.

Gomez-lglesias, A.

A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Ha, S.

Hughes, S.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Hugonin, J. P.

Kampfrath, T.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

Kawasaki, T.

Kivshar, Y. S.

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

Krauss, T. F.

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenović, L. Kuipers, D. M. Beggs, and T. F. Krauss, Opt. Express 18, 14654 (2010).
[CrossRef] [PubMed]

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

J. Li, T. P. White, L. O. Faolain, A. Gomez-Iglesias, and T. F. Krauss, Opt. Express 16, 6227 (2008).
[CrossRef] [PubMed]

T. F. Krauss, Nat. Photon. 2, 448 (2008).
[CrossRef]

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, Opt. Lett. 32, 2638 (2007).
[CrossRef] [PubMed]

A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

Kuipers, L.

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenović, L. Kuipers, D. M. Beggs, and T. F. Krauss, Opt. Express 18, 14654 (2010).
[CrossRef] [PubMed]

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

Lalanne, P.

Langtry, T. N.

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. E 70, 056606 (2004).
[CrossRef]

Li, J.

Mazoyer, S.

McNab, S. J.

McPhedran, R. C.

T. P. White, L. C. Botten, C. M. de Sterke, K. B. Dossou, and R. C. McPhedran, Opt. Lett. 33, 2644 (2008).
[CrossRef] [PubMed]

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. E 70, 056606 (2004).
[CrossRef]

Miller, A.

A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Mori, D.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

T. Baba, T. Kawasaki, H. Sasaki, J. Adachi, and D. Mori, Opt. Express 16, 9245 (2008).
[CrossRef] [PubMed]

O’Brien, D.

A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

O’Faolain, L.

A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Opheij, A.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Rodier, J. C.

Sasaki, H.

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Spasenovic, M.

Sukhorukov, A. A.

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

van Oosten, D.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Vitebskiy, I.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, Phys. Rev. E 71, 036612 (2005).
[CrossRef]

Vlasov, Y. A.

White, T. P.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

J. Li, T. P. White, L. O. Faolain, A. Gomez-Iglesias, and T. F. Krauss, Opt. Express 16, 6227 (2008).
[CrossRef] [PubMed]

T. P. White, L. C. Botten, C. M. de Sterke, K. B. Dossou, and R. C. McPhedran, Opt. Lett. 33, 2644 (2008).
[CrossRef] [PubMed]

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, Opt. Lett. 32, 2638 (2007).
[CrossRef] [PubMed]

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. E 70, 056606 (2004).
[CrossRef]

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

A. Gomez-lglesias, D. O’Brien, L. O’Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Nat. Photon.

T. F. Krauss, Nat. Photon. 2, 448 (2008).
[CrossRef]

T. Baba, Nat. Photon. 2, 465 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, Phys. Rev. E 71, 036612 (2005).
[CrossRef]

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, Phys. Rev. E 70, 056606 (2004).
[CrossRef]

Phys. Rev. Lett.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 123901 (2005).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Geometry of the waveguide. In section (i), the lattice was stretched by 30 nm . (b) Calculated dispersion for the two waveguide sections (dashed black curves) and dispersion retrieved from the numerical fit for propagating and evanescent modes (solid and dashed gray curves, respectively). The black curve was calculated for an infinitely long waveguide. (c) Imaginary component of the wave vector of the evanescent mode. (d) Calculated (dashed curve) and measured (solid curve) group index spectrum. (e) Measured transmission spectrum.

Fig. 2
Fig. 2

Near-field measurements of the electric field above the waveguide. (a) Light is “fast” in both waveguide sections, at a wavelength of λ 1 = 1525 nm . (b) Light is slow in the second section, at λ 2 = 1533.95 nm . The dashed white line indicates the interface between the two waveguide sections.

Fig. 3
Fig. 3

Intensity and field spread. (a)  | E x | 2 d x along the length of the waveguide. The green (bottom) curve is measured at λ 1 = 1525 nm ; the blue (top) curve is measured at λ 2 = 1533.95 nm . (b) Variance of the intensity along the waveguide.

Equations (1)

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σ 2 = ( x μ ) 2 I ( x ) d x I ( x ) d x .

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