Abstract

We present unique dispersion characteristics of high-contrast grating (HCG) hollow-core waveguides and show that slow light can be facilitated using internal resonances developing inside the waveguide walls. In addition, we show a fast and precise method of inferring the dispersion information from the waveguide angular reflectivity spectrum.

© 2010 Optical Society of America

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light(Princeton U. Press, 2008).
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    [CrossRef]
  4. S. Mookherjea and A. Yariv, IEEE J. Sel. Top. Quantum Electron. 8, 448 (2002).
    [CrossRef]
  5. Y. Chen and S. Blair, Opt. Express 12, 3353 (2004).
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  6. T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, Opt. Express 15, 7826 (2007).
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  7. D. Gerace and L. C. Andreani, Phys. Rev. E 69, 056603(2004).
    [CrossRef]
  8. A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
    [CrossRef]
  9. V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, J. Lightwave Technol. 17, 2050 (1999).
    [CrossRef]
  10. Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 17, 1508 (2009).
    [CrossRef] [PubMed]
  11. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
    [CrossRef]
  12. Y. Zhou, M. Moewe, J. Kern, M. C. Huang, and C. J. Chang-Hasnain, Opt. Express 16, 17282 (2008).
    [CrossRef] [PubMed]
  13. V. Karagodsky and C. J. Chang-Hasnain, in Frontiers in Optics Conference (FiO) (Optical Society of America, 2009), paper FThU5.
  14. P. Lalanne, J. P. Hugonin, and P. Chavel, J. Lightwave Technol. 24, 2442 (2006).
    [CrossRef]
  15. V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 18, 16973 (2010).
    [CrossRef] [PubMed]
  16. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981).
    [CrossRef]
  17. A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

2010

2009

2008

2007

2006

2005

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

2004

D. Gerace and L. C. Andreani, Phys. Rev. E 69, 056603(2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

Y. Chen and S. Blair, Opt. Express 12, 3353 (2004).
[CrossRef] [PubMed]

2003

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

2002

S. Mookherjea and A. Yariv, IEEE J. Sel. Top. Quantum Electron. 8, 448 (2002).
[CrossRef]

1999

1981

Andreani, L. C.

D. Gerace and L. C. Andreani, Phys. Rev. E 69, 056603(2004).
[CrossRef]

Astratov, V. N.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, J. Lightwave Technol. 17, 2050 (1999).
[CrossRef]

Blair, S.

Bristow, A. D.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

Chang-Hasnain, C. J.

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 18, 16973 (2010).
[CrossRef] [PubMed]

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 17, 1508 (2009).
[CrossRef] [PubMed]

Y. Zhou, M. Moewe, J. Kern, M. C. Huang, and C. J. Chang-Hasnain, Opt. Express 16, 17282 (2008).
[CrossRef] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

V. Karagodsky and C. J. Chang-Hasnain, in Frontiers in Optics Conference (FiO) (Optical Society of America, 2009), paper FThU5.

Chavel, P.

Chen, Y.

Croucher, M. P.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

Culshaw, I. S.

De La Rue, R. M.

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

Fuchida, A.

A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

Gaylord, T. K.

Gehring, G. A.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

Gerace, D.

D. Gerace and L. C. Andreani, Phys. Rev. E 69, 056603(2004).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Hopkinson, M.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

Huang, M. C.

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

Hugonin, J. P.

Joannopoulos, J. D.

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

Johnson, S. G.

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

Karagodsky, V.

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 18, 16973 (2010).
[CrossRef] [PubMed]

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 17, 1508 (2009).
[CrossRef] [PubMed]

A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

V. Karagodsky and C. J. Chang-Hasnain, in Frontiers in Optics Conference (FiO) (Optical Society of America, 2009), paper FThU5.

Kern, J.

Koyama, F.

A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

Krauss, T. F.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, J. Lightwave Technol. 17, 2050 (1999).
[CrossRef]

Kuramochi, E.

Lalanne, P.

Lee, R. K.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Meade, R. D.

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

Moewe, M.

Moharam, M. G.

Mookherjea, S.

S. Mookherjea and A. Yariv, IEEE J. Sel. Top. Quantum Electron. 8, 448 (2002).
[CrossRef]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

Notomi, M.

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Pesala, B.

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 17, 1508 (2009).
[CrossRef] [PubMed]

A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

Scherer, A.

Sedgwick, F. G.

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 18, 16973 (2010).
[CrossRef] [PubMed]

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 17, 1508 (2009).
[CrossRef] [PubMed]

A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

Skolnick, M. S.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, J. Lightwave Technol. 17, 2050 (1999).
[CrossRef]

Stevenson, R. M.

Tahraoui, A.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

Tanabe, T.

Taniyama, H.

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Whittaker, D. M.

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, J. Lightwave Technol. 17, 2050 (1999).
[CrossRef]

Winn, J. N.

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

Xu, Y.

Yariv, A.

S. Mookherjea and A. Yariv, IEEE J. Sel. Top. Quantum Electron. 8, 448 (2002).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Zhou, Y.

IEEE J. Sel. Top. Quantum Electron.

S. Mookherjea and A. Yariv, IEEE J. Sel. Top. Quantum Electron. 8, 448 (2002).
[CrossRef]

IEEE Photonics Technol. Lett.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

Nature

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

A. D. Bristow, D. M. Whittaker, V. N. Astratov, M. S. Skolnick, A. Tahraoui, T. F. Krauss, M. Hopkinson, M. P. Croucher, and G. A. Gehring, Phys. Rev. B 68, 033303 (2003).
[CrossRef]

Phys. Rev. E

D. Gerace and L. C. Andreani, Phys. Rev. E 69, 056603(2004).
[CrossRef]

Other

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

V. Karagodsky and C. J. Chang-Hasnain, in Frontiers in Optics Conference (FiO) (Optical Society of America, 2009), paper FThU5.

A. Fuchida, B. Pesala, V. Karagodsky, F. G. Sedgwick, F. Koyama, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2010), paper CThW5.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of high-contrast grating (HCG) hollow-core waveguide. The HCG is comprised of material with refractive index in the semiconductor range (3–3.5), surrounded by air. The wave is guided between two highly ( 100 % ) reflective HCG walls. (b) Schematic of the proposed method for inferring the ω - k information of the HCG waveguide by calculating the external reflectivity using swept-angle RCWA. The incidence angle θ is swept and the angles θ m at which resonant reflectivity dips are observed reveal the HCG waveguide modes, the wavenumbers of which are given by: k z = ( ω / c ) sin ( θ m ) . The waveguide parameters (normalized to grating period Λ, since all dimensions are scalable) are core size, D = 15 Λ ; duty cycle (ratio of grating width to period), dc = 50%; grating thickness, t g = 0.25 Λ ; refractive index of HCG bars, n r = 3.48 . Incident plane wave is ŷ polarized.

Fig. 2
Fig. 2

(a) ω - k curves of HCG waveguide showing single mode downshift. At frequencies ω remote from HCG resonance, the modes of HCG waveguide coincide with the modes of a perfect electric conductor (PEC) waveguide. This is because away from resonance the reflectivity phase of a single HCG is a multiple of π, as shown in (b). HCG resonance causes a downshift of one mode (from second to first, from third to second, etc.), because the phase change accumulated during resonance is π. The waveguide parameters are the same as in Fig. 1b. The polarization of waveguide modes is TE. (b) HCG reflectivity near resonance—both absolute value, | r HCG 2 | , and phase, phase ( r HCG 2 ) / 2 —revealing a π phase shift associated with a single resonance. (c) Evolution of the mode profile during the downshift from a second (antisymmetric) to the first (symmetric) mode. For clarity, each mode profile was assigned a different color that matches the color of the corresponding point on the ω - k diagram shown at the inset of Fig. 2c (this inset is a part of the larger ω - k plot at Fig. 2a].

Fig. 3
Fig. 3

ω - k curves of HCG waveguide showing double mode downshift, caused by two adjacent HCG resonances, each causing a downshift of one mode by contributing a phase shift of π. The waveguide parameters (normalized to grating period Λ) are core size, D = 15 Λ ; duty cycle (ratio of grating width to period), dc = 50%; grating thickness, t g = 0.5 Λ (twice the thickness in Fig. 2); refractive index of HCG bars, n r = 3.48 . The polarization of waveguide modes is TE.

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