Abstract

We present a systematic procedure for designing “flat bands” of photonic crystal waveguides for slow light propagation. The procedure aims to maximize the group index - bandwidth product by changing the position of the first two rows of holes of W1 line defect photonic crystal waveguides. A nearly constant group index - bandwidth product is achieved for group indices of 30-90 and as an example, we experimentally demonstrate flat band slow light with nearly constant group indices of 32.5, 44 and 49 over 14 nm, 11 nm and 9.5 nm bandwidth around 1550 nm, respectively.

© 2008 Optical Society of America

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  1. R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, "Applications of slow light in telecommunications," Opt. Photon. News 17, 19-23 (2006).
    [CrossRef]
  2. T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D. 40, 2666-2670 (2007).
    [CrossRef]
  3. Y. A. Vlasov, M. O??Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
    [CrossRef] [PubMed]
  4. M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals, " Nat. Mater. 3, 211-219 (2004).
    [CrossRef] [PubMed]
  5. J. T. Li and J. Y. Zhou, "Nonlinear optical frequency conversion with stopped short light pulses," Opt. Express 14, 2811-2816 (2006).
    [CrossRef] [PubMed]
  6. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
    [CrossRef] [PubMed]
  7. R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, V. Hulst, K. Asakawa, and L. Kuipers, "The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides," Opt. Express 14, 1658-1672 (2006).
    [CrossRef] [PubMed]
  8. D. Mori, S. Kubo, H. Sasaki, and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Lett. 15, 5264-5270 (2007).
  9. A. Yu. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
    [CrossRef]
  10. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, "Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth," Opt. Express 15, 219-226 (2007).
    [CrossRef] [PubMed]
  11. J. M. Brosi, J. Leuthold, and W. Freude, "Microwave-frequency experiments validate optical simulation tools and demonstrate novel dispersion-tailored photonic crystal waveguides," J. Lightwave Technol. 25, 2502-2510 (2007).
    [CrossRef]
  12. L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, "Photonic crystal waveguides with semi-slow light and tailored dispersion properties," Opt. Express 14, 9444-9450 (2006).
    [CrossRef] [PubMed]
  13. S. Kubo. D. Mori, and T. Baba, "Low-group-velocity and low-dispersion slow light in photonic crystal waveguides," Opt. Lett. 32, 2981-2983 (2007).
    [CrossRef] [PubMed]
  14. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  15. 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]
  16. K. L. Lee, J. Bucchignano, J. Gelorme, and R. Viswanathan, "Ultrasonic and dip resist development processes for 50 nm device fabrication," J. Vac. Sci. Technol. B,  15, 2621-2626 (1997).
    [CrossRef]
  17. See http://www.nanophotonics.eu.
  18. L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
    [CrossRef]
  19. J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, "Coupling into slow-mode photonic crystal waveguides," Opt. Lett. 32, 2638-2640 (2007).
    [CrossRef] [PubMed]
  20. A. Gomez-lglesias, D. O??Brien, L. O??Faolain, A. Miller, and T. F. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett. 90, 261107 (2007).
    [CrossRef]
  21. L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, and T. F. Krauss, "Dependence of extrinsic loss on group velocity in photonic crystal waveguides," Opt. Express 15, 13129-13138 (2007).
    [CrossRef] [PubMed]

2007

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D. 40, 2666-2670 (2007).
[CrossRef]

D. Mori, S. Kubo, H. Sasaki, and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Lett. 15, 5264-5270 (2007).

A. Gomez-lglesias, D. O??Brien, L. O??Faolain, A. Miller, and T. F. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, "Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth," Opt. Express 15, 219-226 (2007).
[CrossRef] [PubMed]

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, "Coupling into slow-mode photonic crystal waveguides," Opt. Lett. 32, 2638-2640 (2007).
[CrossRef] [PubMed]

L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, and T. F. Krauss, "Dependence of extrinsic loss on group velocity in photonic crystal waveguides," Opt. Express 15, 13129-13138 (2007).
[CrossRef] [PubMed]

S. Kubo. D. Mori, and T. Baba, "Low-group-velocity and low-dispersion slow light in photonic crystal waveguides," Opt. Lett. 32, 2981-2983 (2007).
[CrossRef] [PubMed]

J. M. Brosi, J. Leuthold, and W. Freude, "Microwave-frequency experiments validate optical simulation tools and demonstrate novel dispersion-tailored photonic crystal waveguides," J. Lightwave Technol. 25, 2502-2510 (2007).
[CrossRef]

2006

2005

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O??Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

2004

M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals, " Nat. Mater. 3, 211-219 (2004).
[CrossRef] [PubMed]

A. Yu. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

2001

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[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]

1997

K. L. Lee, J. Bucchignano, J. Gelorme, and R. Viswanathan, "Ultrasonic and dip resist development processes for 50 nm device fabrication," J. Vac. Sci. Technol. B,  15, 2621-2626 (1997).
[CrossRef]

Asakawa, K.

Baba, T.

D. Mori, S. Kubo, H. Sasaki, and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Lett. 15, 5264-5270 (2007).

Borel, P. I.

Boyd, R. W.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, "Applications of slow light in telecommunications," Opt. Photon. News 17, 19-23 (2006).
[CrossRef]

Brosi, J. M.

Bucchignano, J.

K. L. Lee, J. Bucchignano, J. Gelorme, and R. Viswanathan, "Ultrasonic and dip resist development processes for 50 nm device fabrication," J. Vac. Sci. Technol. B,  15, 2621-2626 (1997).
[CrossRef]

Chong, H.

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

De La Rue, R. M.

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

Eich, M.

A. Yu. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Engelen, R. J. P.

Fage-Pedersen, J.

Frandsen, L. H.

Freude, W.

Gaeta, A. L.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, "Applications of slow light in telecommunications," Opt. Photon. News 17, 19-23 (2006).
[CrossRef]

Gauthier, D. J.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, "Applications of slow light in telecommunications," Opt. Photon. News 17, 19-23 (2006).
[CrossRef]

Gelorme, J.

K. L. Lee, J. Bucchignano, J. Gelorme, and R. Viswanathan, "Ultrasonic and dip resist development processes for 50 nm device fabrication," J. Vac. Sci. Technol. B,  15, 2621-2626 (1997).
[CrossRef]

Gomez-lglesias, A.

A. Gomez-lglesias, D. O??Brien, L. O??Faolain, A. Miller, and T. F. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O??Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Hughes, S.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Hugonin, J. P.

Hulst, V.

Ikeda, N.

Joannopoulos, J. D.

Johnson, S. G.

Korterik, J. P.

Krauss, T. F.

A. Gomez-lglesias, D. O??Brien, L. O??Faolain, A. Miller, and T. F. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, "Coupling into slow-mode photonic crystal waveguides," Opt. Lett. 32, 2638-2640 (2007).
[CrossRef] [PubMed]

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D. 40, 2666-2670 (2007).
[CrossRef]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, "Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth," Opt. Express 15, 219-226 (2007).
[CrossRef] [PubMed]

L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, and T. F. Krauss, "Dependence of extrinsic loss on group velocity in photonic crystal waveguides," Opt. Express 15, 13129-13138 (2007).
[CrossRef] [PubMed]

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

Kubo, S.

D. Mori, S. Kubo, H. Sasaki, and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Lett. 15, 5264-5270 (2007).

S. Kubo. D. Mori, and T. Baba, "Low-group-velocity and low-dispersion slow light in photonic crystal waveguides," Opt. Lett. 32, 2981-2983 (2007).
[CrossRef] [PubMed]

Kuipers, L.

Lalanne, P.

Lavrinenko, A. V.

Lee, K. L.

K. L. Lee, J. Bucchignano, J. Gelorme, and R. Viswanathan, "Ultrasonic and dip resist development processes for 50 nm device fabrication," J. Vac. Sci. Technol. B,  15, 2621-2626 (1997).
[CrossRef]

Leuthold, J.

Li, J. T.

McIntyre, D.

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, M. O??Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Michaeli, A.

Miller, A.

A. Gomez-lglesias, D. O??Brien, L. O??Faolain, A. Miller, and T. F. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Mori, D.

D. Mori, S. Kubo, H. Sasaki, and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Lett. 15, 5264-5270 (2007).

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

O??Boyle, M.

Y. A. Vlasov, M. O??Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

O??Brien, D.

A. Gomez-lglesias, D. O??Brien, L. O??Faolain, A. Miller, and T. F. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," 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, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

O'Brien, D.

O'Faolain, L.

Petrov, A. Yu.

A. Yu. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Salib, M.

Sasaki, H.

D. Mori, S. Kubo, H. Sasaki, and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Lett. 15, 5264-5270 (2007).

Settle, M. D.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Soljacic, M.

M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals, " Nat. Mater. 3, 211-219 (2004).
[CrossRef] [PubMed]

Sugimoto, Y.

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Thoms, S.

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

Viswanathan, R.

K. L. Lee, J. Bucchignano, J. Gelorme, and R. Viswanathan, "Ultrasonic and dip resist development processes for 50 nm device fabrication," J. Vac. Sci. Technol. B,  15, 2621-2626 (1997).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O??Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Watanabe, Y.

White, T. P.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Yuan, X.

L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, and T. F. Krauss, "Dependence of extrinsic loss on group velocity in photonic crystal waveguides," Opt. Express 15, 13129-13138 (2007).
[CrossRef] [PubMed]

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

Zhou, J. Y.

Appl. Phys. Lett.

A. Yu. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

A. Gomez-lglesias, D. O??Brien, L. O??Faolain, A. Miller, and T. F. Krauss, "Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry," Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Electron. Lett.

L. O??Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, "Low-loss propagation in photonic crystal waveguides," Electron. Lett. 42, 1454-1455 (2006).
[CrossRef]

J. Lightwave Technol.

J. Phys. D.

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D. 40, 2666-2670 (2007).
[CrossRef]

J. Vac. Sci. Technol. B

K. L. Lee, J. Bucchignano, J. Gelorme, and R. Viswanathan, "Ultrasonic and dip resist development processes for 50 nm device fabrication," J. Vac. Sci. Technol. B,  15, 2621-2626 (1997).
[CrossRef]

Nat. Mater.

M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals, " Nat. Mater. 3, 211-219 (2004).
[CrossRef] [PubMed]

Nature

Y. A. Vlasov, M. O??Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Opt. Photon. News

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, "Applications of slow light in telecommunications," Opt. Photon. News 17, 19-23 (2006).
[CrossRef]

Phys. Rev. Lett.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Other

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Figures (5)

Fig. 1.
Fig. 1.

Geometry of the modified W1 PhC waveguides: the first and second rows of holes are displaced symmetrically about the waveguide axis. The displacements relative to the unmodified lattice (red lines) are given by s1 and s2, where shifts toward the waveguide centre are defined to be positive. Here, s1<0 and s2>0, as used throughout this paper.

Fig. 2.
Fig. 2.

Systematic maps of (a) 2D and (b) 3D calculations of the group index - bandwidth product as a function of s1 and s2. The color plot and the contours represent ngω/ω) and ng respectively. The rectangle in Fig. 2(a) indicates the calculation region of Fig. 2(b). The three blue circles and green triangles in Fig. 2(b) indicate the calculation points in Fig. 3 and the experimental points in Fig. 5 respectively.

Fig. 3.
Fig. 3.

(a) Calculated dispersion curves and (b) group indices, for the fundamental mode of the modified W1 PhC waveguides with s1 and s2 values indicated by the blue circles in Fig. 2(b). The thick solid red line represents the flat band slow light region. The group index - bandwidth product was around 0.3 in all cases. The result of W1 waveguide is also presented for comparison

Fig. 4.
Fig. 4.

Scanning electron micrograph (SEM) of a W1 type PhC waveguides with s1=-62 nm and s2=0 nm.

Fig. 5.
Fig. 5.

Measured transmission spectra (black solid lines) and experiment (blue solid lines) and calculated (red dashed lines) group index of the PhC waveguides with s1 and s2 values indicated in Fig. 2(b): (a) s1=-52 nm and s2=0 nm, (b) s1=-50 nm and s2=12 nm, and (c) s1=-48 nm and s2=16 nm. The flat band group index and the corresponding group index - bandwidth products are ng=32.5 for ngω/ω)=0.29, ng=44 for ngω/ω)=0.31, and ng=49 for ngω/ω)=0.3 respectively. The result of a normal W1 PhC waveguide is also presented for comparison (d).

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