Abstract

In this study, we propose a special type of slow light photonic crystal (PC) waveguide structure to achieve slow light with an improved delay and bandwidth product (DBP). The waveguide is based on a triangular lattice PC with a line defect imposed by changing the radii and locations of the holes lying along the waveguide centerline. By altering the locations of these central holes, group indices ranging approximately from 25 to 40 are obtained over frequency intervals, attaining a nearly constant group index. It is also observed that the group index spectrum has an S-like shape under certain circumstances. The manipulations of structural parameters easily allow attaining higher or lower group indices. For special configurations, normalized DBPs can be enhanced up to a value of 0.554. According to the best of the authors’ knowledge, this value is the highest value achieved with PC waveguide structures, and this value is achieved without using any special optimization methods such as topology optimization. Group velocity dispersion values of various configurations are minimized to enable proper optical pulse propagation.

© 2012 Optical Society of America

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  14. M. Ebnali-Heidari, C. Grillet, C. Monat, and B. J. Eggleton, “Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,” Opt. Express 17, 1628–1635 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. F. Wang, J. S. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28, 387–397 (2011).
    [CrossRef]
  26. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [CrossRef]
  27. R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. van 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]
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    [CrossRef]
  29. R. S. Tucker, P. Ku, and C. J. Chang-Hasnain, “Delay-bandwidth product and storage density in slow-light optical buffers,” Electron. Lett. 41, 208–209 (2005).
    [CrossRef]
  30. T. Baba, T. Kawasaki, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16, 9245–9253 (2008).
    [CrossRef]
  31. S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion-engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
    [CrossRef]
  32. L. O’Faolain, S. Schulz, D. M. Beggs, T. P. White, L. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, J. Mazoyer, P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
    [CrossRef]
  33. K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
    [CrossRef]
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    [CrossRef]

2011

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

L. Dai, T. Li, and C. Jiang, “Wideband ultralow high-order-dispersion photonic crystal slow-light waveguide,” J. Opt. Soc. Am. B 28, 1622–1626 (2011).
[CrossRef]

R. Matzen, J. S. Jensen, and O. Sigmund, “Systematic design of slow-light photonic waveguides,” J. Opt. Soc. Am. B 28, 2374–2382 (2011).
[CrossRef]

F. Wang, J. S. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28, 387–397 (2011).
[CrossRef]

J. Liang, L-Y. Ren, M-J. Yun, X. Han, and X-J. Wang, “Wideband ultraflat slow light with large group index in a W1 photonic crystal waveguide,” J. Appl. Phys. 110, 063103 (2011).
[CrossRef]

2010

2009

2008

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2, 465–473 (2008).
[CrossRef]

K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
[CrossRef]

T. Baba, T. Kawasaki, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16, 9245–9253 (2008).
[CrossRef]

J. Ma and C. Jiang, “Demonstration of ultraslow modes in asymmetric line-defect photonic crystal waveguides,” IEEE Photon. Technol. Lett. 20, 1237–1239 (2008).
[CrossRef]

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, “Slow-light regime and critical coupling in highly multimode corrugated waveguides,” J. Opt. Soc. Am. B 25, C1–C14 (2008).
[CrossRef]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008).
[CrossRef]

2007

2006

2005

2004

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

2001

1999

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Adachi, J.

Ahopelto, J.

Alam, M. N.

K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
[CrossRef]

Asakawa, K.

Ayas, L.

Baba, T.

Beggs, D. M.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion-engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

L. O’Faolain, S. Schulz, D. M. Beggs, T. P. White, L. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, J. Mazoyer, P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

Benisty, H.

Borel, P. I.

Cambournac, C.

Chang-Hasnain, C. J.

R. S. Tucker, P. Ku, and C. J. Chang-Hasnain, “Delay-bandwidth product and storage density in slow-light optical buffers,” Electron. Lett. 41, 208–209 (2005).
[CrossRef]

Chen, S.

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Citrin, D. S.

Dai, L.

De La Rue, R. M.

de Sterke, M.

C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt. 12, 104003(2010).
[CrossRef]

Ebnali-Heidari, M.

Eggleton, B. J.

Eich, M.

A. Y. 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.

Gao, D.

Gomez-Iglesias, A.

Grillet, C.

Han, J.

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Han, X.

J. Liang, L-Y. Ren, M-J. Yun, X. Han, and X-J. Wang, “Wideband ultraflat slow light with large group index in a W1 photonic crystal waveguide,” J. Appl. Phys. 110, 063103 (2011).
[CrossRef]

Hou, J.

Hou, S.

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Hugonin, P.

Ikeda, N.

Jensen, J. S.

Jensen, K. H.

K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
[CrossRef]

Jiang, C.

Joannopoulos, J.

Joannopoulos, J. D.

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light band-edge waveguides for tunable time delays,” Opt. Express 13, 7145–7159 (2005).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Johnson, S.

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light band-edge waveguides for tunable time delays,” Opt. Express 13, 7145–7159 (2005).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Kawasaki, T.

Khayam, O.

Korterik, J. P.

Krauss, T. F.

Ku, P.

R. S. Tucker, P. Ku, and C. J. Chang-Hasnain, “Delay-bandwidth product and storage density in slow-light optical buffers,” Electron. Lett. 41, 208–209 (2005).
[CrossRef]

Kuipers, L.

Kurt, H.

Lalanne, P.

Lambrecht, A.

K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
[CrossRef]

Lavrinenko, A. V.

Lee, R. K.

Lei, J.

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Li, J.

Li, T.

Liang, J.

J. Liang, L-Y. Ren, M-J. Yun, X. Han, and X-J. Wang, “Wideband ultraflat slow light with large group index in a W1 photonic crystal waveguide,” J. Appl. Phys. 110, 063103 (2011).
[CrossRef]

Lipsanen, H.

Ma, J.

J. Ma and C. Jiang, “Demonstration of ultraslow modes in asymmetric line-defect photonic crystal waveguides,” IEEE Photon. Technol. Lett. 20, 1237–1239 (2008).
[CrossRef]

Matzen, R.

Mazoyer, J.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Melloni, A.

L. O’Faolain, S. Schulz, D. M. Beggs, T. P. White, L. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, J. Mazoyer, P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion-engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

Melo, T.

Mo, W.

Monat, C.

Mori, D.

Morichetti, F.

Mortensen, N. A.

K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
[CrossRef]

Mulot, M.

O’Faolain, L.

Petrov, A. Y.

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

Povinelli, M. L.

Rawal, S.

Ren, L-Y.

J. Liang, L-Y. Ren, M-J. Yun, X. Han, and X-J. Wang, “Wideband ultraflat slow light with large group index in a W1 photonic crystal waveguide,” J. Appl. Phys. 110, 063103 (2011).
[CrossRef]

Sasaki, H.

Säynätjoki, A.

Scherer, A.

Scherer, B.

K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
[CrossRef]

Schulz, S.

Schulz, S. A.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion-engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

Sigmund, O.

Sinha, R. K.

Spasenovic, L.

Sugimoto, Y.

Tucker, R. S.

R. S. Tucker, P. Ku, and C. J. Chang-Hasnain, “Delay-bandwidth product and storage density in slow-light optical buffers,” Electron. Lett. 41, 208–209 (2005).
[CrossRef]

Üstün, K.

van Hulst, N. F.

Wang, D.

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Wang, F.

Wang, X-J.

J. Liang, L-Y. Ren, M-J. Yun, X. Han, and X-J. Wang, “Wideband ultraflat slow light with large group index in a W1 photonic crystal waveguide,” J. Appl. Phys. 110, 063103 (2011).
[CrossRef]

Watanabe, Y.

White, T. P.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Wu, H.

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Yariv, A.

Yuan, L.

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Yun, M-J.

J. Liang, L-Y. Ren, M-J. Yun, X. Han, and X-J. Wang, “Wideband ultraflat slow light with large group index in a W1 photonic crystal waveguide,” J. Appl. Phys. 110, 063103 (2011).
[CrossRef]

Zhang, J.

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Zhou, Z.

Appl. Phys. Lett.

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

Electron. Lett.

R. S. Tucker, P. Ku, and C. J. Chang-Hasnain, “Delay-bandwidth product and storage density in slow-light optical buffers,” Electron. Lett. 41, 208–209 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

J. Ma and C. Jiang, “Demonstration of ultraslow modes in asymmetric line-defect photonic crystal waveguides,” IEEE Photon. Technol. Lett. 20, 1237–1239 (2008).
[CrossRef]

J. Appl. Phys.

J. Liang, L-Y. Ren, M-J. Yun, X. Han, and X-J. Wang, “Wideband ultraflat slow light with large group index in a W1 photonic crystal waveguide,” J. Appl. Phys. 110, 063103 (2011).
[CrossRef]

J. Lightwave Technol.

J. Opt.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion-engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt. 12, 104003(2010).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photon.

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2, 465–473 (2008).
[CrossRef]

Opt. Commun.

K. H. Jensen, M. N. Alam, B. Scherer, A. Lambrecht, and N. A. Mortensen, “Slow-light enhanced light-matter interactions with applications to gas sensing,” Opt. Commun. 281, 5335–5339 (2008).
[CrossRef]

D. Wang, J. Zhang, L. Yuan, J. Lei, S. Chen, J. Han, and S. Hou, “Slow light engineering in polyatomic photonic crystal waveguides based on square lattice,” Opt. Commun. 284, 5829–5832 (2011).
[CrossRef]

Opt. Express

O. Khayam, and H. Benisty, “General recipe for flatbands in photonic crystal waveguides,” Opt. Express 17, 14634–14648 (2009).
[CrossRef]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef]

R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. van 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]

L. O’Faolain, S. Schulz, D. M. Beggs, T. P. White, L. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, J. Mazoyer, P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

T. Baba, T. Kawasaki, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16, 9245–9253 (2008).
[CrossRef]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008).
[CrossRef]

H. Kurt, K. Üstün, and L. Ayas, “Study of different spectral regions and delay bandwidth relation in slow light photonic crystal waveguides,” Opt. Express 18, 26965–26977 (2010).
[CrossRef]

D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13, 9398–9408 (2005).
[CrossRef]

J. Hou, H. Wu, D. S. Citrin, W. Mo, D. Gao, and Z. Zhou, “Wideband slow light in chirped slot photonic-crystal coupled waveguides,” Opt. Express 18, 10567–10580 (2010).
[CrossRef]

S. Rawal, R. K. Sinha, and R. M. De La Rue, “Slow light miniature devices with ultra-flattened dispersion in silicon-on-insulator photonic crystal,” Opt. Express 17, 13315–13325 (2009).
[CrossRef]

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light band-edge waveguides for tunable time delays,” Opt. Express 13, 7145–7159 (2005).
[CrossRef]

A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15, 8323–8328 (2007).
[CrossRef]

M. Ebnali-Heidari, C. Grillet, C. Monat, and B. J. Eggleton, “Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,” Opt. Express 17, 1628–1635 (2009).
[CrossRef]

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]

K. Üstün and H. Kurt, “Ultra slow light achievement in photonic crystals by merging coupled cavities with waveguides,” Opt. Express 18, 21155–21161 (2010).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

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[CrossRef]

Other

J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

J. B. Khurgin and R. S. Tucker, eds., Slow Light: Science and Applications (CRC, 2009).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic representation of a triangular lattice photonic crystal waveguide. The central row of holes is moved along the x and y directions. Additionally, the radii of these holes are tuned during the optimization steps presented in Section 2.

Fig. 2.
Fig. 2.

(a) Dispersion diagram for initial set of parameters (Sx=0.462a, Sy=0, and R=0.25a). The band engineering is performed on the dashed cuve; (b) The h-field distribution of the mode at k=0.50(2π/a). The figure shows that the light is confined in the center region, verifying a waveguide formation.

Fig. 3.
Fig. 3.

(a) Change in dispersion diagram with respect to various Sx values. Sy and R remain constant at 0 and 0.25a, respectively. The lower bandgap limit is shown by the straight line at the lower part of the figure. Linear parts of the dispersion curves have an exceptional importance while achieving slow light with a low group velocity dispersion; (b) The calculated group index spectra of the band diagrams shown in (a). At Sx=0.458a, a dispersion diagram with a chair shape is formed. That is, GVD tends to zero at frequencies near aλ=0.2137. Exceeding this Sx value, an S-like shape is added to the constant part of the chair shape. The local minima and maxima of this S shape exhibit zero GVD.

Fig. 4.
Fig. 4.

Change in group index spectra with respect to various Sy values. Sx and R remain constant at 0.462 and 0.25a, respectively. At lower values of Sy, the deviation in the curve is very small.

Fig. 5.
Fig. 5.

(a) Region of interest of the dispersion diagrams corresponding to various R values. Sx and Sy remain constant at 0.462a and 0, respectively. R values are scanned with a step size of 0.002a. The linear parts of the dispersion diagram near kx=0.452πa can be engineered to attain slow light; (b) The group index spectra of the dispersion curves. The chair shape is preserved with low GVD characteristics.

Fig. 6.
Fig. 6.

(a)–(c) GVD values for Optimization Steps 1, 2, and 3, respectively.

Fig. 7.
Fig. 7.

(a)–(c) TOD values for Optimization Steps 1, 2, and 3, respectively.

Fig. 8.
Fig. 8.

(a) Normalized DBP values that correspond to different Sx values. The other optimization parameters are kept at Sy=0 and R=0.25a. The highest normalized DBP reaches up to 0.441; (b) The normalized DBP values that correspond to different R values. The remaining parameters are fixed at Sx=0.462a and Sy=0.

Fig. 9.
Fig. 9.

Results of additional optimization for large normalized DBP numbers. The dotted curve corresponds to the structure with parameters Sx=0.470a, Sy=0, R=0.25a, and normalized DBP=0.441. The dashed curve corresponds to the structure with parameters Sx=0.478a, Sy=0, R=0.254a, and normalized DBP=0.518. The curve with circles corresponds to the structure with the following parameters: Sx=0.500a, Sy=0, R=0.262a, DBP=0.554.

Fig. 10.
Fig. 10.

Parameter scan in the vicinity of the values that provide the largest normalized DBP value. The sharp decay on the left side of the graph is due to the fact that the S-shaped group index spectrum does not satisfy the ±10% criteria.

Fig. 11.
Fig. 11.

Group index spectra of the three-dimensional slow light photonic structure.

Fig. 12.
Fig. 12.

In-plane loss, out-of-plane loss, and total loss. The shaded region shows the region of interest. There is a sharp increase in loss where the frequencies are closer to the band edge.

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