Abstract

This study presents a systematic optimization procedure to generate slow light with large group index, wideband, and low dispersion in an ellipse-hole photonic crystal waveguide. The group index, bandwidth, and dispersion can be tuned efficiently by changing the orientation of the ellipse holes in the first row and a longitudinal hole position shift of the third row. Under a constant group index criterion of ±10% variation, the corresponding bandwidths of the flat band reach are 13.5, 9.4, 7.8, and 6.1 nm around 1550 nm when the group indices are approximately the constants 46, 63, 78, and 100, respectively. A nearly constant group index–bandwidth product of 0.39 was achieved for all cases. Low-dispersion slow-light propagation was confirmed by studying the relative temporal pulsewidth spreading with the two-dimensional finite difference time-domain method.

© 2014 Optical Society of America

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    [CrossRef]

2013 (2)

2012 (3)

F. Wang, J. S. Jensen, and O. Sigmund, “High-performance slow light photonic crystal waveguides with topology optimized or circular-hole based material layouts,” Photon. Nanostr. Fundam. Appl. 10, 378–388 (2012).
[CrossRef]

K. Üstün and H. Kurt, “Slow light structure with enhanced delay–bandwidth product,” J. Opt. Soc. Am. B 29, 2403–2409 (2012).
[CrossRef]

H. Lotfi, N. Granpayeh, and S. A. Schulz, “Photonic crystal waveguides with ultra-low group velocity,” Opt. Commun. 285, 2743–2745 (2012).
[CrossRef]

2011 (2)

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]

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]

2010 (6)

2009 (2)

2008 (4)

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]

F. Wang, J. Ma, and C. Jiang, “Dispersionless slow wave in novel 2-D photonic crystal line defect waveguides,” J. Lightwave Technol. 26, 1381–1386 (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).

D. M. Beggs, L. O’Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slab using optical methods,” Photon. Nanostr. Fundam. Appl. 6, 213–218 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (4)

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]

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005).
[CrossRef]

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]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).

2004 (2)

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

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

2001 (1)

Beggs, D. M.

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]

D. M. Beggs, L. O’Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slab using optical methods,” Photon. Nanostr. Fundam. Appl. 6, 213–218 (2008).
[CrossRef]

Benjamin, J. E.

M. Christelle, E. H. Majid, and J. E. Benjamin, “Slow light enhancement nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 16, 344–356 (2010).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electro-magnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Borel, P. I.

Cassan, E.

Christelle, M.

M. Christelle, E. H. Majid, and J. E. Benjamin, “Slow light enhancement nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 16, 344–356 (2010).
[CrossRef]

Dai, L.

De La Rue, R. M.

Dong, C.-B.

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]

Fan, S.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Faolain, L. O.

Frandsen, L. H.

Gao, D.

Gao, L.

Gomez-Iglesias, A.

Granpayeh, N.

H. Lotfi, N. Granpayeh, and S. A. Schulz, “Photonic crystal waveguides with ultra-low group velocity,” Opt. Commun. 285, 2743–2745 (2012).
[CrossRef]

Grillet, C.

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]

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]

He, Y.

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]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).

Hugonin, P.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electro-magnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Jensen, J. S.

F. Wang, J. S. Jensen, and O. Sigmund, “High-performance slow light photonic crystal waveguides with topology optimized or circular-hole based material layouts,” Photon. Nanostr. Fundam. Appl. 10, 378–388 (2012).
[CrossRef]

Ji, Y.

Jiang, C.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electro-magnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

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]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electro-magnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

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]

Krauss, T. F.

Kuipers, L.

Kuramochi, E.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).

Kurt, H.

Lalanne, P.

Lavrinenko, A. V.

Leng, F.-C.

Li, J.

Li, T.

Li, X.-M.

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]

Liang, W.-Y.

Lipson, M.

Liu, B.

Long, F.

Lotfi, H.

H. Lotfi, N. Granpayeh, and S. A. Schulz, “Photonic crystal waveguides with ultra-low group velocity,” Opt. Commun. 285, 2743–2745 (2012).
[CrossRef]

Ma, J.

F. Wang, J. Ma, and C. Jiang, “Dispersionless slow wave in novel 2-D photonic crystal line defect waveguides,” J. Lightwave Technol. 26, 1381–1386 (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).

Majid, E. H.

M. Christelle, E. H. Majid, and J. E. Benjamin, “Slow light enhancement nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 16, 344–356 (2010).
[CrossRef]

Mazoyer, J.

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]

Melloni, A.

Monat, C.

Morichetti, F.

Notomi, M.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).

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]

O’Brien, D.

O’Faolain, L.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electro-magnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Pedersen, J. F.

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]

Ramunno, L.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (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]

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]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electro-magnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Schulz, S.

Schulz, S. A.

H. Lotfi, N. Granpayeh, and S. A. Schulz, “Photonic crystal waveguides with ultra-low group velocity,” Opt. Commun. 285, 2743–2745 (2012).
[CrossRef]

Settle, M. D.

Shinya, A.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).

Sigmund, O.

F. Wang, J. S. Jensen, and O. Sigmund, “High-performance slow light photonic crystal waveguides with topology optimized or circular-hole based material layouts,” Photon. Nanostr. Fundam. Appl. 10, 378–388 (2012).
[CrossRef]

Sinha, R.

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]

Spasenovic, L.

Suh, W.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Tang, J.

Tian, H.

Üstün, K.

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]

Wang, B.-Y.

Wang, F.

F. Wang, J. S. Jensen, and O. Sigmund, “High-performance slow light photonic crystal waveguides with topology optimized or circular-hole based material layouts,” Photon. Nanostr. Fundam. Appl. 10, 378–388 (2012).
[CrossRef]

F. Wang, J. Ma, and C. Jiang, “Dispersionless slow wave in novel 2-D photonic crystal line defect waveguides,” J. Lightwave Technol. 26, 1381–1386 (2008).
[CrossRef]

Wang, H.-Z.

Wang, T.

Wang, T.-B.

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]

Wang, Z.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).

White, T. P.

Xiang, L.

Xu, Y.

Yan, W.

Yanik, M. F.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

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]

Yuan, X.

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, X.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electro-magnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Christelle, E. H. Majid, and J. E. Benjamin, “Slow light enhancement nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 16, 344–356 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

J. Appl. Phys. (1)

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. (3)

J. Opt. Soc. Am. B (2)

Nature (1)

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]

Opt. Commun. (1)

H. Lotfi, N. Granpayeh, and S. A. Schulz, “Photonic crystal waveguides with ultra-low group velocity,” Opt. Commun. 285, 2743–2745 (2012).
[CrossRef]

Opt. Express (9)

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]

S. Rawal, R. 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. 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. F. Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express 14, 9444–9450 (2006).
[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]

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]

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]

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[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

(a) Schematic structure of the proposed PCW: the lengths of the long and short shafts of the ellipse are denoted by A and B, respectively. The orientation of the green holes in the first row adjacent to the waveguide has been tuned, and θ denotes the angle between the long axis of the ellipse hole and the y axis, whereas the red holes in the third row have been shifted toward the positive direction of the x axis with a displacement denoted by p. (b) Dispersion diagram for parameters A=0.81a, B=0.73a, θ=65°, and p=0.05a. The band engineering is performed on the red curve. (c) The supercell is considered for PWE calculation.

Fig. 2.
Fig. 2.

(a) Dispersion curves when θ varied from 0° to 90° with p=0. (b) Calculated group index as a function of normalized frequency.

Fig. 3.
Fig. 3.

(a) Dispersion curves for the optimized PCWs; (b) and (c) are the calculated group indices as a function of normalized frequency, and Δω presents the bandwidth of the flat band.

Fig. 4.
Fig. 4.

Ey electric field component distributions of the five optimized PCWs when the wavevector is fixed at k=0.44(2π/a). (a) θ=0 and p=0, (b) θ=35° and p=0, (c) θ=55° and p=0.03a, (d) θ=65° and p=0.05a, and (e) θ=75° and p=0.06a.

Fig. 5.
Fig. 5.

GVD relation of the slow-light PCWs when the group indices are nominally constant with (a) ng=46, (b) ng=63, (c) ng=78, and (d) ng=100.

Fig. 6.
Fig. 6.

Time-domain optical pulse propagation in the slow-light PCW when the group indices are nominally constant with (a) ng=46 and (b) ng=63.

Fig. 7.
Fig. 7.

Dispersion curves of the three PCWs with different parameters. Band 23 is the slow-light band for engineering, and band 22 is the band just below it. The anticrossing points for different PCWs are denoted by A, B, and C.

Fig. 8.
Fig. 8.

(a) Group index ng as a function of the normalized frequency with several δθ and δp. Moreover, δθ and δp denote fabrication errors relative to θ and p. (b) Group index ng as a function of the normalized frequency with several δA and δB. Here, δA and δB denote fabrication errors relative to A and B.

Fig. 9.
Fig. 9.

Group index spectra of the 3D slow-light photonic structure.

Tables (1)

Tables Icon

Table 1. Group Index, GBP, and Bandwidth under Different Optimized Shifting Parameters and Comparison between this Paper and Reference Papers

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