Control of dispersion in photonic crystal waveguides using group symmetry theory

Pierre Colman; Sylvain Combrié; Gaëlle Lehoucq; Alfredo De Rossi

doi:10.1364/OE.20.013108

Control of dispersion in photonic crystal waveguides using group symmetry theory

Pierre Colman, Sylvain Combrié, Gaëlle Lehoucq, and Alfredo De Rossi

Optics Express
Vol. 20,
Issue 12,
pp. 13108-13114
(2012)
•https://doi.org/10.1364/OE.20.013108

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Pierre Colman, Sylvain Combrié, Gaëlle Lehoucq, and Alfredo De Rossi, "Control of dispersion in photonic crystal waveguides using group symmetry theory," Opt. Express 20, 13108-13114 (2012)

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Related Topics
Table of Contents Category
- Photonic Crystals and Devices
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Integrated optics devices (130.3120)
- Photonic crystal waveguides (130.5296)
- Dispersion (260.2030)

About this Article
History
- Original Manuscript: March 7, 2012
- Revised Manuscript: April 12, 2012
- Manuscript Accepted: April 12, 2012
- Published: May 25, 2012

Accessible

Open Access

Abstract

We demonstrate dispersion tailoring by coupling the even and the odd modes in a line-defect photonic crystal waveguide. Coupling is determined ab-initio using group theory analysis, rather than by trial-error optimisation of the design parameters. A family of dispersion curves is generated by controlling a single geometrical parameter. This concept is demonstrated experimentally with very good agreement with theory.

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References

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|
Author
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Publication

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
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[Crossref] [PubMed]
O. Khayam and H. Benisty, “General recipe for flatbands in photonic crystalwaveguides,” Opt. Express 17, 14634–14648 (2009).
[Crossref] [PubMed]
J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[Crossref] [PubMed]
D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]
A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Sel. Area. Commun. 23, 1396–1401 (2005).
[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] [PubMed]
Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34, 1072–1074 (2009).
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A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
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S. Lü, J. Zhao, and D. Zhang, “Flat band slow light in asymmetric photonic crystal waveguide based on microfluidic infiltration,” Appl. Opt. 49, 3930–3934 (2010).
[Crossref] [PubMed]
X. Mao, Y. Huang, W. Zhang, and J. Peng, “Coupling between even- and oddlike modes in a single asymmetric photonic crystal waveguide,” Appl. Phys. Lett. 95, 183106 (2009).
[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]
N. Gutman, W. Dupree, Y. Sun, A. Sukhorukov, and C. de Sterke, “Frozen and broadband slow light in coupled periodic nanowire waveguides,” Opt. Express 20, 3519–3528 (2012).
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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).
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O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” Phys. Rev. B 68, 035110 (2003).
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[Crossref]
A. Parini, P. Hamel, A. De Rossi, S. Combrie, N.-V.-Q. Tran, Y. Gottesman, R. Gabet, A. Talneau, Y. Jaouen, and G. Vadala, “Time-wavelength reflectance maps of photonic crystal waveguides: a new view on disorder-induced scattering,” J. Lightwave Technol. 26, 3794–3802 (2008).
[Crossref]
Q. V. Tran, S. Combrié, P. Colman, and A. D. Rossi, “Photonic crystal membrane waveguides with low insertion losses,” Appl. Phys. Lett. 95, 061105 (2009).
[Crossref]
Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]
A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
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A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. Ó Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “On-chip tunable delay lines in silicon photonics,” IEE Photon. J. 2, 181–194 (2010).
[Crossref]
S. Schultz, L. O’Faolain, D. 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]
P. Colman, S. Combrié, I. Cestier, A. Willinger, G. Eisenstein, A. de Rossi, and G. Lehoucq, “Observation of gain due to four-wave-mixing in dispersion engineered GaInP photonic crystal waveguides,” Opt. Lett. 36, 2629–2631 (2011).
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A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. Ó Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “On-chip tunable delay lines in silicon photonics,” IEE Photon. J. 2, 181–194 (2010).
[Crossref]

S. Schultz, L. O’Faolain, D. 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]

2009 (6)

Q. V. Tran, S. Combrié, P. Colman, and A. D. Rossi, “Photonic crystal membrane waveguides with low insertion losses,” Appl. Phys. Lett. 95, 061105 (2009).
[Crossref]

X. Mao, Y. Huang, W. Zhang, and J. Peng, “Coupling between even- and oddlike modes in a single asymmetric photonic crystal waveguide,” Appl. Phys. Lett. 95, 183106 (2009).
[Crossref]

M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams, “Broadband purcell factor enhancements in photonic-crystal ridge waveguides,” Phys. Rev. B 80, 125307 (2009).
[Crossref]

S. Combrié, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, “High quality gainp nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009).
[Crossref]

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34, 1072–1074 (2009).
[Crossref] [PubMed]

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

2008 (5)

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] [PubMed]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[Crossref]

A. Parini, P. Hamel, A. De Rossi, S. Combrie, N.-V.-Q. Tran, Y. Gottesman, R. Gabet, A. Talneau, Y. Jaouen, and G. Vadala, “Time-wavelength reflectance maps of photonic crystal waveguides: a new view on disorder-induced scattering,” J. Lightwave Technol. 26, 3794–3802 (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]

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

2006 (2)

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).
[Crossref] [PubMed]

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]

2005 (1)

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Sel. Area. Commun. 23, 1396–1401 (2005).
[Crossref]

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]

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]

2003 (2)

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[Crossref] [PubMed]

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” Phys. Rev. B 68, 035110 (2003).
[Crossref]

2001 (1)

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]

Agrawal, G. P.

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).
[Crossref] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

Baba, T.

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]

Beggs, D.

S. Schultz, L. O’Faolain, D. 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]

Benisty, H.

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

Borel, P. I.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

Canciamilla, A.

Cestier, I.

Colman, P.

S. Combrié, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, “High quality gainp nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009).
[Crossref]

Q. V. Tran, S. Combrié, P. Colman, and A. D. Rossi, “Photonic crystal membrane waveguides with low insertion losses,” Appl. Phys. Lett. 95, 061105 (2009).
[Crossref]

Combrie, S.

Combrié, S.

S. Combrié, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, “High quality gainp nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009).
[Crossref]

Q. V. Tran, S. Combrié, P. Colman, and A. D. Rossi, “Photonic crystal membrane waveguides with low insertion losses,” Appl. Phys. Lett. 95, 061105 (2009).
[Crossref]

Dalacu, D.

M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams, “Broadband purcell factor enhancements in photonic-crystal ridge waveguides,” Phys. Rev. B 80, 125307 (2009).
[Crossref]

De La Rue, R.

de Rossi, A.

de Sterke, C.

N. Gutman, W. Dupree, Y. Sun, A. Sukhorukov, and C. de Sterke, “Frozen and broadband slow light in coupled periodic nanowire waveguides,” Opt. Express 20, 3519–3528 (2012).
[Crossref] [PubMed]

Dupree, W.

N. Gutman, W. Dupree, Y. Sun, A. Sukhorukov, and C. de Sterke, “Frozen and broadband slow light in coupled periodic nanowire waveguides,” Opt. Express 20, 3519–3528 (2012).
[Crossref] [PubMed]

Eich, M.

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Sel. Area. Commun. 23, 1396–1401 (2005).
[Crossref]

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

Eisenstein, G.

Fage-Pedersen, J.

Ferrari, C.

Frandsen, L. H.

Gabet, R.

Gomez-Iglesias, A.

Gottesman, Y.

Green, W.

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

Gutman, N.

N. Gutman, W. Dupree, Y. Sun, A. Sukhorukov, and C. de Sterke, “Frozen and broadband slow light in coupled periodic nanowire waveguides,” Opt. Express 20, 3519–3528 (2012).
[Crossref] [PubMed]

Hamachi, Y.

Hamel, P.

Huang, Y.

X. Mao, Y. Huang, W. Zhang, and J. Peng, “Coupling between even- and oddlike modes in a single asymmetric photonic crystal waveguide,” Appl. Phys. Lett. 95, 183106 (2009).
[Crossref]

Hughes, S.

M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams, “Broadband purcell factor enhancements in photonic-crystal ridge waveguides,” Phys. Rev. B 80, 125307 (2009).
[Crossref]

Husko, C.

S. Combrié, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, “High quality gainp nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009).
[Crossref]

Jaouen, Y.

Jiang, C.

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]

Joannopoulos, J. D.

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]

Johnson, S. G.

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]

Kakitsuka, T.

Khayam, O.

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

Knight, J. C.

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[Crossref] [PubMed]

Krauss, T. F.

S. Schultz, L. O’Faolain, D. 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]

Kubo, S.

Kuramochi, E.

Lavrinenko, A. V.

Lehoucq, G.

Li, J.

Lin, Q.

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).
[Crossref] [PubMed]

Lü, S.

S. Lü, J. Zhao, and D. Zhang, “Flat band slow light in asymmetric photonic crystal waveguide based on microfluidic infiltration,” Appl. Opt. 49, 3930–3934 (2010).
[Crossref] [PubMed]

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]

Mao, X.

X. Mao, Y. Huang, W. Zhang, and J. Peng, “Coupling between even- and oddlike modes in a single asymmetric photonic crystal waveguide,” Appl. Phys. Lett. 95, 183106 (2009).
[Crossref]

Matsuo, S.

Melloni, A.

S. Schultz, L. O’Faolain, D. 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]

Mori, D.

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]

Morichetti, F.

Notomi, M.

Ó Faolain, L.

O’Faolain, L.

S. Schultz, L. O’Faolain, D. 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]

Painter, O.

Parini, A.

Patterson, M.

M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams, “Broadband purcell factor enhancements in photonic-crystal ridge waveguides,” Phys. Rev. B 80, 125307 (2009).
[Crossref]

Peng, J.

X. Mao, Y. Huang, W. Zhang, and J. Peng, “Coupling between even- and oddlike modes in a single asymmetric photonic crystal waveguide,” Appl. Phys. Lett. 95, 183106 (2009).
[Crossref]

Petrov, A.

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Sel. Area. Commun. 23, 1396–1401 (2005).
[Crossref]

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]

Rossi, A. D.

S. Combrié, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, “High quality gainp nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009).
[Crossref]

Q. V. Tran, S. Combrié, P. Colman, and A. D. Rossi, “Photonic crystal membrane waveguides with low insertion losses,” Appl. Phys. Lett. 95, 061105 (2009).
[Crossref]

Samarelli, A.

Sato, T.

Schultz, S.

S. Schultz, L. O’Faolain, D. 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]

Shinya, A.

Sorel, M.

Srinivasan, K.

Sukhorukov, A.

N. Gutman, W. Dupree, Y. Sun, A. Sukhorukov, and C. de Sterke, “Frozen and broadband slow light in coupled periodic nanowire waveguides,” Opt. Express 20, 3519–3528 (2012).
[Crossref] [PubMed]

Sun, Y.

N. Gutman, W. Dupree, Y. Sun, A. Sukhorukov, and C. de Sterke, “Frozen and broadband slow light in coupled periodic nanowire waveguides,” Opt. Express 20, 3519–3528 (2012).
[Crossref] [PubMed]

Talneau, A.

Tanabe, T.

Tran, N.-V.-Q.

Tran, Q. V.

Q. V. Tran, S. Combrié, P. Colman, and A. D. Rossi, “Photonic crystal membrane waveguides with low insertion losses,” Appl. Phys. Lett. 95, 061105 (2009).
[Crossref]

S. Combrié, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, “High quality gainp nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009).
[Crossref]

Vadala, G.

Vlasov, Y.

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

White, T. P.

S. Schultz, L. O’Faolain, D. 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]

Williams, R. L.

M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams, “Broadband purcell factor enhancements in photonic-crystal ridge waveguides,” Phys. Rev. B 80, 125307 (2009).
[Crossref]

Willinger, A.

Xia, F.

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

Yin, L.

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).
[Crossref] [PubMed]

Yosia,

Zhang, D.

S. Lü, J. Zhao, and D. Zhang, “Flat band slow light in asymmetric photonic crystal waveguide based on microfluidic infiltration,” Appl. Opt. 49, 3930–3934 (2010).
[Crossref] [PubMed]

Zhang, W.

X. Mao, Y. Huang, W. Zhang, and J. Peng, “Coupling between even- and oddlike modes in a single asymmetric photonic crystal waveguide,” Appl. Phys. Lett. 95, 183106 (2009).
[Crossref]

Zhao, J.

S. Lü, J. Zhao, and D. Zhang, “Flat band slow light in asymmetric photonic crystal waveguide based on microfluidic infiltration,” Appl. Opt. 49, 3930–3934 (2010).
[Crossref] [PubMed]

Appl. Opt. (1)

S. Lü, J. Zhao, and D. Zhang, “Flat band slow light in asymmetric photonic crystal waveguide based on microfluidic infiltration,” Appl. Opt. 49, 3930–3934 (2010).
[Crossref] [PubMed]

Appl. Phys. Lett. (5)

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]

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

X. Mao, Y. Huang, W. Zhang, and J. Peng, “Coupling between even- and oddlike modes in a single asymmetric photonic crystal waveguide,” Appl. Phys. Lett. 95, 183106 (2009).
[Crossref]

S. Combrié, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, “High quality gainp nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009).
[Crossref]

Q. V. Tran, S. Combrié, P. Colman, and A. D. Rossi, “Photonic crystal membrane waveguides with low insertion losses,” Appl. Phys. Lett. 95, 061105 (2009).
[Crossref]

IEE Photon. J. (1)

IEEE J. Sel. Area. Commun. (1)

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Sel. Area. Commun. 23, 1396–1401 (2005).
[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).
[Crossref]

J. Lightwave Technol (1)

J. Opt. (1)

S. Schultz, L. O’Faolain, D. 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]

Nat. Photonics (1)

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[Crossref]

Nature (1)

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Fig. 1 PhC waveguide without (a) and with (b) perturbation. (c) Corresponding band diagram of the initial (perturbed) structure in black (red) line. The cyan markers indicate the modes for which the field distribution is shown in Figs. 2(a) and 2(b). The thin blue line corresponds to the dispersion obtained for a different perturbation as discussed in Fig. 2(d).

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Fig. 2 Spatial distribution of the H_z-field, calculated at K=0.445, (a) Even mode and Odd mode. (b) even-like and odd-like mode for a dielectric perturbatation as presented in (c). (c) Calculated |γ_ee|, |γ_oo| and |γ_eo| coefficients for T=0.15a. Inset : corresponding Δε and its dominant symmetry (colors refers to opposite signs). (d) Idem as (c) but holes are moved in the same direction so the symmetry of Δε is now B₁ instead of A₂.

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Fig. 3 (a) Group index dependence as a function of the wavelength calculated for T= 0.05a, 0.1a, 0.2a. (b) Corresponding measured dispersion. The lattice period is a = 465nm.

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Tables (1)

Table 1 C2v point group symmetry table

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Equations (5)

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| \begin{matrix} ω_{w g {1}} (k) & γ (k) \\ γ^{*} (k) & ω_{w g {2}} (k) \end{matrix} |

| \begin{matrix} ω_{odd} (k) & γ_{o e} (k) & γ_{o s} (k) \\ γ_{o e}^{*} (k) & ω_{even} (k) & γ_{e s} (k) \\ γ_{o s}^{*} (k) & γ_{e s}^{*} (k) & ω_{substrate} (k) \end{matrix} |

γ_{o e} (k) = \iint {\vec{E}}_{odd}^{*} (\vec{r}) \cdot Δ ε (\vec{r}) \cdot {\vec{E}}_{even} (\vec{r}) d \vec{r}

\begin{array}{r} γ_{o o} (k) = \iint {\vec{E}}_{odd}^{*} (\vec{r}) \cdot Δ ε (\vec{r}) \cdot {\vec{E}}_{odd} (\vec{r}) d \vec{r} \\ γ_{e e} (k) = \iint {\vec{E}}_{even}^{*} (\vec{r}) \cdot Δ ε (\vec{r}) \cdot {\vec{E}}_{even} (\vec{r}) d \vec{r} \\ γ_{s s} (k) = \iint {\vec{E}}_{substrate}^{*} (\vec{r}) \cdot Δ ε (\vec{r}) \cdot {\vec{E}}_{substrate} (\vec{r}) d \vec{r} \\ γ_{o s} (k) = \iint {\vec{E}}_{odd}^{*} (\vec{r}) \cdot Δ ε (\vec{r}) \cdot {\vec{E}}_{substrate} (\vec{r}) d \vec{r} \\ γ_{e s} (k) = \iint {\vec{E}}_{even}^{*} (\vec{r}) \cdot Δ ε (\vec{r}) \cdot {\vec{E}}_{substrate} (\vec{r}) d \vec{r} \end{array}

A_{1} = B_{2} \otimes X \otimes B_{1}

	E	C₂ (z)	σ_v (xz)	σ_v (yz)

A₁	1	1	1	1
A₂	1	1	−1	−1
B₁	1	−1	1	−1
B₂	1	−1	−1	1

A₂ ⊗ A₂	1	1	1	1	=A₁
B₁ ⊗ B₂	1	1	−1	−1	=A₂

Abstract

References

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2009 (6)

2008 (5)

2006 (2)

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