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.

© 2012 OSA

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  13. 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).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. 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).
    [CrossRef] [PubMed]

2012

2011

2010

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]

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]

2009

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. B80, 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]

O. Khayam and H. Benisty, “General recipe for flatbands in photonic crystalwaveguides,” Opt. Express17, 14634–14648 (2009).
[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).
[CrossRef] [PubMed]

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]

2008

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics2, 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. Express16, 19382–19387 (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. Express16, 6227–6232 (2008).
[CrossRef] [PubMed]

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]

2006

2005

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

2004

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]

2003

J. C. Knight, “Photonic crystal fibres,” Nature424, 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. B68, 035110 (2003).
[CrossRef]

2001

Agrawal, G. P.

Baba, T.

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]

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.

Borel, P. I.

Boyd, R. W.

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

Canciamilla, A.

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]

Cestier, I.

Colman, P.

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).
[CrossRef] [PubMed]

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.

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]

Combrié, S.

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).
[CrossRef] [PubMed]

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. B80, 125307 (2009).
[CrossRef]

De La Rue, R.

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]

de Rossi, A.

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).
[CrossRef] [PubMed]

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]

de Sterke, C.

Dupree, W.

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.

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]

Frandsen, L. H.

Gabet, R.

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]

Gomez-Iglesias, A.

Gottesman, Y.

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]

Green, W.

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics2, 242–246 (2008).
[CrossRef]

Gutman, N.

Hamachi, Y.

Hamel, P.

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]

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. B80, 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.

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]

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.

Johnson, S. G.

Kakitsuka, T.

Khayam, O.

Knight, J. C.

J. C. Knight, “Photonic crystal fibres,” Nature424, 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]

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]

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. Express16, 6227–6232 (2008).
[CrossRef] [PubMed]

Kubo, S.

Kuramochi, E.

Lavrinenko, A. V.

Lehoucq, G.

Li, J.

Lin, Q.

Lü, S.

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.

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]

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.

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]

Notomi, M.

Ó Faolain, L.

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]

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]

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. Express16, 6227–6232 (2008).
[CrossRef] [PubMed]

Painter, O.

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” Phys. Rev. B68, 035110 (2003).
[CrossRef]

Parini, A.

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]

Patterson, M.

M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams, “Broadband purcell factor enhancements in photonic-crystal ridge waveguides,” Phys. Rev. B80, 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.

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]

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.

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]

Srinivasan, K.

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” Phys. Rev. B68, 035110 (2003).
[CrossRef]

Sukhorukov, A.

Sun, Y.

Talneau, A.

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]

Tanabe, T.

Tran, N.-V.-Q.

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]

Tran, Q. V.

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]

Vadala, G.

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]

Vlasov, Y.

Y. Vlasov, W. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics2, 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]

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Figures (3)

Fig. 1
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).

Fig. 2
Fig. 2

Spatial distribution of the Hz-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 |γee|, |γoo| and |γeo| 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.

Fig. 3
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.

Tables (1)

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Table 1 C2v point group symmetry table

Equations (5)

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| ω w g { 1 } ( k ) γ ( k ) γ * ( k ) ω w g { 2 } ( k ) |
| 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 ) |
γ o e ( k ) = E odd * ( r ) Δ ε ( r ) E even ( r ) d r
γ o o ( k ) = E odd * ( r ) Δ ε ( r ) E odd ( r ) d r γ e e ( k ) = E even * ( r ) Δ ε ( r ) E even ( r ) d r γ s s ( k ) = E substrate * ( r ) Δ ε ( r ) E substrate ( r ) d r γ o s ( k ) = E odd * ( r ) Δ ε ( r ) E substrate ( r ) d r γ e s ( k ) = E even * ( r ) Δ ε ( r ) E substrate ( r ) d r
A 1 = B 2 X B 1

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