Abstract

An efficient numerical scheme developed on the basis of Green’s function method is applied to the investigation of structural effects on the performance of planar grated waveguide at the first resonance wavelengths next to the band-edges. Restricting ourselves to the transverse-electric waves, this study is focused on the effects induced by variations of the grating cell number and the depths of its four outer grooves on both sides. The different patterns of groove depth gradation or apodization considered in this study are all characterized by decreasing depth toward the ends while retaining the longitudinal grating symmetry. The effects of the modifications are expressed in terms of changes in the modal transmittance, reflectance, and out-of-plane scattering loss as well as the group velocity and resonant field enhancement. The most favorable result characterized by 15% transmittance enhancement and 85% loss reduction is achieved for the case with the most gradual changes in the groove depth. It is further shown that, for the investigated range of parameters, both the group velocity and field enhancement can best be improved by increasing the length of the uniform grating, without introducing any modification.

© 2010 Optical Society of America

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2010 (2)

T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, “Asymmetric Mach–Zehnder filter based on self-collimation phenomenon in two-dimensional photonic crystals,” Opt. Express 18, 5384–5389 (2010).
[Crossref] [PubMed]

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[Crossref]

2008 (1)

2007 (2)

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. De Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” Opt. Quantum Electron. 38, 799–813 (2007).
[Crossref]

M. R. Lee and P. M. Fauchet, “Two-dimensional silicon photonic crystal based biosensing platform for protein detection,” Opt. Express 15, 4530–4535 (2007).
[Crossref] [PubMed]

2006 (4)

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[Crossref]

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

S. Noda, “Recent progresses and future prospects of two- and three-dimensional photonic crystals,” J. Lightwave Technol. 24, 4554–4567 (2006).
[Crossref]

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. 38, 123–131 (2006).
[Crossref]

2005 (2)

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. De Angelis, C. R. Stanley, H. M. Van Driel, and J. S. Aitchison, “Design, fabrication, and characterization of deep-etched waveguide gratings,” J. Lightwave Technol. 23, 3832–3842 (2005).
[Crossref]

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

2004 (3)

2003 (1)

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

2002 (1)

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

2001 (2)

M. Paulus and O. J. F. Martin, “Green’s tensor technique for scattering in two dimensional stratified media,” Phys. Rev. E 63, 066615 (2001).
[Crossref]

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

2000 (2)

E. Yablonovitch, “How to be truly photonic,” Science 289, 557–559 (2000).
[Crossref]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

1999 (3)

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[Crossref]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdr’e, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[Crossref]

1998 (3)

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

1995 (1)

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, 1995).

Aitchison, J. S.

Badding, J. V.

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

Baets, R.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Baril, N. F.

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Benisty, H.

Bientsman, P.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Borel, P.

Capasso, F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Cassagne, D.

Cho, A. Y.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Chong, H.

Colombelli, R.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Ctyroký, J.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

De Angelis, C.

De La Rue, R. M.

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdr’e, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[Crossref]

De Ridder, R. M.

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. De Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” Opt. Quantum Electron. 38, 799–813 (2007).
[Crossref]

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Dekker, R.

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. De Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” Opt. Quantum Electron. 38, 799–813 (2007).
[Crossref]

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

Destouches, N.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. 38, 123–131 (2006).
[Crossref]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Driessen, A.

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

Elson, J. M.

Engbers, W. F. A.

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Fauchet, P. M.

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[Crossref]

Fonjallaz, P. -Y.

Frandsen, L.

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

Gmachl, C. F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Halterman, K.

Harpøth, A.

Healy, N.

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

Helfert, S.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Hoekstra, H. J. W. M.

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. De Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” Opt. Quantum Electron. 38, 799–813 (2007).
[Crossref]

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

Hopman, W. C. L.

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. De Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” Opt. Quantum Electron. 38, 799–813 (2007).
[Crossref]

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

Houdr’e, R.

Huang, W. -P.

Hugonin, J. -P.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Imada, M.

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[Crossref]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, 1995).

Jouanin, C.

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

Kautz, J.

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. De Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” Opt. Quantum Electron. 38, 799–813 (2007).
[Crossref]

Kawashima, S.

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[Crossref]

Kee, C. -S.

Kim, J. -E.

Kim, T. -T.

Klaasse, G.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Kleckner, T. C.

Krauss, T. F.

Kristensen, M.

Kuramochi, E.

Labilloy, D.

Lagonigro, L.

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

Lalanne, P.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Lambeck, P. V.

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

Lavrinenko, A.

Lee, L. H.

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[Crossref]

Lee, M. R.

Lee, S. -G.

Linden, S.

Locatelli, A.

Martin, O. J. F.

M. Paulus and O. J. F. Martin, “Green’s tensor technique for scattering in two dimensional stratified media,” Phys. Rev. E 63, 066615 (2001).
[Crossref]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[Crossref]

Meade, R.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, 1995).

Mitsugi, S.

Modotto, D.

Mondia, J. P.

Morandotti, R.

Mu, J. -W.

Muriel, M. A.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[Crossref]

Niemi, T.

Noda, S.

S. Noda, “Recent progresses and future prospects of two- and three-dimensional photonic crystals,” J. Lightwave Technol. 24, 4554–4567 (2006).
[Crossref]

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[Crossref]

Notomi, M.

Oesterle, U.

Okano, M.

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[Crossref]

Painter, O.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Park, H. Y.

Parriaux, O.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. 38, 123–131 (2006).
[Crossref]

Paulus, M.

M. Paulus and O. J. F. Martin, “Green’s tensor technique for scattering in two dimensional stratified media,” Phys. Rev. E 63, 066615 (2001).
[Crossref]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

Peacock, A. C.

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

Petracek, J.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Piller, N. B.

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[Crossref]

Pottier, P.

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

Pregla, R.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Rattier, M.

Risvik, K. M.

Ryu, H. Y.

Sahlgren, B.

Sazio, P. J. A.

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

Scalora, M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Sergent, A. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Shinya, A.

Sider, B.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. 38, 123–131 (2006).
[Crossref]

Sivco, D. L.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Skaar, J.

Smith, C. J. M.

Sparks, J. R.

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

Srinivasan, K.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Stanley, C. R.

Stoffer, R.

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Storøy, H.

Stubbe, R.

Tennant, D. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Thorhauge, M.

Tishchenko, A. V.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. 38, 123–131 (2006).
[Crossref]

Troccoli, M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Van Driel, H. M.

Van Lith, J.

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

Weisbuch, C.

Winn, J.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, 1995).

Yablonovitch, E.

E. Yablonovitch, “How to be truly photonic,” Science 289, 557–559 (2000).
[Crossref]

Yudistira, D.

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[Crossref]

Zhang, H.

Appl. Phys. Lett. (2)

L. Lagonigro, N. Healy, J. R. Sparks, N. F. Baril, P. J. A. Sazio, J. V. Badding, and A. C. Peacock, “Low loss silicon fibers for photonics applications,” Appl. Phys. Lett. 96, 041105 (2010).
[Crossref]

M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006).
[Crossref]

IEEE J. Quantum Electron. (2)

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[Crossref]

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

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

W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11, 11–16 (2005).
[Crossref]

IEEE Photon. Technol. Lett. (1)

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. de Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18, 1855–1857 (2006).
[Crossref]

J. Lightwave Technol. (5)

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Opt. Quantum Electron. (3)

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. 38, 123–131 (2006).
[Crossref]

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. De Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” Opt. Quantum Electron. 38, 799–813 (2007).
[Crossref]

J. Čtyroký, S. Helfert, R. Pregla, P. Bientsman, R. Baets, R. M. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J.-P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34, 455–470 (2002).
[Crossref]

Phys. Rev. E (4)

M. Paulus and O. J. F. Martin, “Green’s tensor technique for scattering in two dimensional stratified media,” Phys. Rev. E 63, 066615 (2001).
[Crossref]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[Crossref]

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Science (2)

E. Yablonovitch, “How to be truly photonic,” Science 289, 557–559 (2000).
[Crossref]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302, 1374–1377 (2003).
[Crossref] [PubMed]

Other (2)

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, 1995).

Cited By

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Figures (7)

Fig. 1
Fig. 1

Basic uniform GWg.

Fig. 2
Fig. 2

GWg structures considered with the modifications at the edge described by the aggregate groove-depth parameters ( g 1 , g 2 , g 3 , g 4 ) and the number of teeth N in the core section.

Fig. 3
Fig. 3

Calculated spectral profiles of T ( λ ) (dashed-line), R ( λ ) (dotted-line), and L ( λ ) (solid-line) presented for the GWg structures of (a) no. 1, (b) no. 6, and (c) no. 12 with N = 8 , as specified in the text. The solid dots indicate the position of resonance wavelength.

Fig. 4
Fig. 4

Variations of resonance wavelength showing the qualitatively different and generally opposite trends of shift with respect to structural variation from no. 1 to no. 12 for N = 8 (black circles), 10 (red squares), and 13 (blue diamonds) at left (a) and (b) right.

Fig. 5
Fig. 5

Variations of (a) T, (b) R, and (c) L at left resonances (left panels) and right resonances (right panels) for N = 8 (black circles), 10 (red squares), and 12 (blue diamonds). Note the consistently flat responses to structural changes of R (b) on the right panel as compared to the relatively complicated albeit consistent responses shown on the corresponding left panel for different N’s.

Fig. 6
Fig. 6

Variations of (a) T, (b) R, and (c) L at left resonances (left panels) and at right resonances (right panels) with respect to modifications in the sequence marked by edge grating parameters: 1 . (0, 0, 0, 80) nm, 2 . (0, 0, 60, 80) nm, 3 . (0, 60, 60, 80) nm, and 4 . (40, 60, 60, 80) nm in increasing smoothness of the { g i } gradation.

Fig. 7
Fig. 7

Comparisons between structure-variation-induced changes in at left resonances (left panels) and right resonances (right panels) of (a) the normalized group velocity and (b) the effect of energy confinement, W, for N = 8 (black circles), 10 (red squares), and 12 (blue diamonds).

Tables (1)

Tables Icon

Table 1 Modified Edge Grating Structures Corresponding to Aggregate Groove-Depth Parameters and the Associated Serial Numbers for the Resulting Structures

Equations (26)

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G ( r , r ) = G B ( r , r ) + A G B ( r , r ) k 0 2 Δ ε ( r ) G ( r , r ) d A ,
G l B ( r , r ) = i 4 π d k x   exp [ i k x ( x x ) ] m l ( k x ; y , y ) ,
m l = k x 2 k l , y [ A l ( y , y ) exp ( i k l , y y ) + B l ( y , y ) exp ( i k l , y y ) ] ,
A 1 I = exp ( i k 1 , y h ) [ f 1 , 2 + f 2 , 3   exp ( 2 i k 2 , y h ) 1 + f 1 , 2 f 2 , 3   exp ( 2 i k 2 , y h ) ] exp ( i k 1 , y y ) ,
A 1 D = Θ ( y y ) exp ( i k 1 , y y ) ,
B 1 I = 0 ,
B 1 D = Θ ( y y ) exp ( i k 1 , y y ) ,
A 2 I = f 2 , 3   exp ( i k 2 , y h ) 1 f 2 , 1 f 2 , 3   exp ( 2 i k 2 , z h ) [ f 2 , 1   exp ( i k 2 , y h ) exp ( i k 2 , y y ) + exp ( i k 2 , y y ) ] ,
A 2 D = Θ ( y y ) exp ( i k 2 , y y ) ,
B 2 I = f 2 , 1   exp ( i k 2 , y h ) 1 f 2 , 1 f 2 , 3   exp ( 2 i k 2 , y h ) [ f 2 , 3   exp ( i k 2 , y h ) exp ( i k 2 , y y ) + exp ( i k 2 , y y ) ] ,
B 2 D = Θ ( y y ) exp ( i k 2 , y y ) ,
A 3 I = 0 ,
A 3 D = Θ ( y y ) exp ( i k 3 , y y ) ,
B 3 I = exp ( i k 3 , y h ) [ f 3 , 2 + f 2 , 1   exp ( 2 i k 2 , y h ) 1 + f 3 , 2 f 2 , 1   exp ( 2 i k 2 , y h ) ] exp ( i k 3 , y y ) ,
B 3 D = Θ ( y y ) exp ( i k 3 , y y ) ,
( A l B l ) = γ y > y ( exp [ i d l ( k l + 1 , y k l , y ) ] f l , l + 1   exp [ i d l ( k l + 1 , y + k l , y ) ] f l , l + 1   exp [ i d l ( k l + 1 , y + k l , y ) ] exp [ i d l ( k l + 1 , y k l , y ) ] ) ( A l + 1 B l + 1 ) ,
( A l B l ) = γ y < y ( exp [ i d l 1 ( k l 1 , y k l , y ) ] f l , l 1   exp [ i d l ( k l 1 , y + k l , y ) ] f l , l 1   exp [ i d l 1 ( k l + 1 , y + k l , y ) ] exp [ i d l 1 ( k l 1 , y k l , y ) ] ) ( A l 1 B l 1 ) ,
f l , l ± 1 = k l , y k l ± 1 , y k l , y + k l ± 1 , y .
G i j = G i j B + i = 1 , j = 1 , i k , j k P G i k B k 0 2 Δ ε k Δ A k G k j + M i k 0 2 Δ ε i G i j L Δ ε i ε B G i j ,
E z ( r ) = E z B ( r ) + A G ( r , r ) k 0 2 Δ ε ( r ) E z B ( r ) d r ,
T = 0 h | E z ( x t , y ; λ ) | 2 d y 0 h | E z , 0 ( x i , y ; λ ) | 2 d y ,
R = 0 h | E z ( x i , y ; λ ) E z , 0 ( x i , y ; λ ) | 2 d y 0 h | E z , 0 ( x i , y ; λ ) | 2 d y ,
L = 1 T R .
v g c = 2 π L G λ 2 d ϕ / d λ .
t = 0 h E z ( x R , y ; λ ) d y 0 h E z , 0 ( x L , y ; λ ) d y ,
W = A ε slab | E | 2 d A ,

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