Abstract

Resonances near regular photonic band edges are limited by quality factors that scale only to the third power of the number of periods. In contrast, resonances near degenerate photonic band edges can scale to the fifth power of the number periods, yielding a route to significant device miniaturization. For applications in silicon integrated photonics, we present the design and analysis of zero-coupling-gap degenerate band edge resonators. Complex band diagrams are computed for the unit cell with periodic boundary conditions that convey characteristics of propagating and evanescent modes. Dispersion features of the band diagram are used to describe changes in resonance scaling in finite length resonators. Resonators with non-zero and zero coupling gap are compared. Analysis of quality factor and resonance frequency indicates significant reduction in the number of periods required to observe fifth power scaling when degenerate band edge resonators are realized with zero-coupling-gap. High transmission is achieved by optimizing the waveguide feed to the resonator. Compact band edge cavities with large optical field distribution are envisioned for light emitters, switches, and sensors.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (1)

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

2013 (3)

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

J. R. Burr, N. Gutman, C. M. de Sterke, I. Vitebskiy, and R. M. Reano, “Degenerate band edge resonances in coupled periodic silicon optical waveguides,” Opt. Express 21(7), 8736–8745 (2013).
[Crossref] [PubMed]

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

2012 (2)

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

N. Gutman, C. Martijn de Sterke, A. A. Sukhorukov, and L. C. Botten, “Slow and frozen light in optical waveguides with multiple gratings: Degenerate band edges and stationary inflection points,” Phys. Rev. A 85(3), 033804 (2012).
[Crossref]

2011 (6)

2010 (1)

2009 (2)

2008 (3)

2007 (2)

2006 (2)

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066613 (2006).
[Crossref] [PubMed]

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

2005 (2)

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036619 (2005).
[Crossref] [PubMed]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

2001 (1)

1994 (2)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

Ahn, B.-H.

Ahn, S.

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

Akahane, Y.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Andreani, L. C.

Asano, T.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Baba, T.

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011).
[Crossref] [PubMed]

Bauer, J.

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994).
[Crossref] [PubMed]

Botten, L. C.

N. Gutman, C. Martijn de Sterke, A. A. Sukhorukov, and L. C. Botten, “Slow and frozen light in optical waveguides with multiple gratings: Degenerate band edges and stationary inflection points,” Phys. Rev. A 85(3), 033804 (2012).
[Crossref]

N. Gutman, L. C. Botten, A. A. Sukhorukov, and C. M. de Sterke, “Degenerate band edges in optical fiber with multiple grating: efficient coupling to slow light,” Opt. Lett. 36(16), 3257–3259 (2011).
[Crossref] [PubMed]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994).
[Crossref] [PubMed]

Boyd, R.

Burr, J. R.

Chigrin, D. N.

De La Rue, R. M.

de Sterke, C. M.

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994).
[Crossref] [PubMed]

Fietz, C.

Figotin, A.

A. Figotin and I. Vitebskiy, “Slow wave phenomena in photonic crystals,” Laser Photonics Rev. 5(2), 201–213 (2011).
[Crossref]

A. Figotin and I. Vitebskiy, “Slow-wave resonance in periodic stacks of anisotropic layers,” Phys. Rev. A 76(5), 053839 (2007).
[Crossref]

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066613 (2006).
[Crossref] [PubMed]

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036619 (2005).
[Crossref] [PubMed]

Fursenko, O.

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

Gutman, N.

Ha, S.

Hama, Y.

Handmer, C. J.

Hayakawa, R.

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

Hirose, K.

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

Ishikura, N.

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011).
[Crossref] [PubMed]

Jeon, H.

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

Jeong, K.-Y.

Joannopoulos, J.

Johnson, N. P.

Johnson, S.

Kawasaki, K.

Kim, J.-Y.

Kim, K. S.

Kim, S.

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

S. Kim, B.-H. Ahn, J.-Y. Kim, K.-Y. Jeong, K. S. Kim, and Y.-H. Lee, “Nanobeam photonic bandedge lasers,” Opt. Express 19(24), 24055–24060 (2011).
[Crossref] [PubMed]

Kivshar, Y. S.

Knopf, A.

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

Kondo, K.

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

Krauss, T. F.

Kuramochi, E.

Kurosaka, Y.

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

Lavrinenko, A. V.

Lee, Y.-H.

Li, J.

Liang, Y.

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

Marschmeyer, S.

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

Martijn de Sterke, C.

N. Gutman, C. Martijn de Sterke, A. A. Sukhorukov, and L. C. Botten, “Slow and frozen light in optical waveguides with multiple gratings: Degenerate band edges and stationary inflection points,” Phys. Rev. A 85(3), 033804 (2012).
[Crossref]

Min, K.

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

Nguyen, H. C.

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

Noda, S.

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Notomi, M.

O’Faolain, L.

Pelinovsky, D. E.

Powell, D. A.

Reano, R. M.

Regreny, P.

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

Roh, Y.-G.

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

Seassal, C.

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

Shadrivov, I. V.

Shinkawa, M.

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011).
[Crossref] [PubMed]

Shvets, G.

Song, B.-S.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Soref, R.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Sorel, M.

Steel, M. J.

Sugiyama, T.

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

Sukhorukov, A. A.

Sun, P.

Suzuki, K.

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011).
[Crossref] [PubMed]

Tanabe, T.

Taniyama, H.

Urzhumov, Y.

Vitebskiy, I.

J. R. Burr, N. Gutman, C. M. de Sterke, I. Vitebskiy, and R. M. Reano, “Degenerate band edge resonances in coupled periodic silicon optical waveguides,” Opt. Express 21(7), 8736–8745 (2013).
[Crossref] [PubMed]

A. Figotin and I. Vitebskiy, “Slow wave phenomena in photonic crystals,” Laser Photonics Rev. 5(2), 201–213 (2011).
[Crossref]

A. Figotin and I. Vitebskiy, “Slow-wave resonance in periodic stacks of anisotropic layers,” Phys. Rev. A 76(5), 053839 (2007).
[Crossref]

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066613 (2006).
[Crossref] [PubMed]

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036619 (2005).
[Crossref] [PubMed]

Watanabe, A.

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

White, T. P.

Winzer, G.

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

Zain, A. R.

Zimmermann, L.

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

Appl. Phys. Express (1)

S. Kim, S. Ahn, K. Min, S. Kim, H. Jeon, P. Regreny, and C. Seassal, “Nano Stepping-Stone Laser,” Appl. Phys. Express 6(4), 042703 (2013).
[Crossref]

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

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

IEICE Electron. Express (1)

T. Baba, H. C. Nguyen, N. Ishikura, K. Suzuki, M. Shinkawa, R. Hayakawa, and K. Kondo, “Photonic crystal slow light devices fabricated by CMOS-compatible process,” IEICE Electron. Express 10(10), 20132002 (2013).
[Crossref]

J. Appl. Phys. (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

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

Laser Photonics Rev. (1)

A. Figotin and I. Vitebskiy, “Slow wave phenomena in photonic crystals,” Laser Photonics Rev. 5(2), 201–213 (2011).
[Crossref]

Mater. Sci. Eng. B (1)

O. Fursenko, J. Bauer, A. Knopf, S. Marschmeyer, L. Zimmermann, and G. Winzer, “Characterization of Si nanowaveguide line edge roughness and its effect on light transmission,” Mater. Sci. Eng. B 177(10), 750–755 (2012).
[Crossref]

Nat. Mater. (1)

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Nat. Photonics (1)

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8(5), 406–411 (2014).
[Crossref]

Opt. Express (11)

S. Kim, B.-H. Ahn, J.-Y. Kim, K.-Y. Jeong, K. S. Kim, and Y.-H. Lee, “Nanobeam photonic bandedge lasers,” Opt. Express 19(24), 24055–24060 (2011).
[Crossref] [PubMed]

A. R. Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16(16), 12084–12089 (2008).
[Crossref] [PubMed]

E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y.-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18(15), 15859–15869 (2010).
[Crossref] [PubMed]

A. A. Sukhorukov, C. J. Handmer, C. M. de Sterke, and M. J. Steel, “Slow light with flat or offset band edges in few-mode fiber with two gratings,” Opt. Express 15(26), 17954–17959 (2007).
[Crossref] [PubMed]

J. R. Burr, N. Gutman, C. M. de Sterke, I. Vitebskiy, and R. M. Reano, “Degenerate band edge resonances in coupled periodic silicon optical waveguides,” Opt. Express 21(7), 8736–8745 (2013).
[Crossref] [PubMed]

M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19(22), 22208–22218 (2011).
[Crossref] [PubMed]

T. P. White, L. O’Faolain, J. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16(21), 17076–17081 (2008).
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C. Fietz, Y. Urzhumov, and G. Shvets, “Complex k band diagrams of 3D metamaterial/photonic crystals,” Opt. Express 19(20), 19027–19041 (2011).
[Crossref] [PubMed]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref] [PubMed]

A. A. Sukhorukov, S. Ha, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Dispersion extraction with near-field measurements in periodic waveguides,” Opt. Express 17(5), 3716–3721 (2009).
[Crossref] [PubMed]

P. Sun and R. M. Reano, “Cantilever couplers for intra-chip coupling to silicon photonic integrated circuits,” Opt. Express 17(6), 4565–4574 (2009).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (2)

N. Gutman, C. Martijn de Sterke, A. A. Sukhorukov, and L. C. Botten, “Slow and frozen light in optical waveguides with multiple gratings: Degenerate band edges and stationary inflection points,” Phys. Rev. A 85(3), 033804 (2012).
[Crossref]

A. Figotin and I. Vitebskiy, “Slow-wave resonance in periodic stacks of anisotropic layers,” Phys. Rev. A 76(5), 053839 (2007).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036619 (2005).
[Crossref] [PubMed]

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(6), 066613 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials,” Phys. Rev. Lett. 73(10), 1368–1371 (1994).
[Crossref] [PubMed]

Other (2)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the flow of light (Princeton University, 2011).

D. Pozar, Microwave Engineering (John Wiley & Sons, 2005).

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Figures (8)

Fig. 1
Fig. 1 Coupling-gap degenerate band edge (cgDBE) periodic structure realized in silicon-on-insulator. (a) Top-down view, (b) Cross-section.
Fig. 2
Fig. 2 Zero-coupling-gap DBE (zcgDBE) periodic structure realized in silicon-on-insulator. (a) Top-down view, (b) Cross-section.
Fig. 3
Fig. 3 Complex dispersion relationships calculated from 3D FEM. (a) Strip waveguide, (b) Strip waveguide with holes, (c) Coupling-gap RBE, (d) Coupling-gap DBE, (e) Zero-coupling-gap RBE, (f) Zero-coupling-gap DBE.
Fig. 4
Fig. 4 Comparison of quartic dispersion regimes for DBE designs with and without a coupling gap. (a) cgDBE and (b) zcgDBE.
Fig. 5
Fig. 5 Finite length zcgDBE resonator. (a) Transmission resonances, (b) Electric field magnitude, (c) Bloch mode decomposition for first resonance. For definiteness, the number of periods is N = 30 and the period a = 380 nm.
Fig. 6
Fig. 6 (a) Frequency of first resonance, relative to the band edge, versus number of periods for cgDBE and zcgDBE resonators. (b) Q-factor of first resonance versus the number of periods.
Fig. 7
Fig. 7 Top view of zcgDBE resonator with y-junction terminations.
Fig. 8
Fig. 8 Port 1 excitation of zcgDBE resonator with ZL as parameter. (a) Outgoing power at Port 1, (b) Outgoing power at port 4, (c) Electric field distribution for first resonance. For definiteness, the number of periods is N = 30 and the period a = 380 nm.

Equations (7)

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ω ω 0 = 1 2! 2 ω k 2 | k 0 (k k 0 ) 2 + 1 4! 4 ω k 4 | k 0 (k k 0 ) 4 +
ω ω 0 = D 2 (k k 0 ) 2 ,
ω ω 0 = D 4 (k k 0 ) 4 ,
Δkπ/ (aN)
Δ ω RBE D 2 (π/ (aN) ) 2 ,
Δ ω DBE D 4 (π/ (aN) ) 4 ,
β 1 | α | 2 e jϕ , 0α1, 0ϕ2π.

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