Abstract

An effective approach is proposed to broaden the spectrum of high-efficiency second harmonic generation in a one-dimensional photonic crystal based on the cascaded structure. By controlling the thickness of the joint layer, it is possible to realize a flat-top or quasiflat-top impurity band centered at the fundamental wavelength due to mode splitting effect in coupled cavities. Simulation results reveal that the spectrum of generated second harmonic exhibits a hump-like or multi-peak profile with wavelength tuning. It is a salient feature that the spectral stability of efficiency enhancement could be greatly improved compared to the conventional Lorentzian profile while maintaining an ultrahigh Q factor. Such merit of spectra re-shaping can significantly relax the stringent requirements for ultrahigh-Q microcavities in practical applications, e.g. fabrication inaccuracy, thermal variation, and wavelength detuning.

© 2013 OSA

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  1. H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-Localized modes,” Phys. Rev. Lett.108(11), 113901 (2012).
    [CrossRef] [PubMed]
  2. D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
    [CrossRef] [PubMed]
  3. J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
    [CrossRef]
  4. T. W. Lu and P. T. Lee, “Ultra-high sensitivity optical stress sensor based on double-layered photonic crystal microcavity,” Opt. Express17(3), 1518–1526 (2009).
    [CrossRef] [PubMed]
  5. S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
    [CrossRef] [PubMed]
  6. F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
    [CrossRef]
  7. F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
    [CrossRef]
  8. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
    [CrossRef] [PubMed]
  9. B. Shi, Z. M. Jiang, and X. Wang, “Defective photonic crystals with greatly enhanced second-harmonic generation,” Opt. Lett.26(15), 1194–1196 (2001).
    [CrossRef] [PubMed]
  10. J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag 2008).
  11. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express14(26), 12670–12678 (2006).
    [CrossRef] [PubMed]
  12. S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
    [CrossRef]
  13. P. Royo, R. P. Stanley, and M. Ilegems, “Coupling of impurity modes in one-dimensional periodic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(1), 016604 (2001).
    [CrossRef] [PubMed]
  14. M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
    [CrossRef]
  15. M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84(10), 2140–2143 (2000).
    [CrossRef] [PubMed]
  16. E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
    [CrossRef] [PubMed]
  17. J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).
  18. Y. H. Ja, “Using the shooting methos to solve boundary-value problems involving nonlinear coupled-wave equations,” Opt. Quantum Electron.15(6), 529–538 (1983).
    [CrossRef]
  19. R. Li, J. Chen, Q. Xu, F. F. Ren, Y. X. Fan, J. Ding, and H. T. Wang, “Saturation effect and forward-dominant second-harmonic generation in single-defect photonic crystals with dual localizations,” Opt. Lett.31(22), 3327–3329 (2006).
    [CrossRef] [PubMed]
  20. M. L. Ren and Z. Y. Li, “High conversion efficiency of second harmonic generation in a short nonlinear photonic crystal with distributed Bragg reflector mirrors,” Appl. Phys., A Mater. Sci. Process.107(1), 71–76 (2012).
    [CrossRef]
  21. G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
    [CrossRef] [PubMed]

2012 (3)

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-Localized modes,” Phys. Rev. Lett.108(11), 113901 (2012).
[CrossRef] [PubMed]

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

M. L. Ren and Z. Y. Li, “High conversion efficiency of second harmonic generation in a short nonlinear photonic crystal with distributed Bragg reflector mirrors,” Appl. Phys., A Mater. Sci. Process.107(1), 71–76 (2012).
[CrossRef]

2011 (1)

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

2010 (2)

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

2009 (1)

2007 (1)

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

2006 (3)

2004 (1)

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

2003 (1)

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

2002 (1)

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

2001 (2)

P. Royo, R. P. Stanley, and M. Ilegems, “Coupling of impurity modes in one-dimensional periodic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(1), 016604 (2001).
[CrossRef] [PubMed]

B. Shi, Z. M. Jiang, and X. Wang, “Defective photonic crystals with greatly enhanced second-harmonic generation,” Opt. Lett.26(15), 1194–1196 (2001).
[CrossRef] [PubMed]

2000 (1)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84(10), 2140–2143 (2000).
[CrossRef] [PubMed]

1999 (2)

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

1983 (1)

Y. H. Ja, “Using the shooting methos to solve boundary-value problems involving nonlinear coupled-wave equations,” Opt. Quantum Electron.15(6), 529–538 (1983).
[CrossRef]

Arcizet, O.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

Asakawa, K.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

Azaña, J.

Azña, J.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Bayer, M.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84(10), 2140–2143 (2000).
[CrossRef] [PubMed]

Bertolotti, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Beveratos, A.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

Bloemer, M. J.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Bowden, C. M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Braive, R.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

Centini, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Chen, J.

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

R. Li, J. Chen, Q. Xu, F. F. Ren, Y. X. Fan, J. Ding, and H. T. Wang, “Saturation effect and forward-dominant second-harmonic generation in single-defect photonic crystals with dual localizations,” Opt. Lett.31(22), 3327–3329 (2006).
[CrossRef] [PubMed]

Cheng, C.

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

Chigrin, D. N.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

Clausen, A. T.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

D’Aguanno, G.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Ding, J.

Ding, J. P.

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

Englund, D.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Fan, S.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Fan, Y. X.

R. Li, J. Chen, Q. Xu, F. F. Ren, Y. X. Fan, J. Ding, and H. T. Wang, “Saturation effect and forward-dominant second-harmonic generation in single-defect photonic crystals with dual localizations,” Opt. Lett.31(22), 3327–3329 (2006).
[CrossRef] [PubMed]

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

Faraon, A.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Fejer, M. M.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Forchel, A.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

Galili, M.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Gavartin, E.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

Gutbrod, T.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

Harris, J. S.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Hirao, K.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

Hu, H.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Huo, Y.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Ikeda, N.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

Ilegems, M.

P. Royo, R. P. Stanley, and M. Ilegems, “Coupling of impurity modes in one-dimensional periodic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(1), 016604 (2001).
[CrossRef] [PubMed]

Ishikawa, H.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

Ja, Y. H.

Y. H. Ja, “Using the shooting methos to solve boundary-value problems involving nonlinear coupled-wave equations,” Opt. Quantum Electron.15(6), 529–538 (1983).
[CrossRef]

Jeppesen, P.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Jiang, Z. M.

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Kippenberg, T. J.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

Knipp, P. A.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

Kroha, J.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

Kulishov, M.

Lan, S.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

Lavrinenko, A. V.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

Lee, P. T.

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Li, R.

R. Li, J. Chen, Q. Xu, F. F. Ren, Y. X. Fan, J. Ding, and H. T. Wang, “Saturation effect and forward-dominant second-harmonic generation in single-defect photonic crystals with dual localizations,” Opt. Lett.31(22), 3327–3329 (2006).
[CrossRef] [PubMed]

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

Li, Z. Y.

M. L. Ren and Z. Y. Li, “High conversion efficiency of second harmonic generation in a short nonlinear photonic crystal with distributed Bragg reflector mirrors,” Appl. Phys., A Mater. Sci. Process.107(1), 71–76 (2012).
[CrossRef]

Lodahl, P.

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-Localized modes,” Phys. Rev. Lett.108(11), 113901 (2012).
[CrossRef] [PubMed]

Lu, T. W.

Majumdar, A.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Mulvad, H. C. H.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Nishikawa, S.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Oxenløwe, L. K.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84(10), 2140–2143 (2000).
[CrossRef] [PubMed]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Palushani, E.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Pan, J.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Park, Y.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express14(26), 12670–12678 (2006).
[CrossRef] [PubMed]

Petroff, P.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Povinelli, M. L.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Qiu, J.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

Reinecke, T. L.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

Reithmaier, J. P.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

Ren, F. F.

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

R. Li, J. Chen, Q. Xu, F. F. Ren, Y. X. Fan, J. Ding, and H. T. Wang, “Saturation effect and forward-dominant second-harmonic generation in single-defect photonic crystals with dual localizations,” Opt. Lett.31(22), 3327–3329 (2006).
[CrossRef] [PubMed]

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

Ren, M. L.

M. L. Ren and Z. Y. Li, “High conversion efficiency of second harmonic generation in a short nonlinear photonic crystal with distributed Bragg reflector mirrors,” Appl. Phys., A Mater. Sci. Process.107(1), 71–76 (2012).
[CrossRef]

Robert-Philip, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

Royo, P.

P. Royo, R. P. Stanley, and M. Ilegems, “Coupling of impurity modes in one-dimensional periodic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(1), 016604 (2001).
[CrossRef] [PubMed]

Sagnes, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

Sandhu, S.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Sapienza, L.

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-Localized modes,” Phys. Rev. Lett.108(11), 113901 (2012).
[CrossRef] [PubMed]

Scalora, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Shi, B.

Si, J.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

Sibilia, C.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Slavík, R.

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express14(26), 12670–12678 (2006).
[CrossRef] [PubMed]

Smolka, S.

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-Localized modes,” Phys. Rev. Lett.108(11), 113901 (2012).
[CrossRef] [PubMed]

Stanley, R. P.

P. Royo, R. P. Stanley, and M. Ilegems, “Coupling of impurity modes in one-dimensional periodic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(1), 016604 (2001).
[CrossRef] [PubMed]

Stoltz, N.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Stuhrmann, N.

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Sugimoto, Y.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84(10), 2140–2143 (2000).
[CrossRef] [PubMed]

Thyrrestrup, H.

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-Localized modes,” Phys. Rev. Lett.108(11), 113901 (2012).
[CrossRef] [PubMed]

Toishi, M.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Vuckovic, J.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Wang, H. T.

R. Li, J. Chen, Q. Xu, F. F. Ren, Y. X. Fan, J. Ding, and H. T. Wang, “Saturation effect and forward-dominant second-harmonic generation in single-defect photonic crystals with dual localizations,” Opt. Lett.31(22), 3327–3329 (2006).
[CrossRef] [PubMed]

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

Wang, X.

Werner, R.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

Xu, Q.

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Zhukovsky, S. V.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett.97(10), 101102 (2010).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

M. L. Ren and Z. Y. Li, “High conversion efficiency of second harmonic generation in a short nonlinear photonic crystal with distributed Bragg reflector mirrors,” Appl. Phys., A Mater. Sci. Process.107(1), 71–76 (2012).
[CrossRef]

Int. J. Opt. (1)

J. Azña, L. K. Oxenløwe, E. Palushani, R. Slavík, M. Galili, H. C. H. Mulvad, H. Hu, Y. Park, A. T. Clausen, and P. Jeppesen, “In-fiber subpicosecond pulse shaping for nonlinear optical telecommunication data processing at 640 Gbit/s,” Int. J. Opt.2012, 895281 (2012).

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

Y. H. Ja, “Using the shooting methos to solve boundary-value problems involving nonlinear coupled-wave equations,” Opt. Quantum Electron.15(6), 529–538 (1983).
[CrossRef]

Phys. Rev. B (3)

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hirao, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B70(24), 245109 (2004).
[CrossRef]

F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity,” Phys. Rev. B73(3), 033104 (2006).
[CrossRef]

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B65(16), 165208 (2002).
[CrossRef]

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

P. Royo, R. P. Stanley, and M. Ilegems, “Coupling of impurity modes in one-dimensional periodic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(1), 016604 (2001).
[CrossRef] [PubMed]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(1), 016606 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, “Optical demonstration of a crystal band structure formation,” Phys. Rev. Lett.83(25), 5374–5377 (1999).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84(10), 2140–2143 (2000).
[CrossRef] [PubMed]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett.106(20), 203902 (2011).
[CrossRef] [PubMed]

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett.99(7), 073902 (2007).
[CrossRef] [PubMed]

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-Localized modes,” Phys. Rev. Lett.108(11), 113901 (2012).
[CrossRef] [PubMed]

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010).
[CrossRef] [PubMed]

Science (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Other (1)

J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer-Verlag 2008).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of PCMC structures. (a) Single PCMC, (b) double-cascaded PCMC, and (c) multiple-cascaded PCMC.

Fig. 2
Fig. 2

The dependence of the resonance peaks on the air gap distance dJ in a double-cascaded PCMC with PN = 5. The transmission spectra are shifted upwards for clarity with offset = 1.

Fig. 3
Fig. 3

(a) The simulated phase and (b) transmission spectra of the coupled cavity modes in single and cascaded PCMCs with N = 1 to 4. The structures are with PN = 5 and dJ = dL.

Fig. 4
Fig. 4

The SHG efficiency as a function of wavelength tuning in a double-cascaded PCMC with various air gap distance dJ. The incident FW intensities are given as (a) 10 and (b) 100 MW/cm2, respectively. The efficiency spectra are shifted upwards for clarity with offset = 0.1. (c) The dependence of peak position of efficiency curve on thickness of layer J for (a) and (b).

Fig. 5
Fig. 5

(a) The dependence of SHG efficiency on the incident FW intensity for the examples of N = 1, 2, 3, and 4 with dJ = dL. (b) The comparison of high-efficiency spectral linewidth in PCMC structures with N = 1 to 4 under I0FM = 200 MW/cm2.

Fig. 6
Fig. 6

The dependence of (a)-(d) forward and (e)-(h) backward FW and SH output on the incident FW power intensity for the PCMC structures with N = 1 to 4 and dJ = dL.

Equations (1)

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d 2 E 1 d x 2 + ω 1 2 c 2 n 1 2 E 1 =2 ω 1 2 c 2 χ (2) E 1 E 2 , d 2 E 2 d x 2 + ω 2 2 c 2 n 2 2 E 2 = ω 2 2 c 2 χ (2) E 1 2 .

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