Abstract

A conventional one-dimensional photonic crystal with a conjugated pair of ε-negative and μ-negative defects has been presented, and only the defects are presumed to possess quadratic nonlinearity. Large enhancement of second-harmonic generation is predicted in numerical simulation. Interface and volume nonlinearity are both utilized in the process of second-harmonic generation due to the strong localization of the fundamental wave.

© 2009 Optical Society of America

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  1. H. Kogelnik and C. V. Shank, "Stimulated emission in a periodic structure," Appl. Phys. Lett. 18, 152-154 (1971).
    [CrossRef]
  2. V. P. Bykov, "Spontaneous emission in a periodic structure," Zh. Expr. Teor. Fiz. 62, 505-513 (1972).
  3. Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
    [CrossRef] [PubMed]
  4. A. J. Ward, J. B. Pendry, and W. J. Stewart, "Photonic dispersion surfaces," J. Phys.: Condens.Matter 7,2217-2224 (1995).
    [CrossRef]
  5. M. J. Bloemer and M. Scalora, "Transmissive properties of Ag/MgF2 Photonic Band Gaps," Appl. Phys. Lett. 72,1676-1678 (1998).
    [CrossRef]
  6. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
    [CrossRef]
  7. 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. B 70,245109 (2004).
    [CrossRef]
  8. P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
    [CrossRef]
  9. 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. B 73,033104 (2006).
    [CrossRef]
  10. G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and M. Scalora, "Large enhancement of second harmonic generation near the zero-n gap of a negative index Bragg grating," Phys. Rev. E 73,036603 (2006).
    [CrossRef]
  11. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773 (1996).
    [CrossRef] [PubMed]
  12. L. G. Wang, H. Chen, and S. Y. Zhu, "Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials," Phys. Rev. B 70,245102 (2004).
    [CrossRef]
  13. H. T. Jiang, H. Chen, and S. Y. Zhu, "Localized gap-edge fields of one-dimensional photonic crystals with an e-negative and a m-negative defect," Phys. Rev. E 73,046601 (2006).
    [CrossRef]
  14. A. Alu and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51,2558-2571 (2003).
    [CrossRef]
  15. N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, "Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect," Phys. Rev. E 65,046607 (2002).
    [CrossRef]
  16. A. Alu, N. Engheta, and R. W. Ziolkowski, "Finite-difference time-domain analysis of the tunneling and growing exponential in a pair of epsilon-negative and mu-negative slabs," Phys. Rev. E 74,016604 (2006).
    [CrossRef]
  17. N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, "Second harmonic generation from a positivenegative index material heterostructure," Phys. Rev. E 72,066612 (2005).
    [CrossRef]
  18. G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
    [CrossRef]

2006 (4)

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. B 73,033104 (2006).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and M. Scalora, "Large enhancement of second harmonic generation near the zero-n gap of a negative index Bragg grating," Phys. Rev. E 73,036603 (2006).
[CrossRef]

H. T. Jiang, H. Chen, and S. Y. Zhu, "Localized gap-edge fields of one-dimensional photonic crystals with an e-negative and a m-negative defect," Phys. Rev. E 73,046601 (2006).
[CrossRef]

A. Alu, N. Engheta, and R. W. Ziolkowski, "Finite-difference time-domain analysis of the tunneling and growing exponential in a pair of epsilon-negative and mu-negative slabs," Phys. Rev. E 74,016604 (2006).
[CrossRef]

2005 (2)

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, "Second harmonic generation from a positivenegative index material heterostructure," Phys. Rev. E 72,066612 (2005).
[CrossRef]

P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
[CrossRef]

2004 (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. B 70,245109 (2004).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, "Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials," Phys. Rev. B 70,245102 (2004).
[CrossRef]

2003 (1)

A. Alu and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51,2558-2571 (2003).
[CrossRef]

2002 (1)

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, "Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect," Phys. Rev. E 65,046607 (2002).
[CrossRef]

1998 (2)

M. J. Bloemer and M. Scalora, "Transmissive properties of Ag/MgF2 Photonic Band Gaps," Appl. Phys. Lett. 72,1676-1678 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

1997 (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773 (1996).
[CrossRef] [PubMed]

1995 (1)

A. J. Ward, J. B. Pendry, and W. J. Stewart, "Photonic dispersion surfaces," J. Phys.: Condens.Matter 7,2217-2224 (1995).
[CrossRef]

1972 (1)

V. P. Bykov, "Spontaneous emission in a periodic structure," Zh. Expr. Teor. Fiz. 62, 505-513 (1972).

1971 (1)

H. Kogelnik and C. V. Shank, "Stimulated emission in a periodic structure," Appl. Phys. Lett. 18, 152-154 (1971).
[CrossRef]

Alu, A.

A. Alu, N. Engheta, and R. W. Ziolkowski, "Finite-difference time-domain analysis of the tunneling and growing exponential in a pair of epsilon-negative and mu-negative slabs," Phys. Rev. E 74,016604 (2006).
[CrossRef]

A. Alu and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51,2558-2571 (2003).
[CrossRef]

Bloemer, M. J.

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and M. Scalora, "Large enhancement of second harmonic generation near the zero-n gap of a negative index Bragg grating," Phys. Rev. E 73,036603 (2006).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, "Second harmonic generation from a positivenegative index material heterostructure," Phys. Rev. E 72,066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
[CrossRef]

M. J. Bloemer and M. Scalora, "Transmissive properties of Ag/MgF2 Photonic Band Gaps," Appl. Phys. Lett. 72,1676-1678 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[CrossRef]

Bowden, C. M.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[CrossRef]

Bykov, V. P.

V. P. Bykov, "Spontaneous emission in a periodic structure," Zh. Expr. Teor. Fiz. 62, 505-513 (1972).

Cartwright, A. N.

P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
[CrossRef]

Chen, C.

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

Chen, H.

H. T. Jiang, H. Chen, and S. Y. Zhu, "Localized gap-edge fields of one-dimensional photonic crystals with an e-negative and a m-negative defect," Phys. Rev. E 73,046601 (2006).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, "Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials," Phys. Rev. B 70,245102 (2004).
[CrossRef]

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, "Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect," Phys. Rev. E 65,046607 (2002).
[CrossRef]

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. B 73,033104 (2006).
[CrossRef]

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. B 73,033104 (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. B 70,245109 (2004).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and M. Scalora, "Large enhancement of second harmonic generation near the zero-n gap of a negative index Bragg grating," Phys. Rev. E 73,036603 (2006).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, "Second harmonic generation from a positivenegative index material heterostructure," Phys. Rev. E 72,066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
[CrossRef]

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. B 73,033104 (2006).
[CrossRef]

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[CrossRef]

Engheta, N.

A. Alu, N. Engheta, and R. W. Ziolkowski, "Finite-difference time-domain analysis of the tunneling and growing exponential in a pair of epsilon-negative and mu-negative slabs," Phys. Rev. E 74,016604 (2006).
[CrossRef]

A. Alu and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51,2558-2571 (2003).
[CrossRef]

Fan, S

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

Fan, Y. X.

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. B 73,033104 (2006).
[CrossRef]

Fink, Y.

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

Haus, J.W.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[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. B 70,245109 (2004).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773 (1996).
[CrossRef] [PubMed]

Hsiao, V. K. S.

P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
[CrossRef]

Jiang, H. T.

H. T. Jiang, H. Chen, and S. Y. Zhu, "Localized gap-edge fields of one-dimensional photonic crystals with an e-negative and a m-negative defect," Phys. Rev. E 73,046601 (2006).
[CrossRef]

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

Kogelnik, H.

H. Kogelnik and C. V. Shank, "Stimulated emission in a periodic structure," Appl. Phys. Lett. 18, 152-154 (1971).
[CrossRef]

Li, R.

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. B 73,033104 (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. B 70,245109 (2004).
[CrossRef]

Liu, N. H.

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, "Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect," Phys. Rev. E 65,046607 (2002).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[CrossRef]

Markowicz, P. P.

P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
[CrossRef]

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and M. Scalora, "Large enhancement of second harmonic generation near the zero-n gap of a negative index Bragg grating," Phys. Rev. E 73,036603 (2006).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, "Second harmonic generation from a positivenegative index material heterostructure," Phys. Rev. E 72,066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
[CrossRef]

Michel, J.

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773 (1996).
[CrossRef] [PubMed]

A. J. Ward, J. B. Pendry, and W. J. Stewart, "Photonic dispersion surfaces," J. Phys.: Condens.Matter 7,2217-2224 (1995).
[CrossRef]

Prasad, P. N.

P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
[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. B 70,245109 (2004).
[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. B 73,033104 (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. B 70,245109 (2004).
[CrossRef]

Scalora, M.

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and M. Scalora, "Large enhancement of second harmonic generation near the zero-n gap of a negative index Bragg grating," Phys. Rev. E 73,036603 (2006).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, "Second harmonic generation from a positivenegative index material heterostructure," Phys. Rev. E 72,066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
[CrossRef]

M. J. Bloemer and M. Scalora, "Transmissive properties of Ag/MgF2 Photonic Band Gaps," Appl. Phys. Lett. 72,1676-1678 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[CrossRef]

Shank, C. V.

H. Kogelnik and C. V. Shank, "Stimulated emission in a periodic structure," Appl. Phys. Lett. 18, 152-154 (1971).
[CrossRef]

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. B 70,245109 (2004).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773 (1996).
[CrossRef] [PubMed]

A. J. Ward, J. B. Pendry, and W. J. Stewart, "Photonic dispersion surfaces," J. Phys.: Condens.Matter 7,2217-2224 (1995).
[CrossRef]

Thomas, E. L.

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

Tiryaki, H.

P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
[CrossRef]

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[CrossRef]

Wang, H. T.

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. B 73,033104 (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. B 70,245109 (2004).
[CrossRef]

Wang, L. G.

L. G. Wang, H. Chen, and S. Y. Zhu, "Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials," Phys. Rev. B 70,245102 (2004).
[CrossRef]

Ward, A. J.

A. J. Ward, J. B. Pendry, and W. J. Stewart, "Photonic dispersion surfaces," J. Phys.: Condens.Matter 7,2217-2224 (1995).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

Wu, X.

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, "Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect," Phys. Rev. E 65,046607 (2002).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773 (1996).
[CrossRef] [PubMed]

Zheltikov, A. M.

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
[CrossRef]

Zhu, S. Y.

H. T. Jiang, H. Chen, and S. Y. Zhu, "Localized gap-edge fields of one-dimensional photonic crystals with an e-negative and a m-negative defect," Phys. Rev. E 73,046601 (2006).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, "Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials," Phys. Rev. B 70,245102 (2004).
[CrossRef]

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, "Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect," Phys. Rev. E 65,046607 (2002).
[CrossRef]

Ziolkowski, R. W.

A. Alu, N. Engheta, and R. W. Ziolkowski, "Finite-difference time-domain analysis of the tunneling and growing exponential in a pair of epsilon-negative and mu-negative slabs," Phys. Rev. E 74,016604 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

H. Kogelnik and C. V. Shank, "Stimulated emission in a periodic structure," Appl. Phys. Lett. 18, 152-154 (1971).
[CrossRef]

P. P. Markowicz, V. K. S. Hsiao, H. Tiryaki, A. N. Cartwright, and P. N. Prasad, "Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating," Appl. Phys. Lett. 87,051102 (2005).
[CrossRef]

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[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Alu and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51,2558-2571 (2003).
[CrossRef]

J. Phys.: Condens.Matter (1)

A. J. Ward, J. B. Pendry, and W. J. Stewart, "Photonic dispersion surfaces," J. Phys.: Condens.Matter 7,2217-2224 (1995).
[CrossRef]

Phys. Rev. A (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J.W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56,3166-3174 (1997).
[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. B 70,245109 (2004).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, "Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials," Phys. Rev. B 70,245102 (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. B 73,033104 (2006).
[CrossRef]

Phys. Rev. E (6)

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and M. Scalora, "Large enhancement of second harmonic generation near the zero-n gap of a negative index Bragg grating," Phys. Rev. E 73,036603 (2006).
[CrossRef]

H. T. Jiang, H. Chen, and S. Y. Zhu, "Localized gap-edge fields of one-dimensional photonic crystals with an e-negative and a m-negative defect," Phys. Rev. E 73,046601 (2006).
[CrossRef]

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, "Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect," Phys. Rev. E 65,046607 (2002).
[CrossRef]

A. Alu, N. Engheta, and R. W. Ziolkowski, "Finite-difference time-domain analysis of the tunneling and growing exponential in a pair of epsilon-negative and mu-negative slabs," Phys. Rev. E 74,016604 (2006).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and M. Scalora, "Second harmonic generation from a positivenegative index material heterostructure," Phys. Rev. E 72,066612 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, "Density of modes and tunneling times in finite, one-dimensional, photonic crystals: a comprehensive analysis," Phys. Rev. E 70,016612 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773 (1996).
[CrossRef] [PubMed]

Science (1)

Y. Fink, J. N. Winn, S Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Reflector," Science 282,1679-1682 (1998).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

(Color online) conventional PC with a pair of MNG-EMN defects.

Fig. 2.
Fig. 2.

(Color online) (a) Transmittance of conventional PC and convention PC with a pair of MNG-ENG defects. εA = 9, μA = 1, εB = 2, μB = 1, εC = ε 1, μ C = μ 1 α ω 2 + γ m , ε D = ε 2 β ω 2 + γ e , , μD = μ 2, dA = dB = 18mm. The red solid line represents conventional PC. The green dashed and the blue doted line represents conventional PC with a pair of MNG-ENG defects with dC = dD = 48 mm and dC = dD = 18 mm respectively. ε 1 = μ 1 = 1, ε 2 = μ 2 = 1, α = β = 400, γm = γe = 2π × 3 × 10-6. (b) Relative electric field intensity distribution of FW of the conventional PC with a pair of MNG-ENG defects with dC = dD = 48 mm.

Fig. 3.
Fig. 3.

(Color online) (a) The localization peak or the conversion efficiency versus the thickness of ENG or MNG material, the parameter are chosen as in Fig. 2(a). The input power is 1MW/cm2. (b) Dependence of the conversion efficiency VS the input power for the structure in Fig. 2(b). (The η of conventional PCs has been magnified by a factor of 105).

Fig. 4.
Fig. 4.

(a) (Color online) The localization peak and the conversion efficiency VS the period number (PN) of the surrounded conventional PCs. The input power is 1MW/cm2. (b) the transmittance of the structure when the FW is at the second transmission resonance.

Equations (6)

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ε C = ε 1 , μ C = μ 1 α ω 2 + γ m ,
ε D = ε 2 β ω 2 + γ e , μ D = μ 2 ,
d 2 E ω d z 2 + ω 2 ε ω ( z ) μ ω ( z ) E ω c 2 = 2 ω 2 c 2 μ ω d ( 2 ) ( z ) E ω * E 2 ω
d 2 E 2 ω d z 2 + ( 2 ω ) 2 ε 2 ω ( z ) μ 2 ω ( z ) E 2 ω c 2 = 2 ( 2 ω ) 2 c 2 μ 2 ω d ( 2 ) ( z ) E ω 2
η = 2 ω 2 L 2 ε 0 c 3 ( 1 L 0 L d ( 2 ) ( z ) [ Φ ω + ( z ) ] 2 Φ 2 ω ( z ) dz 2
+ 1 L 0 L d ( 2 ) ( z ) [ Φ ω + ( z ) ] 2 Φ 2 ω + ( z ) dz 2 ) I ω Input

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