Abstract

The effect of surface truncation on the electromagnetic density of modes (DOM) in photonic crystals (PCs) is investigated theoretically. It shows that for PCs with surface truncation parameter τ0 or τ0.5, the DOM has asymmetric properties on the two edges of the first bandgap in normal incidence. Moreover, DOM at band edges has much larger values in the PC with appropriate truncation than that in the PC without truncation. Also, the effect of surface truncation on a band-edge laser is discussed, and the case of the oblique incident is also discussed.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to χ(2) interactions," Phys. Rev. E 64, 016609 (2001).
    [CrossRef]
  16. V. Romero-Rochý'n, R. P. Duarte-Zamorano, S. Nilsen-Hofseth, and R. G. Barrera, " `Superluminal' transmission of light pulses through optically opaque barriers," Phys. Rev. E 63, 027601 (2001).
    [CrossRef]
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    [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]
  19. S. Severini, A. Settimi, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Second quantization and atomic spontaneous emission inside one-dimensional photonic crystals via a quasinormal-modes approach," Phys. Rev. E 70, 056614 (2004).
    [CrossRef]
  20. M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
    [CrossRef] [PubMed]
  21. A. Settimi, S. Severini, M. Centini, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Coherent control of stimulated emission inside one-dimensional photonic crystals," Phys. Rev. E 71, 066606 (2005).
    [CrossRef]
  22. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991).
    [CrossRef]
  23. J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band gaps material," J. Mod. Opt. 41, 257-262 (1994).
    [CrossRef]
  24. F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 (1999).
    [CrossRef]
  25. M. Scalora, J. P. Dowling, A. S. Manka, C. M. Bowden, and J. W. Haus, "Pulse propagation near highly reflective surfaces: applications to photonic band-gap structures and the question of superluminal tunneling times," Phys. Rev. A 52, 726-734 (1995).
    [CrossRef] [PubMed]
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2006 (1)

Z. Wang and D. Liu, "Effect of refractive index of environment medium on electromagnetic mode density in photonic band gaps," Appl. Phys. B: Photophys. Laser Chem. 82, 549-553 (2006).
[CrossRef]

2005 (1)

A. Settimi, S. Severini, M. Centini, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Coherent control of stimulated emission inside one-dimensional photonic crystals," Phys. Rev. E 71, 066606 (2005).
[CrossRef]

2004 (2)

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]

S. Severini, A. Settimi, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Second quantization and atomic spontaneous emission inside one-dimensional photonic crystals via a quasinormal-modes approach," Phys. Rev. E 70, 056614 (2004).
[CrossRef]

2003 (2)

A. Settimi, S. Severini, N. Mattiucci, C. Sibilia, M. Centini, G. D'Aguanno, M. Bertolotti, M. Scalora, M. Bloemer, and C. M. Bowden, "Quasinormal-mode description of waves in one-dimensional photonic crystals," Phys. Rev. E 68, 026614 (2003).
[CrossRef]

G. Boedecker and C. Henkel, "All-frequency effective medium theory of a photonic crystal," Opt. Express 11, 1590 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (2)

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to χ(2) interactions," Phys. Rev. E 64, 016609 (2001).
[CrossRef]

V. Romero-Rochý'n, R. P. Duarte-Zamorano, S. Nilsen-Hofseth, and R. G. Barrera, " `Superluminal' transmission of light pulses through optically opaque barriers," Phys. Rev. E 63, 027601 (2001).
[CrossRef]

1999 (3)

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, "Resonant and localized electromagnetic modes in finite superlattices," Phys. Rev. B 61, 2059-2064 (1999).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 (1999).
[CrossRef]

A. Moroz, "Minima and maxima of the local density of states for one-dimensional periodic systems," Europhys. Lett. 46, 419 (1999).
[CrossRef]

1996 (2)

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

J. M. Bendickson and J. P. Dowling, "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)

M. Scalora, J. P. Dowling, A. S. Manka, C. M. Bowden, and J. W. Haus, "Pulse propagation near highly reflective surfaces: applications to photonic band-gap structures and the question of superluminal tunneling times," Phys. Rev. A 52, 726-734 (1995).
[CrossRef] [PubMed]

1994 (2)

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, 1896-1899 (1994).
[CrossRef]

J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band gaps material," J. Mod. Opt. 41, 257-262 (1994).
[CrossRef]

1992 (1)

N. D. Sankey, D. F. Prelewitz, and T. G. Brown, "All-optical switching in a nonlinear periodic-waveguide structure," Appl. Phys. Lett. 60, 1427-1429 (1992).
[CrossRef]

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991).
[CrossRef]

1990 (1)

C. M. deSterke and J. E. Sipe, "Switching dynamics of finite periodic nonlinear media: a numerical study," Phys. Rev. A 42, 2858-2869 (1990).
[CrossRef]

1989 (1)

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

1988 (1)

S. John and R. Rangarajan, "Optimal structures for classical wave localization: an alternative to the ioffe-regel criterion," Phys. Rev. B 38, 10101-10104 (1988).
[CrossRef]

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Appl. Phys. B: Photophys. Laser Chem. (1)

Z. Wang and D. Liu, "Effect of refractive index of environment medium on electromagnetic mode density in photonic band gaps," Appl. Phys. B: Photophys. Laser Chem. 82, 549-553 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

N. D. Sankey, D. F. Prelewitz, and T. G. Brown, "All-optical switching in a nonlinear periodic-waveguide structure," Appl. Phys. Lett. 60, 1427-1429 (1992).
[CrossRef]

Europhys. Lett. (1)

A. Moroz, "Minima and maxima of the local density of states for one-dimensional periodic systems," Europhys. Lett. 46, 419 (1999).
[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, 1896-1899 (1994).
[CrossRef]

J. Mod. Opt. (1)

J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band gaps material," J. Mod. Opt. 41, 257-262 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (3)

M. Scalora, J. P. Dowling, A. S. Manka, C. M. Bowden, and J. W. Haus, "Pulse propagation near highly reflective surfaces: applications to photonic band-gap structures and the question of superluminal tunneling times," Phys. Rev. A 52, 726-734 (1995).
[CrossRef] [PubMed]

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

C. M. deSterke and J. E. Sipe, "Switching dynamics of finite periodic nonlinear media: a numerical study," Phys. Rev. A 42, 2858-2869 (1990).
[CrossRef]

Phys. Rev. B (4)

S. John and R. Rangarajan, "Optimal structures for classical wave localization: an alternative to the ioffe-regel criterion," Phys. Rev. B 38, 10101-10104 (1988).
[CrossRef]

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, "Resonant and localized electromagnetic modes in finite superlattices," Phys. Rev. B 61, 2059-2064 (1999).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 (1999).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991).
[CrossRef]

Phys. Rev. E (8)

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

A. Settimi, S. Severini, N. Mattiucci, C. Sibilia, M. Centini, G. D'Aguanno, M. Bertolotti, M. Scalora, M. Bloemer, and C. M. Bowden, "Quasinormal-mode description of waves in one-dimensional photonic crystals," Phys. Rev. E 68, 026614 (2003).
[CrossRef]

M. Wubs and A. Lagendijk, "Local optical density of states in finite crystals of plane scatterers," Phys. Rev. E 65, 046612 (2002).
[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]

S. Severini, A. Settimi, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Second quantization and atomic spontaneous emission inside one-dimensional photonic crystals via a quasinormal-modes approach," Phys. Rev. E 70, 056614 (2004).
[CrossRef]

A. Settimi, S. Severini, M. Centini, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Coherent control of stimulated emission inside one-dimensional photonic crystals," Phys. Rev. E 71, 066606 (2005).
[CrossRef]

G. D'Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to χ(2) interactions," Phys. Rev. E 64, 016609 (2001).
[CrossRef]

V. Romero-Rochý'n, R. P. Duarte-Zamorano, S. Nilsen-Hofseth, and R. G. Barrera, " `Superluminal' transmission of light pulses through optically opaque barriers," Phys. Rev. E 63, 027601 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Other (1)

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Chap. 1.

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of the finite multilayered period structure.

Fig. 2
Fig. 2

Electromagnetic DOM changes with relative frequency of the incident wave under the condition of n = 5 .

Fig. 3
Fig. 3

Normalized electromagnetic DOM changes with relative frequency under the condition of σ = 5.25 .

Fig. 4
Fig. 4

Normalized electromagnetic DOM changes with relative frequency under the condition of σ = 5.1 and 5.2. (a) τ = 0.1 ; (b) τ = 0.2 .

Fig. 5
Fig. 5

Electromagnetic DOM at the low (solid curve) and high (dashed curve) frequency band edge changes with the periodic number σ under the condition n = 5 and in normal incidence.

Fig. 6
Fig. 6

Electromagnetic DOM at midgap changes with the periodic number σ under the condition n = 5 and in normal incidence.

Fig. 7
Fig. 7

Local DOS at the high frequency band edge of the first bandgap in the third cell. The solid curve is for the photonic crystal with σ = 5.4 , and the dotted curve is for the case with σ = 5 .

Fig. 8
Fig. 8

Electromagnetic DOM at the low (solid curve) and high (dashed curve) frequency band edge of the first bandgap changes with σ (oblique incident θ = 30 ° ).

Fig. 9
Fig. 9

Electromagnetic DOM at midgap changes with the periodic number σ under the condition n = 5 (oblique incident θ = 30 ° ).

Equations (4)

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M j = [ cos δ j i η j sin δ j i η j sin δ j cos δ j ] ,
η j = { ϵ j μ j cos θ j TE μ j ϵ j cos θ j TM } .
t = 2 η 0 M 11 η 0 + M 21 + M 12 η k + 1 η 0 + M 22 η k + 1 ,
ρ ( ω ) = d k d ω = 1 d ( ( y x x y ) ( x 2 + y 2 ) ) ,

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