Abstract

We analyze a dielectric waveguide with a photonic crystal core. Using constant frequency contour analysis, we show that the modal behavior of this structure is drastically different from that of a conventional slab waveguide. In particular, at a given frequency the lowest-order guided mode can have an odd symmetry or can have more than one nodal plane in its field distribution. Also, there exist several single-mode regions with a different modal profile in each region. Finally, a single-mode waveguide for the fundamental mode with a large core and strong confinement can be realized. All these behaviors are confirmed by our three-dimensional finite-difference time-domain simulations.

© 2006 Optical Society of America

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  1. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
    [CrossRef] [PubMed]
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
    [CrossRef] [PubMed]
  3. J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, Opt. Lett. 21, 1547 (1996).
    [CrossRef] [PubMed]
  4. M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
    [CrossRef]
  5. C. Martijn de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, Opt. Lett. 29, 1384 (2004).
    [CrossRef]
  6. X. Yu and S. Fan, Phys. Rev. E 70, 036612 (2004).
    [CrossRef]
  7. W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
    [CrossRef]
  8. C. R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).
  9. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).
  10. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 273 (2001).
    [CrossRef]
  11. S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
    [CrossRef]
  12. A. E. Siegman, Lasers (University Science, 1986).

2004 (2)

2002 (2)

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
[CrossRef]

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

2001 (1)

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 273 (2001).
[CrossRef]

1999 (2)

S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

1996 (2)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Allard, M.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Asatryan, A. A.

Atkin, D. M.

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

Botten, L. C.

Charbonneau-Lefort, M.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

de Sterke, C. Martijn

Fan, S.

X. Yu and S. Fan, Phys. Rev. E 70, 036612 (2004).
[CrossRef]

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Istrate, E.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 273 (2001).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 273 (2001).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Lau, W. T.

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

McPhedran, R. C.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Pollock, C. R.

C. R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).

Poon, J.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Russell, P. St.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

Sargent, E. H.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

White, T. P.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).

Yu, X.

X. Yu and S. Fan, Phys. Rev. E 70, 036612 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

Opt. Express (1)

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 273 (2001).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

S. G. Johnson, S. Fan, P. R. Villeneuve, L. A. Kolodziejski, and J. D. Joannopoulos, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. H. Sargent, Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Phys. Rev. E (1)

X. Yu and S. Fan, Phys. Rev. E 70, 036612 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Science (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Other (3)

A. E. Siegman, Lasers (University Science, 1986).

C. R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).

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Figures (5)

Fig. 1
Fig. 1

(a) Waveguide with a photonic crystal core. The crystal consists of a square lattice of air holes introduced into a dielectric ( ϵ = 12 ) slab waveguide suspended in air. The hole radius is 0.42 a , and the thickness is 0.5 a . (b) and (c) Constant frequency contours for the first and second TE-like bands of the corresponding infinite photonic crystal slab, respectively. In (c), regions that lie above the light cone are shaded.

Fig. 2
Fig. 2

Modal properties of the photonic crystal core waveguide shown in Fig. 1a, with widths d of 2 a , 3 a , and 4 a . For each width, lines with different colors indicate the frequency ranges in which modes with different orders exist.

Fig. 3
Fig. 3

Steady-state magnetic field ( H z -component) distributions at frequency f = 0.30 ( c a ) for a photonic crystal core waveguide excited by sources with (a) odd or (b) even symmetry. The width of the waveguide is 2 a . Red and blue represent large positive and negative amplitudes, respectively. The small radiation leakage in (a) is due to the modal mismatch between the PhC and the dielectric slab regions.

Fig. 4
Fig. 4

Regions of frequency and width in which only a 0th-order mode is supported for (a) a photonic crystal core waveguide and (b) a conventional waveguide.

Fig. 5
Fig. 5

Steady-state magnetic field distributions at frequency f = 0.37 ( c a ) for a photonic crystal core waveguide excited by sources with (a) even or (b) odd symmetry. The width of the waveguide is 8 a . The point dipoles are placed in positions that optimize the modal matching.

Equations (4)

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k ( ω ) > n air ω c .
2 k d ϕ c ϕ s = 2 m π ,
m k d π .
H k ( r ) = e i k r u k ( r ) ,

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