Abstract

Two-dimensional photonic crystal linear defect waveguides on semiconductor substrates are studied. It is predicted that the out-of-plane radiation loss can be reduced by shifting one side of the photonic crystal cladding by one-half period with respect to the other along the propagation direction.

© 2004 Optical Society of America

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References

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  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. S. John, Phys. Rev. Lett. 58, 2486 (1987).
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    [CrossRef]
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  6. A. Talneau, L. Le Gouezigou, and N. Bouadma, Opt. Lett. 26, 1259 (2001).
    [CrossRef]
  7. C. J. M. Smith, Appl. Phys. Lett. 77, 2813 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
  9. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, Berlin, 1980).
    [CrossRef]

2003 (1)

2001 (2)

A. Talneau, L. Le Gouezigou, and N. Bouadma, Opt. Lett. 26, 1259 (2001).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

2000 (2)

C. J. M. Smith, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, Appl. Phys. Lett. 76, 952 (2000).
[CrossRef]

1999 (1)

T. Baba, N. Fukaya, and J. Yonekura, Electron. Lett. 35, 654 (1999).
[CrossRef]

1987 (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Asakawa, K.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

Baba, T.

T. Baba, N. Fukaya, and J. Yonekura, Electron. Lett. 35, 654 (1999).
[CrossRef]

Bouadma, N.

Bulirsch, R.

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, Berlin, 1980).
[CrossRef]

Carlsson, N.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

Fukaya, N.

T. Baba, N. Fukaya, and J. Yonekura, Electron. Lett. 35, 654 (1999).
[CrossRef]

Ikeda, N.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

Inoue, K.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Kawai, N.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

Kim, C.

Kim, W. J.

Kosaka, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, Appl. Phys. Lett. 76, 952 (2000).
[CrossRef]

Kuang, W.

Le Gouezigou, L.

O’Brien, J. D.

Smith, C. J. M.

C. J. M. Smith, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Stapleton, A.

Stoer, J.

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, Berlin, 1980).
[CrossRef]

Sugimoto, Y.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

Talneau, A.

Tokushima, M.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, Appl. Phys. Lett. 76, 952 (2000).
[CrossRef]

Tomita, A.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, Appl. Phys. Lett. 76, 952 (2000).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yamada, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, Appl. Phys. Lett. 76, 952 (2000).
[CrossRef]

Yonekura, J.

T. Baba, N. Fukaya, and J. Yonekura, Electron. Lett. 35, 654 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, Appl. Phys. Lett. 79, 4286 (2001).
[CrossRef]

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, Appl. Phys. Lett. 76, 952 (2000).
[CrossRef]

C. J. M. Smith, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Electron. Lett. (1)

T. Baba, N. Fukaya, and J. Yonekura, Electron. Lett. 35, 654 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Other (1)

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, Berlin, 1980).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Photonic band diagram for a type A single-line photonic crystal defect waveguide in an extended Brillouin zone scheme. The defect mode analyzed for out-of-plane radiation loss is marked by the thick curve. (b) In-plane dielectric distribution of the waveguide and (c) its Fourier transform. (d) Fourier transform of Hz at the midplane for the defect waveguide mode at βy=0.2π/a, and (e) Hz2 shown in the cross section of the same mode with waveguide dielectric distribution overlaid by dotted lines. All contours are in gray scale; the darker, the higher the magnitude. The adjacent gray levels differ in magnitude by a decade.

Fig. 2
Fig. 2

(a) Photonic band diagram for a type B single-line photonic crystal defect waveguide in a reduced Brillouin zone scheme. The defect mode analyzed for out-of-plane radiation loss is marked by the thick curve. (b) Fourier transform of the in-plane waveguide dielectric distribution. (c) Hz2 cross section for the defect waveguide mode at βy=0.5π/a. The dotted lines outline the waveguide dielectric distribution. The field contour has one additional gray level compared with 1(e) to identify the radiation path.

Fig. 3
Fig. 3

Out-of-plane radiation loss as a function of normalized frequency for the photonic crystal defect slab waveguides modeled in this work. The lattice constant a=480 nm is assumed for a type A deeply etched waveguide (a) and 380 nm for type B (b). Points are calculated values and curves are B-spline curve fits.9

Equations (1)

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Ex,y,z,t=ncnAfβAx,z×expiωt-β+nb1-b22y,

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