Abstract

As previously reported [Opt. Lett. 29, 2791 (2004) ], one-dimensional photonic crystals exhibit a decrease in their normal reflectivity if their interfaces are not flat. We show that the homogenization approximation accurately predicts this diminished optical response by comparing results with finite-difference time-domain (FDTD) simulations applied to the same roughened structures. Within the parameter range tested (rms roughness <20% and rms wavelengths <100% of the photonic crystal periodicity), the homogenization approximation accurately reproduces the reflectivities obtained by the FDTD simulations, which are much more computationally expensive.

© 2005 Optical Society of America

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References

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  1. K. R. Maskaly, G. R. Maskaly, W. C. Carter, and J. L. Maxwell, Opt. Lett. 29, 2791 (2004).
    [CrossRef] [PubMed]
  2. A. Sentenac, G. Toso, and M. Saillard, J. Opt. Soc. Am. A 15, 924 (1998).
    [CrossRef]
  3. T. K. Gaylord, W. E. Baird, and M. G. Moharam, Appl. Opt. 25, 4562 (1986).
    [CrossRef]
  4. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, 1994).
    [CrossRef]
  5. J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).
  6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

2004 (1)

1998 (1)

1986 (1)

Baird, W. E.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Carter, W. C.

Gaylord, T. K.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).

Maskaly, G. R.

Maskaly, K. R.

Maxwell, J. L.

Moharam, M. G.

Saillard, M.

Sentenac, A.

Toso, G.

Voronovich, G.

G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, 1994).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (3)

G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, 1994).
[CrossRef]

J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the homogenization approximation for a single rough interface.

Fig. 2
Fig. 2

Application of the homogenization approximation to the roughened quarter-wave stacks. The dielectric constant is averaged across each row of the input structure. The smoothed profile is then converted into a series of layers.

Fig. 3
Fig. 3

Comparison of the FDTD results with the results of the homogenization approximation for several 4-bilayer systems, where n 1 denotes the high refractive index value of the simulated 1DPCs and n 2 denotes the low index value. The FDTD data are shown by the black circles, while the homogenization approximation results are given by the gray triangles.

Equations (4)

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Δ r = 1 r rough r smooth ,
R [ 1 L 0 L ( y y 0 ) 2 d x ] 1 2 [ 1 n 1 n ( y y 0 ) 2 ] 1 2 ,
W = { 1 n pv 1 n pv [ x pv ( 2 ) x pv ( 1 ) ] 2 } 1 2 .
a = λ 4 n 1 + λ 4 n 2 ,

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