Abstract

A very efficient numerical tool to electromagnetically analyze random structures is proposed. The principle is treating random structure as superposition of diffraction gratings. Then, influence of each component grating can be computed with any electromagnetic grating theory which is well established for its accuracy and computation speed. This article explains how to treat obtained data in detail. Applied to single-tiered scatteres, the proposed method gives comparable results with a standard way based on FDTD method in far shorter time.

© 2008 Optical Society of America

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References

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  1. C. F. Bohren, "Scattering by particles," in Handbook of Optics I, M. Bass, ed., (McGraw-Hill, New York, 1995), pp. 6.1-6.21.
  2. T. Dogaru, L. Collins, and L. Carin, "Optimal time-domain detection of a deterministic target buried under a randomly rough interface," IEEE Trans. Antennas Propag. 49,313-326 (2001).
    [CrossRef]
  3. F. D. Hastings, J. B. Schneider, and S. L. Shira, "A Monte-Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).
  4. K. Edee, B. Guizal, G. Granet, and A. Moreau, "Beam implementation in a nonorthogonal cooridinate system: Application to the scattering from random rough surfaces," J. Opt. Soc. Am. A 25, 796-804 (2008).
    [CrossRef]
  5. T. Kojima and T. Kawai, "Numerical analysis of detected signal characteristics from a blue laser optical disk model with random rough surfaces by FDTD method," IEICE Trans. Electron. E 90-C, 1599-1605 (2007).
    [CrossRef]
  6. M.-Y. Ng and W.-C. Liu, "Super-resolution and frequency-dependent efficiency of near-field optical disks with silver nanoparticles," Opt. Express 13, 9422-9430 (2005).
    [CrossRef] [PubMed]
  7. H. Ichikawa, "Subwavelength triangular random gratings," J. Mod. Opt. 49, 1893-1906 (2002).
    [CrossRef]
  8. J. Turunen, "Diffraction theory of microrelief gratings" in Micro-Optics, H. P. Herzig, ed., (Taylor & Francis, London, 1997).
  9. H. Ichikawa and H. Kikuta, "Dynamic guided-mode resonant grating filter with quadratic electro-optic effect," J. Opt. Soc. Am. A 22, 1311-1318 (2005).
    [CrossRef]

2008 (1)

2007 (1)

T. Kojima and T. Kawai, "Numerical analysis of detected signal characteristics from a blue laser optical disk model with random rough surfaces by FDTD method," IEICE Trans. Electron. E 90-C, 1599-1605 (2007).
[CrossRef]

2005 (2)

2002 (1)

H. Ichikawa, "Subwavelength triangular random gratings," J. Mod. Opt. 49, 1893-1906 (2002).
[CrossRef]

2001 (1)

T. Dogaru, L. Collins, and L. Carin, "Optimal time-domain detection of a deterministic target buried under a randomly rough interface," IEEE Trans. Antennas Propag. 49,313-326 (2001).
[CrossRef]

1995 (1)

F. D. Hastings, J. B. Schneider, and S. L. Shira, "A Monte-Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

Carin, L.

T. Dogaru, L. Collins, and L. Carin, "Optimal time-domain detection of a deterministic target buried under a randomly rough interface," IEEE Trans. Antennas Propag. 49,313-326 (2001).
[CrossRef]

Collins, L.

T. Dogaru, L. Collins, and L. Carin, "Optimal time-domain detection of a deterministic target buried under a randomly rough interface," IEEE Trans. Antennas Propag. 49,313-326 (2001).
[CrossRef]

Dogaru, T.

T. Dogaru, L. Collins, and L. Carin, "Optimal time-domain detection of a deterministic target buried under a randomly rough interface," IEEE Trans. Antennas Propag. 49,313-326 (2001).
[CrossRef]

Edee, K.

Granet, G.

Guizal, B.

Hastings, F. D.

F. D. Hastings, J. B. Schneider, and S. L. Shira, "A Monte-Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

Ichikawa, H.

Kawai, T.

T. Kojima and T. Kawai, "Numerical analysis of detected signal characteristics from a blue laser optical disk model with random rough surfaces by FDTD method," IEICE Trans. Electron. E 90-C, 1599-1605 (2007).
[CrossRef]

Kikuta, H.

Kojima, T.

T. Kojima and T. Kawai, "Numerical analysis of detected signal characteristics from a blue laser optical disk model with random rough surfaces by FDTD method," IEICE Trans. Electron. E 90-C, 1599-1605 (2007).
[CrossRef]

Liu, W.-C.

Moreau, A.

Ng, M.-Y.

Schneider, J. B.

F. D. Hastings, J. B. Schneider, and S. L. Shira, "A Monte-Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

Shira, S. L.

F. D. Hastings, J. B. Schneider, and S. L. Shira, "A Monte-Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

E (1)

T. Kojima and T. Kawai, "Numerical analysis of detected signal characteristics from a blue laser optical disk model with random rough surfaces by FDTD method," IEICE Trans. Electron. E 90-C, 1599-1605 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

T. Dogaru, L. Collins, and L. Carin, "Optimal time-domain detection of a deterministic target buried under a randomly rough interface," IEEE Trans. Antennas Propag. 49,313-326 (2001).
[CrossRef]

F. D. Hastings, J. B. Schneider, and S. L. Shira, "A Monte-Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

J. Mod. Opt. (1)

H. Ichikawa, "Subwavelength triangular random gratings," J. Mod. Opt. 49, 1893-1906 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Other (2)

C. F. Bohren, "Scattering by particles," in Handbook of Optics I, M. Bass, ed., (McGraw-Hill, New York, 1995), pp. 6.1-6.21.

J. Turunen, "Diffraction theory of microrelief gratings" in Micro-Optics, H. P. Herzig, ed., (Taylor & Francis, London, 1997).

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Figures (8)

Fig. 1.
Fig. 1.

Scattering problem considered. Horizontal double-headed arrows denote local periods.

Fig. 2.
Fig. 2.

Analyzed area for the FDTD method.

Fig. 3.
Fig. 3.

Power spectra obtained with the FDTD method. (a) Average values. (b) Standard deviation values. Each color denotes the number of random structures considered. Because of normal incidence, θ<0 is omitted from the figures.

Fig. 4.
Fig. 4.

Normal distribution and component gratings. Horizontal axis denotes grating periods.

Fig. 5.
Fig. 5.

The concept of superposition of gratings. ηm (dj ) is power of mth diffraction order of the jth component grating. Only three gratings are shown for simplicity.

Fig. 6.
Fig. 6.

Comparing power spectra of the GSM and the FDTD method. oe-16-11-8292-i001: Δd=0.17λ. oe-16-11-8292-i002: Δd=0.076λ. (a) Transmission. (b) Reflection.

Fig. 7.
Fig. 7.

Hypothetical experiment: observation of scattered light by a random structure illuminated by a beam of finite width.

Fig. 8.
Fig. 8.

Finite beam size causes absolute values of observed power level.

Equations (7)

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C m ( i , k ) = DFT t { F n ( i , k ) } ,
A l ( k ) = DFT s { C 1 ( i , k ) } ,
η ( θ ) = { η m ( d j ) j γ j , ( m 0 ) , j η 0 ( d j ) j γ j ( m = 0 ) ,
p ( x ) = exp ( x 2 a 2 ) ,
q ( x ) = exp ( x 2 b 2 ) ,
f ( x ) = p ( ξ ) q ( x ξ ) d ξ = ab a 2 + b 2 π exp [ x 2 ( a 2 + b 2 ) ] ,
b π exp ( x 2 a 2 ) .

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