Abstract

Extremely asymmetrical scattering (EAS) is a highly resonant type of Bragg scattering with a strong resonant increase of the scattered wave amplitude inside and outside the grating. EAS is realized when the scattered wave propagates parallel to the grating boundaries. We present a rigorous algorithm for the analysis of non-steady-state EAS, and investigate the relaxation of the incident and scattered wave amplitudes to their steady-state values. Non-steady-state EAS of bulk TE electromagnetic waves is analyzed in narrow and wide, slanted, holographic gratings. Typical relaxation times are determined and compared with previous rough estimations. Physical explanation of the predicted effects is presented.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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Appl. Opt.

Diffractive Optics and Micro-Optics

D. K. Gramotnev, �Frequency response of extremely asymmetrical scattering of electromagnetic waves in periodic gratings,� in Diffractive Optics and Micro-Optics, OSA Technical Digest (Optical Society of America, Washington DC, 2000), pp. 165�167.

J. Mod. Opt.

D. K. Gramotnev, T. A. Nieminen, and T. A. Hopper, �Extremely asymmetrical scattering in gratings with varying mean structural parameters,� J. Mod. Opt. (accepted for publication).

J. Opt. Soc. Am. A

J. Phys. D

D. K. Gramotnev, �A new method of analysis of extremely asymmetrical scattering of waves in periodic Bragg arrays,� J. Phys. D 30 2056�2062 (1997).
[CrossRef]

J. Phys. Soc. Japan.

S. Kishino, A. Noda, and K. Kohra, �Anomalous enhancement of transmitted intensity of diffraction of x-rays from a single crystal,� J. Phys. Soc. Japan. 33 158�166 (1972).
[CrossRef]

Opt. Commun.

T. A. Nieminen and D. K. Gramotnev, �Rigorous analysis of extremely asymmetrical scattering of electromagnetic waves in slanted periodic gratings,� Opt. Commun. 189 175�186 (2001).
[CrossRef]

Opt. Quant. Electron.

D. K. Gramotnev and D. F. P. Pile, �Double-resonant extremely asymmetrical scattering of electromagnetic waves in non-uniform periodic arrays,� Opt. Quant. Electron. 32 1097�1124 (2000).
[CrossRef]

D. K. Gramotnev, �Grazing-angle scattering of electromagnetic waves in periodic Bragg arrays,� Opt. Quant. Electron. 33 253�288 (2001).
[CrossRef]

Phys. Lett. A

D. K. Gramotnev, �Extremely asymmetrical scattering of Rayleigh waves in periodic groove arrays,� Phys. Lett. A 20, 184-190 (1995).
[CrossRef]

Supplementary Material (3)

» Media 1: GIF (469 KB)     
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Figures (3)

Fig. 1.
Fig. 1.

The geometry of EAS in a slanted periodic grating.

Fig. 2.
Fig. 2.

Animations showing the approach of amplitudes of the scattered (bottom graphs) and incident (top graphs) waves to the steady-state solutions (light lines). The grating widths are (a) L = 10μm, (b) L = 28 μm ≈ L c, and (c) L = 80 μm. The vertical dotted lines show the grating boundaries. [Media 1] [Media 2] [Media 3]

Fig. 3.
Fig. 3.

The time dependencies of normalized non-steady-state amplitudes of (a–c) the first diffracted order (scattered wave) |E 1|E 00|, and (d) the zeroth diffracted order (transmitted wave) |E 0(x = L)/E 00|. The grating widths are L = 10 μm ((a) and curve (i) in (d)), L = 28 μm ≈ L c ((b) and curve (ii) in (d)), and L = 80 μm ((c) and curve (iii) in (d)). The scattered wave amplitudes (a–c) are shown at (1) the front boundary (x = 0), (2) the rear boundary (x = L), and (3) the middle of the grating (x = L/2).

Equations (3)

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s = + g exp ( i q x x + i q y y ) + g exp ( i q x x i q y y ) , if 0 < x < L ,
s = , if x < 0 or x > L ,
k 1 ( ω 0 ) = k 0 ( ω 0 ) q ,

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