Diffraction of gratings with rough edges

Torcal-Milla, Francisco José; Sanchez‐Brea, Luis Miguel; Bernabéu, Eusebio

doi:10.1364/oe.16.019757

Cited by 38 publications

(15 citation statements)

References 17 publications

(19 reference statements)

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“…4b) that appears much weaker compared with theoretical predictions. The reason for this washed-out resonance is the inhomogeneous broadening induced by structural imperfections and surface corrugations [17]. In contrast to nanostructures with typical dimensions of 10 − 100 nm the surface fluctuations here are in the same order of magnitude as the Al 2 O 3 layer thickness yielding a much stronger impact on the spectral observables.…”

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confidence: 83%

Plasmonic modes of extreme subwavelength nanocavities

et al. 2010

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We study the physics of a new type of subwavelength nanocavities. They are based on U-shaped metal-insulator-metal waveguides supporting the excitation of surface plasmon polaritons. The nanocavity arrays are excited by plane waves at either a normal or oblique incidence. Because of their finite length, discrete modes emerge within the nanocavity. We show that the excitation symmetry with respect to the cavity ends permits the observation of even and odd modes. Our investigations include near- and far-field simulations and predict a strong spectral far-field response of the comparably small nanoresonators. The strong near-field enhancement observed in the cavity at resonance might be suitable to increase the efficiency of nonlinear optical effects and quantum analogies and might facilitate the development of optical elements, such as active plasmonic devices.

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confidence: 83%

Plasmonic modes of extreme subwavelength nanocavities

et al. 2010

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“…For instance, Bergner et al [10] use a similar approach to generate rough line edge profiles of 2D-binary gratings to calculate its impact on the angular dependence of the specular, 0th order reflectance at wavelengths around 633 nm. Torcal-Milla et al [13] have investigated gratings with rough edges in the visible optical range by applying the Rayleigh-Sommerfeld approach for near field simulations and the Fraunhofer approximation for the far field pattern. They found an exponential attenuation of the light intensities in terms of σ and the diffraction order as well.…”

Section: Introductionmentioning

confidence: 99%

Modelling line edge roughness in periodic line-space structures by Fourier optics to improve scatterometry

Gross

Heidenreich

Henn

et al. 2014

J. Eur. Opt. Soc.-Rapid Publ.

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In the present paper, we propose a 2D-Fourier transform method as a simple and efficient algorithm for stochastical and numerical studies to investigate the systematic impacts of line edge roughness on light diffraction pattern of periodic line-space structures. The key concept is the generation of ensembles of rough apertures composed of many slits, to calculate the irradiance of the illuminated rough apertures far away from the aperture plane, and a comparison of their light intensities to those of the undisturbed, 'non-rough' aperture. We apply the Fraunhofer approximation and interpret the rough apertures as binary 2D-gratings to compute their diffraction patterns very efficiently as the 2D-Fourier transform of the light distribution of the source plane. The rough edges of the aperture slits are generated by means of power spectrum density (PSD) functions, which are often used in metrology of rough geometries. The mean efficiencies of the rough apertures reveal a systematic exponential decrease for higher diffraction orders if compared to the diffraction pattern of the unperturbed aperture. This confirms former results, obtained by rigorous calculations with computational expensive finite element methods (FEM) for a simplified roughness model. The implicated model extension for scatterometry by an exponential damping factor for the calculated efficiencies allows to determine the standard deviation σ r of line edge roughness along with the critical dimensions (CDs), i.e., line widths, heights and other profile properties in the sub-micrometer range. First comparisons with the corresponding roughness value determined by 3D atomic force microscopy (3D AFM) reveal encouraging results.

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“…This modulation along the z-axis is known as Talbot effect and produces the mentioned replication of the fringes pattern at some certain distances. Several works have been published about Talbot effect considering that the diffraction grating is not perfect, for example, surface roughness on the grating [1][2][3][4], flaws [5], rough edges of the strips, [6]. In this work, we analyze the self-imaging process when the grating is ideal but the illumination beam presents a certain aberration.…”

Section: Introductionmentioning

confidence: 99%

Talbot effect with aberrated beams

Torcal-Milla

Sanchez‐Brea

Bernabéu

2009

Modeling Aspects in Optical Metrology II

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Diffraction gratings are one of the most used elements in optics and even in other fields of science. They are used also like part of measurement devices in scientific and industrial applications. As it is well known, self-imaging effect appears when a diffraction grating is illuminated with a coherent beam, such as a plane wave. This effect has been analyzed in depth and its behavior is well known under ideal grating and illumination conditions. Usually, the illumination beam is not perfectly collimated but presents a certain degree of aberration. The motivation of this work is to try to explain the behavior of the self-images of an ideal amplitude grating when it is illuminated by a non-perfect beam, that is, an aberrated beam. The known of this effect can help to understand how much the aberration of the light beam affects to the diffraction pattern, and more in depth, to the self-imaging phenomenon. The results presented in this work can be very useful in metrology applications, since sometimes the contrast obtained experimentally does not correspond to the theoretical predictions, usually due to aberrations in the light beam. For this, we have used a formalism based in the Rayleigh-Sommerfeld approach. We have modeled the aberrations by using the Zernike polynomials. On the other hand, we have considered all kinds of aberrations, spherical, coma, tilt, astigmatism, etc. As it is expected the contrast of the self-images decrease when the order of them increases and also when the aberration degree increase. In some cases, contrast inversion is also produced for high aberrations.

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Diffraction of gratings with rough edges

Cited by 38 publications

References 17 publications

Plasmonic modes of extreme subwavelength nanocavities

Plasmonic modes of extreme subwavelength nanocavities

Modelling line edge roughness in periodic line-space structures by Fourier optics to improve scatterometry

Talbot effect with aberrated beams

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