Critical dimension metrology of a plasmonic photonic crystal based on Mueller matrix ellipsometry and the reduced Rayleigh equation

Banon, Jean-Philippe; Nesse, Torstein; Ghadyani, Z.; Kildemo, Morten; Simonsen, Ingve

doi:10.1364/ol.42.002631

Cited by 9 publications

(16 citation statements)

References 23 publications

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“…[16]; only a brief summary of the method is presented here. This method has previously been used for the investigations of the two-dimensional rough surface scattering of light from metallic or perfectly conducting surfaces [16,17,18]; from and through single dielectric interfaces [17,19,20] and film geometries [21,22,23]. In this method, an ensemble of realizations of the surface profile function ζ j (x ) is generated by the use of the Fourier filtering method [24] on a square grid of N x ×N x surface points, covering an area of S = L 2 in the (ê 1 ,ê 2 )-plane.…”

Section: Nonperturbative Methodsmentioning

confidence: 99%

“…(18) and (20) by applying them respectively at a 3 = + and a 1 = − and by using Eqs. (23) and (24) for the model of the field expansion. This yields the following two decoupled integral equations for the reflection or transmission amplitudes, the so-called reduced Rayleigh equations, that can be written in the following general form, for X = R or T [15]…”

Section: The Reduced Rayleigh Equationsmentioning

confidence: 99%

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Selective enhancement of Selényi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

2018

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By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, we present a detailed study of the scattering of light from two-dimensional weakly rough dielectric films. It is shown that for several rough film configurations, Selényi interference rings exist in the diffusely scattered light. For film systems supported by dielectric substrates where only one of the two interfaces of the film is weakly rough and the other planar, Selényi interference rings are observed at angular positions that can be determined from simple phase arguments. For such single-rough-interface films, we find and explain by a single scattering model that the contrast in the interference patterns is better when the top interface of the film (the interface facing the incident light) is rough than when the bottom interface is rough. When both film interfaces are rough, Selényi interference rings exist but a potential cross-correlation of the two rough interfaces of the film can be used to selectively enhance some of the interference rings while others are attenuated and might even disappear. This feature may in principle be used in determining the correlation properties of interfaces of films that otherwise would be difficult to access.

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Section: Nonperturbative Methodsmentioning

confidence: 99%

Section: The Reduced Rayleigh Equationsmentioning

confidence: 99%

Selective enhancement of Selényi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

2018

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“…where c is the speed of the field in the liquid. The field satisfies either (a) the Dirichlet boundary condition ψ(x|ω) x3=ζ(x ) = 0 (2) or (b) the Neumann boundary condition…”

Section: Scattering Theorymentioning

confidence: 99%

“…In several resent papers the present authors have studied theoretically and computationally the diffraction of ppolarized light from a perfectly conducting grating [1] and from a high-index dielectric grating [2], and the diffraction of a shear horizontally polarized acoustic wave from a gating ruled on the surface of an isotropic elastic medium [3]. Each of these media does not support a surface wave when the surface bounding it is planar, but supports one when it is periodically corrugated.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we extend the work presented in Refs. [1][2][3] to the case of diffraction of a scalar plane wave from a doubly-periodic grating (often called a bigrating or a cross-grating), fabricated on a surface of the medium that when planar does not support a surface wave, but can support one when it is doubly periodic. Specifically, we consider the diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or the Neumann boundary condition is satisfied.…”

Section: Introductionmentioning

confidence: 99%

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Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces

Maradudin

Pérez-Chávez

Jędrzejewski

et al. 2018

Low Temperature Physics

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The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with results of a rigorous Green's function numerical calculation. * aamaradu@uci.edu † Ingve.Simonsen@ntnu.no arXiv:1801.09951v1 [physics.optics]

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Systematic analysis of the Rayleigh–Wood anomalies and the symmetry relations of 2D‐periodic nanostructures by imaging spectroscopic ellipsometry

Okano¹,

Duwe²,

Sivis

et al. 2023

Applied Research

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Periodic arrays of metallic nanostructures were fabricated by electron beam lithography and studied by means of spectroscopic imaging ellipsometry in the near infrared to ultraviolet spectral ranges. The sample consists of gold nanodisc and nanorod gratings on a silicon substrate. Spectroscopic imaging ellipsometry, allowing for the simultaneous observation of all gratings with microscopic resolution, was used to systematically analyze the varying grating and nanostructure parameters. The ellipsometric spectra obtained for a full in‐plane sample rotation proved to be a highly sensitive measure of the gratings’ Rayleigh–Wood anomalies. Their dependence on the sample azimuth was in excellent agreement with the Rayleigh lines calculated from the grating parameters and could be tracked for both the ambient‐to‐grating and the grating–substrate interfaces. Contrary to other studies on similarly sized nanoparticle arrays, we found no indication of localized plasmon resonance in the visible range of the spectrum, but only a weak NIR response truncated by the Rayleigh lines. Finally, the symmetry of the structures was investigated by imaging Mueller‐matrix measurements.

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Critical dimension metrology of a plasmonic photonic crystal based on Mueller matrix ellipsometry and the reduced Rayleigh equation

Cited by 9 publications

References 23 publications

Selective enhancement of Selényi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

Selective enhancement of Selényi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces

Systematic analysis of the Rayleigh–Wood anomalies and the symmetry relations of 2D‐periodic nanostructures by imaging spectroscopic ellipsometry

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