Rough Mirrors Research Articles

THz photometers for solar flare observations from space

Fil: Kaufmann, Pierre. Universidade Estadual de Campinas; Brasil. Universidade Presbiteriana Mackenzie; Brasil

Rough Mirror as a Quantum State Selector: Analysis and Design

We report analysis of rough mirrors used as the gravitational state selectors in neutron beam and similar experiments. The key to mirror properties is its roughness correlation function (CF) which is extracted from the precision optical scanning measurements of the surface profile. To identify CF in the presence of fluctuation-driven fat tails, we perform numerical experiments with computer-generated random surfaces with the known CF. These numerical experiments provide a reliable identification procedure which we apply to the actual rough mirror. The extracted CF allows us to make predictions for ongoing GRANIT experiments. We also propose a radically new design for rough mirrors based on Monte Carlo simulations for the 1D Ising model. The implementation of this design provides a controlled environment with predictable scattering properties.

Erratum: Casimir effect with rough metallic mirrors [Phys. Rev. A72, 012115 (2005)

Received 21 October 2012DOI:https://doi.org/10.1103/PhysRevA.86.059901©2012 American Physical Society

Application of the boundary integral equation method to very small wavelength-to-period diffraction problems

Diffraction from 1D multilayer gratings having arbitrary border profiles including edges is considered for small wavelength-to-period (λ/d) ratios, the most difficult case for any rigorous numerical method. The boundary integral equation theory is so flexible that we can indicate a few areas where it can be modified. In this work, special attention is paid to the main aspects of the Modified Boundary Integral Equation Method for λ/d ≪ 1 as well as to a more general treatment of the energy conservation law applicable to multilayer absorption gratings. Three types of small λ/d problems are known from optical applications: (a) shallow gratings working in the X-ray and extreme ultraviolet ranges, both at near-normal and grazing angles, (b) deep echelle gratings with a steep working facet illuminated along its normal by light of any wavelength, and (c) rough mirrors and gratings in which rough boundaries can be represented by a large-d grating, and which contain a number of random asperities illuminated at any angle and wavelength. Numerical examples of diverse in-plane diffraction problems are presented.

Application of the rigorous method to x-ray and neutron beam scattering on rough surfaces

The paper presents a comprehensive numerical analysis of x-ray and neutron scattering from finite-conducting rough surfaces which is performed in the frame of the boundary integral equation method in a rigorous formulation for high ratios of characteristic dimension to wavelength. The single integral equation obtained involves boundary integrals of the single and double layer potentials. A more general treatment of the energy conservation law applicable to absorption gratings and rough mirrors is considered. In order to compute the scattering intensity of rough surfaces using the forward electromagnetic solver, Monte Carlo simulation is employed to average the deterministic diffraction grating efficiency due to individual surfaces over an ensemble of realizations. Some rules appropriate for numerical implementation of the theory at small wavelength-to-period ratios are presented. The difference between the rigorous approach and approximations can be clearly seen in specular reflectances of Au mirrors with different roughness parameters at wavelengths where grazing incidence occurs at close to or larger than the critical angle. This difference may give rise to wrong estimates of rms roughness and correlation length if they are obtained by comparing experimental data with calculations. Besides, the rigorous approach permits taking into account any known roughness statistics and allows exact computation of diffuse scattering.

Casimir effect with rough metallic mirrors

We calculate the second order roughness correction to the Casimir energy for two parallel metallic mirrors. Our results may also be applied to the plane-sphere geometry used in most experiments. The metallic mirrors are described by the plasma model, with arbitrary values for the plasma wavelength, the mirror separation and the roughness correlation length, with the roughness amplitude remaining the smallest length scale for perturbation theory to hold. From the analysis of the intracavity field fluctuations, we obtain the Casimir energy correction in terms of generalized reflection operators, which account for diffraction and polarization coupling in the scattering by the rough surfaces. We present simple analytical expressions for several limiting cases, as well as numerical results that allow for a reliable calculation of the roughness correction in real experiments. The correction is larger than the result of the Proximity Force Approximation, which is obtained from our theory as a limiting case (very smooth surfaces).

Membrane Structure Characterization Using Variable-Period X-Ray Standing Waves

The variable-period x-ray standing wave (XSW) technique is emerging as a powerful tool for studying membrane structure. However, two significant problems arise when the method is used to characterize membranes of thickness d L < 100 Å. First, the surface roughness, σ r, of the supporting reflecting mirror convolutes with the intrinsic half-width of the marker atom distribution in the membrane, σ in, and contributes to an apparent half-width, σ, which is measured in the XSW experiment. Here we show how the latter terms are related quantitatively [ σ in = ( σ 2 − σ r 2) 1/2], such that rough mirrors give rise to larger marker atom distribution widths, σ, and how the required quantity σ in can be determined in the XSW measurement. Second, when the mean position of the marker atom layer, 〈 z〉, is close to one or both boundaries of the membrane, its distribution function is truncated at the boundary. In such cases, we show why marker atom distribution should be expressed in terms of its first and second moments. We also demonstrate by numerical simulations of realistic samples how the physical parameters, σ r, σ, 〈 z〉, and d L, affect x-ray reflectivity and fluorescence yield profiles as an aid in their interpretation.

Theory of Fabry-Perot interferometer with statistically rough mirrors

Theory of Fabry-Perot interferometer with statistically rough mirrors

Linear coupling, frequency shifts, and losses in a ring laser with rough mirrors

Linear coupling, frequency shifts, and losses in a ring laser with rough mirrors