New perturbation theory of diffraction gratings and its application to the study of ghosts

Dusséaux, Richard; Faure, Claire; Chandezon, J.; Molinet, F.

doi:10.1364/josaa.12.001271

Cited by 12 publications

(8 citation statements)

References 18 publications

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“…Consequently, r * n is also an eigenvalue of the scattering matrix. This property have been already shown for the diffraction grating studied in the translation system [16,17].…”

Section: Properties Of the Scattering Matrix And Of The Eigenvalue Spsupporting

confidence: 64%

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Scattering of a Plane Wave by a 1-Dimensional Rough Surface Study in a Nonorthogonal Coordinate System

Dusséaux¹,

Oliveira²

2001

PIER

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We present a method giving the field scattered by a plane surface with a cylindrical local perturbation illuminated by a plane wave. The theory is based on Maxwell's equations in covariant form written in a nonorthogonal coordinate system fitted to the surface profile. The covariant components of electric and magnetic vectors are solutions of a differential eigenvalue system. A Method of Moments (PPMoM) with Pulses for basis and weighting functions is applied for solving this system in the spectral domain. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. Their amplitudes are found by solving the boundary conditions. Above a given deformation, the Rayleigh integral is valid and becomes identified with one of covariant components of the scattered field. Applying the PPMo Method to this equality, we obtain the asymptotic field and the scattering pattern. The method is numerically investigated in the far-field zone, by means of convergence tests on the spectral amplitudes and on the power balance criterion. The theory is verified by comparison with results obtained by a rigorous method.

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“…Consequently, r * n is also an eigenvalue of the scattering matrix. This property have been already shown for the diffraction grating studied in the translation system [16,17].…”

Section: Properties Of the Scattering Matrix And Of The Eigenvalue Spsupporting

confidence: 64%

“…Substituting expressions (13) and (14) into system (12) and taking the inner product of the intermediate equations with each basis function b q (α), we obtain a set of differential equations relating coefficients F q (α) and G q (α) to each other (17).…”

Section: The Scattering Matrixmentioning

confidence: 99%

Scattering of a Plane Wave by a 1-Dimensional Rough Surface Study in a Nonorthogonal Coordinate System

Dusséaux¹,

Oliveira²

2001

PIER

Self Cite

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“…We introduce -Ghost‖ concept to explain the unusual diffraction phenomena, such as deformed hexagram-shaped diffraction patterns, by using earlier ghosts theory of onedimensional grating for reference [10,11]. In this paper, ghost fringes are defined as false, blur or deformed images in a diffraction patterns.…”

Section: Ghost Diffraction Imagementioning

confidence: 99%

Diffraction of transmission light through triangular apertures in array of retro-reflective microprisms

Tan¹,

Chen²

2012

Appl. Opt.

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Abstract:The array of micro-prisms was described by model of multi-period blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction array theorem. The relation between zonal /line ghost fringes and imperfectly fabricated array structures was analyzed.Geometrical performances (e.g., the dihedral angle of micro-prism) were tested by measuring the features of diffraction patterns of samples from three retro-reflective sheeting manufacturers.

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“…A rigorous statement of the boundary-value problem is used, taking into account the transmitted and reflected diffraction orders [9,10]. The wave equation is solved using perturbation theory [11][12][13][14]. We compare the expression for the first diffraction order obtained in the first approximation of the perturbation theory with the corresponding expression obtained in simplified consideration, as the hologram thickness (d) tends to zero.…”

Section: Introductionmentioning

confidence: 99%

Is it possible to consider a thin hologram as a slide?

Smolovich

2023

Optik

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New perturbation theory of diffraction gratings and its application to the study of ghosts

Cited by 12 publications

References 18 publications

Scattering of a Plane Wave by a 1-Dimensional Rough Surface Study in a Nonorthogonal Coordinate System

Scattering of a Plane Wave by a 1-Dimensional Rough Surface Study in a Nonorthogonal Coordinate System

Diffraction of transmission light through triangular apertures in array of retro-reflective microprisms

Is it possible to consider a thin hologram as a slide?

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