A Study of the Fourth-Order Small Perturbation Method for Scattering From Two-Layer Rough Surfaces

Demir, M.A.; Johnson, Joel T.; Zajdel, Tom J.

doi:10.1109/tgrs.2011.2182614

Cited by 42 publications

(35 citation statements)

References 25 publications

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“…Second and higher-order perturbative developments have also been investigated [9,[26][27][28][29]. It is worth highlighting that pertinent analytical developments following a boundary perturbation approach can be particularly cumbersome [27]; conversely, rigorous second-order volumetric-perturbative developments demand for an appropriate mathematical playground (the distribution theory for discontinuous test functions) [9].…”

Section: Perturbative Methodsmentioning

confidence: 99%

“…It is worth highlighting that pertinent analytical developments following a boundary perturbation approach can be particularly cumbersome [27]; conversely, rigorous second-order volumetric-perturbative developments demand for an appropriate mathematical playground (the distribution theory for discontinuous test functions) [9]. In particular, in [27] the predictions of the fourth-order perturbation have been examined for scattering from two rough surfaces in a layered geometry. Accordingly, the interaction effects between the two surfaces can, in some cases, be the dominant contribution to cross-pol returns.…”

Section: Perturbative Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

Imperatore

Iodice

Pastorino

et al. 2017

International Journal of Antennas and Propagation

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This paper addresses the subject of electromagnetic wave scattering in layered media, thus covering the recent progress achieved with different approaches. Existing theories and models are analyzed, classified, and summarized on the basis of their characteristics. Emphasis is placed on both theoretical and practical application. Finally, patterns and trends in the current literature are identified and critically discussed.

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Section: Perturbative Methodsmentioning

confidence: 99%

Section: Perturbative Methodsmentioning

confidence: 99%

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

Imperatore

Iodice

Pastorino

et al. 2017

International Journal of Antennas and Propagation

View full text Add to dashboard Cite

show abstract

“…Here we need to find how |G 0 (k ix )| behaves in order to examine the validity of solution (11). We will come back to this issue later in Section 4.…”

Section: Zeroth Order Solutionmentioning

confidence: 99%

“…The small perturbation method has been studied for random rough surface scattering extensively [1][2][3][4][5][6][7][8][9][10][11][12]. Recently, the method has been studied for multi-layered random rough surfaces [2,5,7] as an analytical method which has advantages over numerical methods for multiple rough interfaces.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Scattering From One Dimensional Random Rough Surfaces of Dielectric Layered Media With Waveguide Modes Using Second Order Small Perturbation Method

Sanamzadeh¹,

Tsang²,

Johnson³

et al. 2018

PIER B

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Abstract-An alternative formulation of the Small Perturbation Method (SPM) in solving electromagnetic scattering from multi-layer random rough surfaces to resolve singularities in spectral integrals is presented. Non-monotonic permittivity changes will allow a multi-layer structure to support guided modes. The presence of these guided modes translates to poles in the zeroth order Green's function of the media for the surface fields. The poles appear in the first and second order perturbation solutions based on a iterative procedure. Thus, evaluating the spectral integrals to obtain the spatial fields becomes problematic. The Sommerfeld integration path instead of real line integrals is introduced by analytic continuation of the integrand into complex spectral space. It is verified that this alternative spectral integration method is valid for both monotonic and non-monotonic cases.

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“…High order corrections are included in [8][9][10][11][12][13][14], where fourth and higher order corrections are discussed in [11]. The SPM has also been extended to multilayer structures with an arbitrary number of layers [15][16][17][18], and the fourth order SPM has been applied to a two-layer geometry in [19]. The KA is a high-frequency approach valid for large curvature roughness, and has been extended to two-layer structure in [20,21].…”

Section: Introductionmentioning

confidence: 99%

Scattering and Transmission of Waves in Multiple Random Rough Surfaces: Energy Conservation Studies With the Second Order Small Perturbation Method

Wang¹,

Tsang²,

Johnson³

et al. 2016

PIER

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Abstract-Energy conservation is an important consideration in wave scattering and transmission from random rough surfaces and is particularly important in passive microwave remote sensing. In this paper, we study energy conservation in scattering from layered random rough surfaces using the second order small perturbation method (SPM2). SPM2 includes both first order incoherent scattering and a second order correction to the coherent fields. They are combined to compute the total reflected and transmitted powers, as a sum of integrations over wavenumber k x , in which each integration includes the surface power spectra of a rough interface weighted by an emission kernel function (assuming the roughness of each interface is uncorrelated). We calculate the corresponding kernel functions which are the power spectral densities for one-dimensional (1D) surfaces in 2D scattering problems and examine numerical results for the cases of 2 rough interfaces and 51 rough interfaces. Because it is known that the SPM when evaluated to second order conserves energy, and it can be applied to second order for arbitrary surface power spectra, energy conservation can be shown to be satisfied for each value of k x in the kernel functions. The numerical examples show that energy conservation is obeyed for any dielectric contrast, any layer configuration and interface, and arbitrary roughness spectra. The values of reflected or transmitted powers predicted, however, are accurate only to second order in small surface roughness.

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A Study of the Fourth-Order Small Perturbation Method for Scattering From Two-Layer Rough Surfaces

Cited by 42 publications

References 25 publications

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

Electromagnetic Scattering From One Dimensional Random Rough Surfaces of Dielectric Layered Media With Waveguide Modes Using Second Order Small Perturbation Method

Scattering and Transmission of Waves in Multiple Random Rough Surfaces: Energy Conservation Studies With the Second Order Small Perturbation Method

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