Scattering of Electromagnetic Waves: Theories and Applications

Tsang, Leung; Kong, Jin Au; Ding, Kung‐Hau

doi:10.1002/0471224286

Cited by 816 publications

(789 citation statements)

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“…Describing the scattering process off the nanoprobe in the basis of vector spherical harmonics (VSHs), we follow the notation of Tsang et al 1 . To simplify the theoretical description of the energy transfer through the interface and the interaction of the scattered fields with the latter, we transfer the effect of the interface to the basis functions M …”

Section: S1 Detailed Description Of the Influence Of The Substratementioning

confidence: 99%

Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams

et al. 2013

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Highly confined vectorial electromagnetic field distributions represent an excellent tool for detailed studies in nano-optics and high resolution microscopy, such as nonlinear microscopy 1 , advanced fluorescence imaging 2-4 or nanoplasmonics 5,6 . Such field distributions can be generated, for instance, by tight focussing of polarized light beams [7][8][9][10] . To guarantee high quality and resolution in the investigation of objects with sub-wavelength dimensions, the precise knowledge of the spatial distribution of the exciting vectorial field is of utmost importance. Full-field reconstruction methods presented so far involved, for instance, complex near-field techniques 11,12 . Here, we demonstrate a simple and straight-forward to implement measurement scheme and reconstruction algorithm based on the scattering signal of a single spherical nanoparticle as a field-probe. We are able to reconstruct the amplitudes of the individual focal field components as well as their relative phase distributions with sub-wavelength resolution from a single scan measurement without the need for polarization analysis of the scattered light. This scheme can help to improve modern microscopy and nanoscopy techniques.In the optical analysis of sub-wavelength objects such as cellular structures 13 , plasmonic particles 5,6,14 or single spins 3 , nano-optical tools including highly resolving microscopy techniques are used. Because such methods utilise complex and highly confined vector fields, the exact knowledge of the corresponding spatial field distributions is crucial. In the last decades, several techniques have been proposed to map these focal fields, such as using metal knife edges 15,16 to probe the total electric energy density distribution, fluorescence molecules 17 , tapered fibres 18,19 or tip-based methods 12 to image specific field orientations, or near-field scanning optical microscope (NSOM) techniques to extract amplitude and even phase information 11 . These NSOM-based methods require complex measurement and detection schemes and calibration procedures to allow for amplitude and phase a) Electronic mail: thomas.bauer@mpl.mpg.de mapping of individual field components. As an alternative approach for measuring phase information also a single particle scattering scheme was proposed recently 22 , where the authors show that Mie-scattering can distinguish the topological charge of vortex-beams.We now demonstrate a precise and easily implementable field reconstruction technique for highly confined field distributions created by arbitrary focusing systems, based on, what we call, Mie-scattering nanointerferometry. The basic concept of this reconstruction method for highly confined focal field distributions can be understood as follows. We use a metallic nanosphere on a glass substrate as local field sensor and scan it stepwise through the focal field distribution under investigation. If the particle size is chosen small enough, it will be excited by the local electric field E(r 0 ) only. Its response can be described,...

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Section: S1 Detailed Description Of the Influence Of The Substratementioning

confidence: 99%

Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams

et al. 2013

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“…In this paper, specular reflection property of the rough sea surface scattering is applied to reduce the coupling area on the sea surface. This property shows that the main scattering energy is concentrated at the specular direction which is 10 dB higher than the scatterings at other directions [17]. Therefore, the coupling area on the sea surface can be truncated according to the specular reflection.…”

Section: Reducing the Coupling Areasmentioning

confidence: 97%

“…Especially when there are several targets over the surface, it is rather time-consuming to solve the mutual interactions. In order to improve the efficiency of the method, coupling area of the sea surface is truncated according to geometrical optical principle [17]. Then, a fast far-field approximation (FAFFA) [18] is used to calculate the mutual EM coupling interactions between the targets and the sea surface.…”

Section: Introductionmentioning

confidence: 99%

Numerical Approach on Doppler Spectrum Analysis for Moving Targets Above a Time-Evolving Sea Surface

Qi¹,

Zhao

Nie³

2013

PIER

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Abstract-In order to analyze the Doppler spectrum of threedimensional (3-D) moving targets above a time-evolving sea surface, a hybrid method with acceleration techniques is proposed to simulate the electromagnetic (EM) scattering from the composite moving model. This hybrid iterative method combines Kirchhoff approximation (KA) and the multilevel fast multipole algorithm (MLFMA) to solve the EM backscattering from the rough sea surface and the targets, respectively, then mutual EM coupling effects between them are taken into account through an iterative process. To overcome the vast computational cost in the iterative process, acceleration approaches which can greatly reduce the calculation time are applied. Coupling area on the sea surface is truncated according to geometrical optic principle. Then a fast far-field approximation (FAFFA) is applied to speed up the mutual interactions between the targets and the sea surface. A successive iteration method is proposed to reduce the convergence steps for the MLFMA process. The accuracy and efficiency of this hybrid method with accelerations are demonstrated. Doppler spectra of backscattering signals obtained from such numerical EM simulations are compared for different incident angles, target velocities and surface models. The broadening effects of the Doppler spectra due to the mutual EM coupling interactions are studied.

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“…It should be noted that the definition of scattering coefficient here is different from that in [22] by a factor cos θ i so that the integration of σ ol over all scattering angles is cos θ i rather than unity. The bistatic scattering coefficient of (1) is commonly evaluated through the geometric optics (GO) approximation to yield…”

Section: The Two-scale Modelmentioning

confidence: 99%

“…Scattering from the large scale wave is evaluated with the Kirchhoff approximation (KA), which is given by [22] …”

Section: The Two-scale Modelmentioning

confidence: 99%

Comparison of the Two-Scale and Three-Scale Models for Bistatic Electromagnetic Scattering From Ocean Surfaces

Luo¹,

Du²

2013

PIER

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Abstract-With rapid development of satellite technology in monitoring the ocean, a good understanding of the physical processes involved in the electromagnetic ocean-surface interaction is required. The composite surface models are usually applied in the analysis of the interaction, hence a systematical check of their region of validity is desirable. Based on a generalized minimal residual procedure which is right preconditioned (GMRES-RP) that we have recently developed which has demonstrated the desirable properties of a numerical algorithm: robust and efficient, in this paper, for bistatic scattering from one dimensional ocean surfaces, we carry out a systematic assessment of the performance of the popular two-scale model and the advanced three-scale model under different conditions of ocean surface wind speeds, polarizations, frequencies, and incidence angles. It is found that the two-scale model in general captures the bistatic scattering pattern, yet the accuracy of geometrical optics (GO) for the large scale wave brings considerable impact on the overall accuracy. If the evaluation of the contribution of the large scale wave is instead using direct numerical integration for the corresponding Kirchhoff integral, impressive improvements are frequently observed, especially at low frequency (L and C bands) and low wind speed (3 m/s). But care should be taken when apply two-scale method with numerical integration, since there are cases where visible discrepancy with method of moment (MoM) are observed. On the other hand, the threescale model is found in very good agreement with MoM across the considered ocean surface wind speeds, polarizations, frequencies, and incidence angles, hence represents a much advanced model over the two-scale model.

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Scattering of Electromagnetic Waves: Theories and Applications

Cited by 816 publications

References 0 publications

Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams

Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams

Numerical Approach on Doppler Spectrum Analysis for Moving Targets Above a Time-Evolving Sea Surface

Comparison of the Two-Scale and Three-Scale Models for Bistatic Electromagnetic Scattering From Ocean Surfaces

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