Generalization of the optical theorem for monochromatic electromagnetic beams of arbitrary wavefront in cylindrical coordinates

Mitri, F.G.

doi:10.1016/j.jqsrt.2015.07.016

Cited by 34 publications

(19 citation statements)

References 53 publications

(78 reference statements)

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“…In the primed system of coordinates, the effective electric field component incident on the second cylinder is deduced from Eq. (9) such that, (15) Subsequently, the formulation of the scattering in the far-field [35] can be used, since the problem in hand is now reduced to the single-object case. This procedure leads to exact mathematical expressions without any approximations.…”

Section: Methodsmentioning

confidence: 99%

“…In the far-field limit, the cylindrical Bessel and Hankel functions of the first kind take the following forms, respectively,     The expression for the intrinsic scattering cross-sections for the cylinders 1 and 2 can be obtained from the previous analysis [35] for the single scatterer in arbitrary-shaped beams as The expression for the intrinsic absorption cross-section is also determined from [35] by noticing that the polarization of the incident plane waves is TM (i.e., axial polarization of the incident field). Therefore, based on Eqs.…”

Section: Methodsmentioning

confidence: 99%

“…Therefore, based on Eqs. (9)-(11) in [35], the intrinsic absorption cross-section is obtained as Finally, the expression for the extinction cross-section is obtained from Eqs. (16) and (17) as…”

Section: Methodsmentioning

confidence: 99%

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Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Mitri

2019

Journal of Modern Optics

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In this work, exact mathematical expansions for the intrinsic electromagnetic (EM) or optical cross-sections (i.e., extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous medium are derived. The incident illuminating field is an axially-polarized electric field composed of plane travelling waves with an arbitrary angle of incidence in the polar plane. The formalism is based on the multipole modal expansion method in cylindrical coordinates and the translational addition theorem applicable to any range of frequencies. An effective EM field, incident on the probed cylinder, is defined first, which includes the initial and re-scattered field from the second cylinder. Subsequently, it is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross-sections based on integrating their corresponding time-averaged intensities over the surface of the probed object by applying the Poynting theorem. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. Emphasis is given on varying the interparticle distance, the angle of incidence, and the dimensionless sizes of the cylinders. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross-sections.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Mitri

2019

Journal of Modern Optics

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“…It also served as the foundation of the connection between dispersion relation and causality 27 . A wide variety of applications of the optical 25 theorem includes phase shift estimation from measurements of the differential scattering cross-section in quantum mechanics 28 , evaluation of cracks in elastic solids 29,30 , diffraction tomography 31 , analysis of attenuation effects from scatterers 32 , Green's function reconstruction in inhomogeneous elastic solid medium 33 , seismic interferometry 34 , and calculation of energy loss in solids with dislocation 35 , to name a few. In ultrasonic nondestructive testing (NDT) 36 , an ultrasound wave is employed to investigate solid structures with 30 inclusions, dislocation, and microcracks 37 .…”

Section: Introductionmentioning

confidence: 99%

Extended optical theorem in isotropic solids and its application to the elastic radiation force

Leão-Neto

Lopes

Silva

2017

Journal of Applied Physics

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The optical theorem is an important tool for scattering analysis in acoustics, electromagnetism, and quantum mechanics. We derive an extended version of the optical theorem for the scattering of elastic waves by a spherical inclusion embedded in a linear elastic solid using a vector spherical harmonics representation of the waves. The sphere can be a rigid, empty cavity, elastic, viscoelastic, or layered material. The theorem expresses the extinction cross-section, i.e. the time-averaged power extracted from the incoming beam per its intensity, regarding the partial-wave expansion coefficients of the incident and scattered waves. We establish the optical theorem for a longitudinal spherically focused beam scattered by a sphere. Moreover, we use the optical theorem formalism to obtain the radiation force exerted on an inclusion by an incident plane wave and focused beam. Considering an iron sphere embedded in an aluminum matrix, we compute the scattering and elastic radiation force efficiencies. In addition, the elastic radiation force is obtained on a stainless steel sphere embedded in a tissue-like medium (soft solid). Remarkably, we find a relative difference of up to 98% between our findings and previous lossless liquid models. Regarding some applications, the obtained results have a direct impact on ultrasound-based elastography techniques, ultrasonic nondestructive testing, as well as implantable devices activated by ultrasound.

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“…, those coefficients become complex where the imaginary part represents the rate of absorption[41] (for a passive object) or amplification[49] (for an active emitting source object). In terms of the phase shifts, Eq.…”

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confidence: 99%

Optical radiation force (per–length) on an electrically conducting elliptical cylinder having a smooth or ribbed surface

Mitri¹

2019

OSA Continuum

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The aim of this work is to develop a formal semi-analytical model using the modal expansion method in cylindrical coordinates to calculate the optical/electromagnetic (EM) radiation force-per-length experienced by an infinitely long electrically-conducting elliptical cylinder having a smooth or wavy/corrugated surface in EM plane progressive waves with different polarizations. In this analysis, one of the semi-axes of the elliptical cylinder coincides with the direction of the incident field. Initially, the modal matching method is used to determine the scattering coefficients by imposing appropriate boundary conditions and solving numerically a linear system of equations by matrix inversion. In this method, standard cylindrical (Bessel and Hankel) wave functions are used. Subsequently, simplified expressions leading to exact series expansions for the optical/EM radiation forces assuming either electric (TM) of magnetic (TE) plane wave incidences are provided without any approximations, in addition to integral equations demonstrating the direct relationship of the radiation force with the square of the scattered field magnitude. An important application of these integral equations concerns the accurate determination of the radiation force from the measurement of the scattered field by any 2D non-absorptive object of arbitrary shape in plane waves. Numerical computations for the non-dimensional radiation force function are performed for electrically conducting elliptic and circular cylinders having a smooth or ribbed/corrugated surface. Adequate convergence plots confirm the validity and correctness of the method to evaluate the radiation force with no limitation to a particular frequency range (i.e. Rayleigh, Mie or geometrical optics regimes). Particular emphases are given on the aspect ratio, the non-dimensional size of the cylinder, the corrugation characteristic of its surface, and the polarization of the incident field. The results are particularly relevant in optical tweezers and other related applications in fluid dynamics, where the shape and stability of a cylindrical drop stressed by a uniform external electric/magnetic field are altered. Furthermore, a direct analogy with the acoustical counterpart is noted and discussed.

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Generalization of the optical theorem for monochromatic electromagnetic beams of arbitrary wavefront in cylindrical coordinates

Cited by 34 publications

References 53 publications

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Extended optical theorem in isotropic solids and its application to the elastic radiation force

Optical radiation force (per–length) on an electrically conducting elliptical cylinder having a smooth or ribbed surface

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