Failure of the optical theorem for Gaussian-beam scattering by a spherical particle

Lock, James A.; Hodges, Joseph T.; Gouesbet, G.

doi:10.1364/josaa.12.002708

Cited by 44 publications

(31 citation statements)

References 27 publications

(30 reference statements)

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“…(23), (24) show that both the absorption and scattering cross-sections are not the mere difference/sum of the individual resonance and perfectly conducting background terms; there is an interference factor as described by Eq. (29).…”

Section: Theoretical Analysismentioning

confidence: 99%

“…Several formulations exist for acoustical [21,22], quantum [23], and optical Gaussian beams [24] (and others of arbitrary shape [25]) that possess some degree of amplitude roll-off in the transverse direction. Though in principle those formalisms are applicable to any object of arbitrary shape, computing the extinction, scattering, and absorption cross sections (or their corresponding efficiencies) of elongated (cylindrical-like) objects with the analytical models in spherical coordinates, leads to numerical instabilities and significant inaccuracies.…”

Section: Introductionmentioning

confidence: 99%

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

Mitri

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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Section: Theoretical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Mitri

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…This well-known identity, often addressed as the "optical theorem" for its generality, applies to the scattering from any object illuminated by a linearly polarized plane wave [17][18]. Clearly, Eq.…”

Section: Introductionmentioning

confidence: 99%

How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem?

Alù

Engheta

2010

J. Nanophoton

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A few decades ago, Kerker et al. [J. Opt. Soc. Am. 73, 765-767 (1983)] theoretically pointed out the interesting possibility of conceiving small magnetodielectric spheres that may provide zero scattering in the forward direction, despite significantly larger scattering in any other direction. Recent experimental and theoretical papers on the topic have further discussed this possibility in more realistic scenarios. Inspecting some of their analyses, it seems indeed possible to conceive nanoparticles characterized by a scattering pattern with a sharp minimum, although not zero, in the forward direction. From a theoretical standpoint, however, it is well known that the total scattered power from any object has to be proportional to a portion of the scattered field in the forward direction, implying that very small or zero forward scattering should be synonymous to even smaller or zero total scattering, regardless of the nature of the object and of its design. Using analytical theory and an accurate scattering formulation, we clarify the nature of this apparent paradox and the limitations of this anomalous phenomenon in terms of particle size. In this way, we shed some new light on theoretical and experimental papers on the topic, identifying relevant missteps in some of their physical interpretation, and considering the general possibility of verifying these effects. This discussion may also be relevant to some cloaking applications using exotic artificial materials. 765-767 (1983)] theoretically pointed out the interesting possibility of conceiving small magnetodielectric spheres that may provide zero scattering in the forward direction, despite significantly larger scattering in any other direction. Recent experimental and theoretical papers on the topic have further discussed this possibility in more realistic scenarios. Inspecting some of their analyses, it seems indeed possible to conceive nanoparticles characterized by a scattering pattern with a sharp minimum, although not zero, in the forward direction. From a theoretical standpoint, however, it is well known that the total scattered power from any object has to be proportional to a portion of the scattered field in the forward direction, implying that very small or zero forward scattering should be synonymous to even smaller or zero total scattering, regardless of the nature of the object and of its design. Using analytical theory and an accurate scattering formulation, we clarify the nature of this apparent paradox and the limitations of this anomalous phenomenon in terms of particle size. In this way, we shed some new light on theoretical and experimental papers on the topic, identifying relevant missteps in some of their physical interpretation, and considering the general possibility of verifying these effects. This discussion may also be relevant to some cloaking applications using exotic artificial materials.

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“…3,4 Later on, other generalizations have been considered for the case of random scatterers, for stochastic incident fields, for the specific case of two monochromatic plane waves of the same frequency propagating in different directions, 5 for a wide class of partially coherent beams, 6 and also for the case when the incident field contains evanescent waves. More than 10 years ago, I established ͑with coworkers͒ that Eq.…”

Section: Introductionmentioning

confidence: 99%

On the optical theorem and non-plane-wave scattering in quantum mechanics

Gouesbet

2009

Journal of Mathematical Physics

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In quantum mechanics, the optical theorem states that the extinction cross section is equal ͑within a prefactor 4 / k, in which k is a quantum wave number͒ to the imaginary part of the forward scattering angular function. This theorem is valid for plane wave scattering. We discuss modifications required for non-plane-wave scattering and establish a generalized expression for the extinction cross section in quantum mechanics. Examples are provided for two kinds of quantum shaped beams, namely, Gaussian and Bessel beams.

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Failure of the optical theorem for Gaussian-beam scattering by a spherical particle

Cited by 44 publications

References 27 publications

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

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

How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem?

On the optical theorem and non-plane-wave scattering in quantum mechanics

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