Diffraction Effects in Semiclassical Scattering

Nussenzveig, H. M.

doi:10.1017/cbo9780511599903

Cited by 240 publications

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“…The only singularities that are met are the poles of the S-matrix lying in the CAM plane. They are known as Regge poles [7,8] and are determined by solving…”

Section: Semiclassical Analysismentioning

confidence: 99%

Resonant magnetic vortices

Décanini

Folacci

2003

Phys. Rev. A

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By using the complex angular momentum method, we provide a semiclassical analysis of electron scattering by a magnetic vortex of Aharonov-Bohm-type. Regge poles of the S-matrix are associated with surface waves orbiting around the vortex and supported by a magnetic field discontinuity. Rapid variations of sharp characteristic shapes can be observed on scattering cross sections. They correspond to quasibound states which are Breit-Wigner-type resonances associated with surface waves and which can be considered as quantum analogues of acoustic whispering-gallery modes. Such a resonant magnetic vortex could provide a new kind of artificial atom while the semiclassical approach developed here could be profitably extended in various areas of the physics of vortices.

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“…The only singularities that are met are the poles of the S-matrix lying in the CAM plane. They are known as Regge poles [7,8] and are determined by solving…”

Section: Semiclassical Analysismentioning

confidence: 99%

Resonant magnetic vortices

Décanini

Folacci

2003

Phys. Rev. A

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“…The smoothing of these singularities corresponds to the passage from the classical to the semi-classical approximation. As we have already noted several times, the obtained representation is far from being complete, as it does not represent the direct components of the collision: diffraction, direct reflection and forward glory contribution [15].…”

Section: Orbiting Resonances and Bound-statesmentioning

confidence: 99%

“…Thus, we can say that the near-forward diffractive scattering by a potential of this type, that is having a long-range tail, is not due to edge diffraction, but is rather produced by the contributions of very large angular momentum paths that undergo small deflection caused by the tail of the potential (see Ref. [15]). …”

Section: Final Remarksmentioning

confidence: 99%

“…Although these phenomena can be quite naturally interpreted in the framework of scattering theory [6], their semiclassical nature calls for a more refined analysis, mainly geometrical, which has been partially performed by several authors, and notably by Berry [7,8,9]. In this spirit, it has been also advocated the use of the complex angular momentum plane polology, especially by Bosanac [10,11,12], Connor [13,14] and Nussenzveig (see in particular his book [15] and the references quoted therein). In the latter approach, however, some problems remain, and a detailed phenomenological analysis is in part still missing.…”

Section: Introductionmentioning

confidence: 99%

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Orbiting resonances and bound states in molecular scattering

Micheli

Viano

2002

Phys. Rev. A

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A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states. Then a single pole trajectory, that connects a rotational band of bound states and orbiting resonances, is obtained. These complex angular momentum singularities are derived through a geometrical theory of the orbiting. The downward crossing of the phase-shifts through π/2, due to the repulsive region of the molecular potential, is estimated by using a simple hard-core model. Some remarks about the difference between diffracted rays and orbiting are also given.

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“…The results have implications, for example, for scattering in the atmosphere and colloidal suspensions. DOI: 10.1103/PhysRevLett.104.173902 PACS numbers: 42.25.Fx, 42.25.Kb In the usual description of light scattering by a homogeneous sphere (the scalar analogue of the well-known Mie scattering) it is generally assumed that the incident field is spatially fully coherent [1][2][3][4][5]. In practice, this assumption is not always justified.…”

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Effects of Spatial Coherence on the Angular Distribution of Radiant Intensity Generated by Scattering on a Sphere

et al. 2010

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In the analysis of light scattering on a sphere it is implicitly assumed that the incident field is spatially fully coherent. However, under usual circumstances the field is partially coherent. We generalize the partial waves expansion method to this situation and examine the influence of the degree of coherence of the incident field on the radiant intensity of the scattered field in the far zone. We show that when the coherence length of the incident field is comparable to, or is smaller than, the radius of the sphere, the angular distribution of the radiant intensity depends strongly on the degree of coherence. The results have implications, for example, for scattering in the atmosphere and colloidal suspensions. DOI: 10.1103/PhysRevLett.104.173902 PACS numbers: 42.25.Fx, 42.25.Kb In the usual description of light scattering by a homogeneous sphere (the scalar analogue of the well-known Mie scattering) it is generally assumed that the incident field is spatially fully coherent [1][2][3][4][5]. In practice, this assumption is not always justified. Examples are fields generated by multimode lasers, and fields that have passed through a random medium such as the turbulent atmosphere. Hardly any studies have been devoted to this more general case (see, however, [6]). The extinguished power due to scattering of random fields on a random medium has been analyzed in [7,8], and certain reciprocity relations for cases of this kind were derived in [9]. The extinguished power from scattering a random field on deterministic media was discussed in [10,11]. However, the influence of the state of coherence of the incident field on the angular distribution of the scattered field seems to have been studied only in two publications [12,13].In this Letter we analyze the scattering of a wide class of beams of any state of coherence on a homogeneous spherical scatterer, namely, beams of the well-known Gaussian Schell-model class (see [14], Sec. 5.6.4). We present numerical examples that show how the effective spectral coherence length (i.e., the coherence length at a fixed frequency) of the incident beam affects the angular distribution of the radiant intensity of the scattered field.Let us first consider a plane, monochromatic scalar wave of unit amplitude, propagating in a direction specified by a real unit vector u 0 , incident on a deterministic, spherical scatterer occupying a volume V (see Fig. 1 whereHere r denotes the position vector of a point in space, t the time, and ! the angular frequency. Also, k ¼ !=c ¼ 2 = is the wave number, c being the speed of light in vacuum and denotes the wavelength. The timeindependent part Uðr; !Þ of the total field that results from scattering of the plane wave on a sphere may be expressed as the sum of the incident field U ðiÞ ðr; !Þ and the scattered field U ðsÞ ðr; !Þ, viz., Uðr; !Þ ¼ U ðiÞ ðr; !Þ þ U ðsÞ ðr; !Þ:The scattered field in the far-zone of the scatterer, at an observation point r ¼ ru (u 2 ¼ 1) is given by the asymptotic formula

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Diffraction Effects in Semiclassical Scattering

Cited by 240 publications

References 0 publications

Resonant magnetic vortices

Resonant magnetic vortices

Orbiting resonances and bound states in molecular scattering

Effects of Spatial Coherence on the Angular Distribution of Radiant Intensity Generated by Scattering on a Sphere

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