Scattering of an electromagnetic plane wave by a Luneburg lens III Finely stratified sphere model

Lock, James A.

doi:10.1364/josaa.25.002991

Cited by 26 publications

(25 citation statements)

References 28 publications

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“…In this section the effective potential approach is discussed for TE scattering. The finely stratified sphere model is implemented and discussed in [7]. The differential equation of Eq.…”

Section: Effective Potential Approach For Te Scatteringmentioning

confidence: 99%

“…Instead, these states slowly decay as they leak through the centrifugal barrier of Eq. (28) 34) is the approximate size parameter for the formation of a TE-polarized MDR in the partial wave n of radial order S. In [7] this prediction is numerically tested, and the TM resonant size parameters are obtained. By way of comparison, for scattering by a homogeneous sphere with n slightly larger than ka, the radial effective potential consists of a centrifugal barrier outside the particle and an approximately linearly decreasing well, i.e., an Airy well, just inside the particle surface that also supports TE and TM resonances.…”

Section: ͑29͒mentioning

confidence: 99%

“…Also, since the deepest part of the well for a modified Luneburg lens lies further inside the sphere than does the deepest part of the Airy well, the Luneburg lens MDRs should also lie deeper inside the sphere, whereas the homogeneous sphere MDRs lie just beneath the sphere surface. These issues are treated more quantitatively and fully in [7].…”

Section: ͑29͒mentioning

confidence: 99%

“…The fine oscillatory structure for Ͼ 100°is due to interference of orbiting radiation shed by the ray with grazing incidence at the top of the sphere and the counterpropagating orbiting radiation shed by the ray with grazing incidence at the bottom of the sphere. All the effects qualitatively described here are treated quantitatively in [7] using a finely stratified multilayer sphere to model the modified Luneburg lens.…”

Section: Physical Optics Model Of Scattering Of the Orbiting Ray By Amentioning

confidence: 99%

“…This Debye series has a slightly different physical interpretation than it does for a homogeneous sphere, which is commented on in Appendix B as well. The results obtained here and in [1] are numerically tested in [7] where a modified Luneburg lens is approximated by a finely stratified multilayer sphere. In [7] also, a new algorithm for computing scattering by a multilayer sphere based on an analogy to the successive doubling strategy of the fast Fourier transform (FFT) algorithm is developed and implemented.…”

Section: Introductionmentioning

confidence: 99%

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Scattering of an electromagnetic plane wave by a Luneburg lens II Wave theory

Lock

2008

J. Opt. Soc. Am. A

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“…In this section the effective potential approach is discussed for TE scattering. The finely stratified sphere model is implemented and discussed in [7]. The differential equation of Eq.…”

Section: Effective Potential Approach For Te Scatteringmentioning

confidence: 99%

Section: ͑29͒mentioning

confidence: 99%

Section: ͑29͒mentioning

confidence: 99%

Section: Physical Optics Model Of Scattering Of the Orbiting Ray By Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scattering of an electromagnetic plane wave by a Luneburg lens II Wave theory

Lock

2008

J. Opt. Soc. Am. A

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“Rainbows” in Homogeneous and Radially Inhomogeneous Spheres: Connections with Ray, Wave, and Potential Scattering Theory

Adam

2013

Springer Proceedings in Mathematics &Amp; Statistics

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This chapter represents an attempt to summarize some of the direct and indirect connections that exist between ray theory, wave theory and potential scattering theory. Such connections have been noted in the past, and have been exploited to some degree, but in the opinion of this author, there is much more yet to be pursued in this regard. This article provides the framework for more detailed analysis in the future. In order to gain a better appreciation for a topic, it is frequently of value to examine it from as many complementary levels of description as possible, and that is the objective here. Drawing in part on the work of Nussenzveig, Lock, Debye and others, the mathematical nature of the rainbow is discussed from several perspectives. The primary bow is the lowest-order bow that can occur by scattering from a spherical drop with constant refractive index n, but zero-order (or direct transmission) bows can exist when the sphere is radially inhomogeneous. The refractive index profile automatically defines a scattering potential, but with a significant difference compared to the standard quantum mechanical form: the potential is k-dependent. A consequence of this is that there are no bound states for this system. The correspondences between the resonant modes in scattering by a potential of the 'well-barrier' type and the behavior of electromagnetic 'rays' in a transparent (or dielectric) sphere are discussed. The poles and saddle points of the associated scattering matrix have quite profound connections to electromagnetic tunneling, resonances and 'rainbows' arising within and from the sphere. The links between the various mathematical and physical viewpoints are most easily appreciated in the case of constant n, thus providing insight into possible extensions to these descriptions for bows of arbitrary order in radially inhomogeneous spheres (and cylinders).

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Light Scattering by Large Bubbles

Onofri

Sentis

2017

Springer Series in Light Scattering

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Scattering of an electromagnetic plane wave by a Luneburg lens III Finely stratified sphere model

Cited by 26 publications

References 28 publications

Scattering of an electromagnetic plane wave by a Luneburg lens II Wave theory

Scattering of an electromagnetic plane wave by a Luneburg lens II Wave theory

“Rainbows” in Homogeneous and Radially Inhomogeneous Spheres: Connections with Ray, Wave, and Potential Scattering Theory

Light Scattering by Large Bubbles

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