Scattering of an electromagnetic plane wave by a Luneburg lens I Ray theory

Lock, James A.

doi:10.1364/josaa.25.002971

Cited by 34 publications

(37 citation statements)

References 28 publications

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“…24 of Ref. [1], further reinforcing the correspondence between the radial propagation of partial waves and the curved trajectories of rays. When the partial wave number increases to X = 1, the classically allowed region ends at r = a, the slope of U eff inside the sphere is negative as r → a, and the partial wave radial function is evanescent for the entire lens interior.…”

Section: B Modified Luneburg Lens With F ͼmentioning

confidence: 55%

“…As was seen in [1], the geometrical ray corresponding to the X = 1 partial wave strikes the lens surface with grazing incidence and travels in a circular arc on the surface for a quarter cycle before breaking free and scattering at 90°. But intuitively, once the initially grazing ray is traversing the lens surface, there appears to be no special physical constraint that would limit the ray to orbit for only a quarter cycle.…”

Section: Classical Orbiting In a Luneburg Lens With F =1mentioning

confidence: 91%

“…Finally, Eq. (38d) was derived in [1]. This analysis encounters difficulties at the nongeneric angle = / 2 for two reasons.…”

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

confidence: 99%

“…The first paper [1] considered ray theory transmission through a sphere of radius a whose dielectric constant N 2 ͑r͒ varies parabolically in r in such a way that the focal point of all the transmitted rays is fa. Such a sphere is called a modified Luneburg lens.…”

Section: Introductionmentioning

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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Section: B Modified Luneburg Lens With F ͼmentioning

confidence: 55%

Section: Classical Orbiting In a Luneburg Lens With F =1mentioning

confidence: 91%

“…Finally, Eq. (38d) was derived in [1]. This analysis encounters difficulties at the nongeneric angle = / 2 for two reasons.…”

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

confidence: 99%

Section: Introductionmentioning

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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