Does chaotic scattering affect the extinction efficiency in quasi-spherical scatterers?

AbstractMie-type scattering features such as ripples (i.e., sharp shape-resonance peaks) and wiggles (i.e., broad oscillations), are frequently-observed scattering phenomena in infrared microspectroscopy of cells and tissues. They appear in general when the wavelength of electromagnetic radiation is of the same order as the size of the scatterer. By use of approximations to the Mie solutions for spheres, iterative algorithms have been developed to retrieve pure absorbance spectra. However, the question remains to what extent the Mie solutions, and approximations thereof, describe the extinction efficiency in practical situations where the shapes of scatterers deviate considerably from spheres. The aim of the current study is to investigate how deviations from a spherical scatterer can change the extinction properties of the scatterer in the context of chaos in wave systems. For this purpose, we investigate a chaotic scatterer and compare it with an elliptically shaped scatterer, which exhibits only regular scattering. We find that chaotic scattering has an accelerating effect on the disappearance of Mie ripples. We further show that the presence of absorption and the high numerical aperture of infrared microscopes does not explain the absence of ripples in most measurements of biological samples.

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Broadening of the tilt-effect peak in the drag of dislocations in metals due to chaotic scattering of electrons

Philosophical Magazine A ◽

10.1080/014186101300012462 ◽

2001 ◽

Vol 81 (1) ◽

pp. 137-144

Author(s):

E. Vigueras, A. A. Krokhin, T. J. Mckr

Keyword(s):

Chaotic Scattering

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Devil-staircase behavior of dynamical invariants in chaotic scattering

Physica D Nonlinear Phenomena ◽

10.1016/s0167-2789(00)00059-2 ◽

2000 ◽

Vol 142 (3-4) ◽

pp. 197-216 ◽

Cited By ~ 2

Author(s):

Karol Życzkowski ◽

Ying-Cheng Lai

Keyword(s):

Chaotic Scattering ◽

Dynamical Invariants

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A degenerate bifurcation to chaotic scattering in a multicentre potential

Journal of Physics A General Physics ◽

10.1088/0305-4470/28/23/029 ◽

1995 ◽

Vol 28 (23) ◽

pp. 6887-6902 ◽

Cited By ~ 24

Author(s):

C Lipp ◽

C Jung

Keyword(s):

Chaotic Scattering ◽

Degenerate Bifurcation

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Convergence of the Semiclassical Approximation for Chaotic Scattering

Physical Review Letters ◽

10.1103/physrevlett.73.244 ◽

1994 ◽

Vol 73 (2) ◽

pp. 244-247 ◽

Cited By ~ 11

Author(s):

J. H. Jensen

Keyword(s):

Semiclassical Approximation ◽

Chaotic Scattering

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Chaotic scattering on a double well: Periodic orbits, symbolic dynamics, and scaling

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.165953 ◽

1993 ◽

Vol 3 (4) ◽

pp. 475-485 ◽

Cited By ~ 10

Author(s):

Vincent Daniels ◽

Michel Vallières ◽

Jian‐Min Yuan

Keyword(s):

Periodic Orbits ◽

Symbolic Dynamics ◽

Chaotic Scattering

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CHAOTIC SCATTERING IN TIME-DEPENDENT HAMILTONIAN SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127491000488 ◽

1991 ◽

Vol 01 (03) ◽

pp. 667-679 ◽

Cited By ~ 12

Author(s):

YING-CHENG LAI ◽

CELSO GREBOGI

Keyword(s):

Phase Space ◽

Measure Zero ◽

Invariant Set ◽

Time Dependent ◽

Invariant Sets ◽

Physical Origin ◽

Chaotic Scattering ◽

Periodic Oscillations ◽

Surface Of Section ◽

Oscillating Potential

We consider the classical scattering of particles in a one-degree-of-freedom, time-dependent Hamiltonian system. We demonstrate that chaotic scattering can be induced by periodic oscillations in the position of the potential. We study the invariant sets on a surface of section for different amplitudes of the oscillating potential. It is found that for small amplitudes, the phase space consists of nonescaping KAM islands and an escaping set. The escaping set is made up of a nonhyperbolic set that gives rise to chaotic scattering and remains of KAM islands. For large amplitudes, the phase space contains a Lebesgue measure zero invariant set that gives rise to chaotic scattering. In this regime, we also discuss the physical origin of the Cantor set responsible for the chaotic scattering and calculate its fractal dimension.

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