Extreme Waves and Branching Flows in Optical Media

Mattheakis, Marios; Tsironis, G. P.

doi:10.1007/978-3-319-21045-2_18

Cited by 7 publications

(7 citation statements)

References 40 publications

(147 reference statements)

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“…This special characteristic of the Luneburg lens can be analyzed by using geometrical optics based on Fermat's principle [37]. For this purpose, a quasi-two-dimensional (2D) ray solution is conducted by using the 2D medium which has the same index distribution characteristic as Luneburg lenses [38]. By combining Fermat's principle with the Lagrangian optics, the ray tracing equation for a single Luneburg lens can be represented as follows [39][40][41]:…”

Section: Ray-theory Model Of the Cloaking By Luneburg Lensmentioning

confidence: 99%

“…Since the refractive index distribution of the Luneburg lens is a function of r, so differential length ds can be rewritten as ds = Here, the shortest path that is followed by a light ray according to Fermat's principle can be obtained by the minimization of the integral of (A2). In this regard, to obtain the derivative of (A2), the Euler-Lagrange equation can be used where the Lagrangian is L(ϕ, φ, r) = n(r) 1 + r 2 φ2 [38,41]:…”

Section: Appendix: Derivation Of Ray Trajectory Equationmentioning

confidence: 99%

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Analytical, numerical, and experimental investigation of a Luneburg lens system for directional cloaking

et al. 2019

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In this study, the design of a directional cloaking based on the Luneburg lens system is proposed and its operating principle is experimentally verified. The cloaking concept is analytically investigated via geometrical optics and numerically realized with the help of the finite-difference time-domain method. In order to benefit from its unique focusing and/or collimating characteristics of light, the Luneburg lens is used. We show that by the proper combination of Luneburg lenses in an array form, incident light bypasses the region between junctions of the lenses, i.e., the "dark zone." Hence, direct interaction of an object with propagating light is prevented if one places the object to be cloaked inside that dark zone. This effect is used for hiding an object which is made of a perfectly electric conductor material. In order to design an implementable cloaking device, the Luneburg lens is discretized into a photonic crystal structure having gradually varying air cylindrical holes in a dielectric material by using Maxwell Garnett effective medium approximations. Experimental verifications of the designed cloaking structure are performed at microwave frequencies of around 8 GHz. The proposed structure is fabricated by three-dimensional printing of dielectric polylactide material and a brass metallic alloy is utilized in place of the perfectly electric conductor material in microwave experiments. Good agreement between numerical and experimental results is found.

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Section: Ray-theory Model Of the Cloaking By Luneburg Lensmentioning

confidence: 99%

Section: Appendix: Derivation Of Ray Trajectory Equationmentioning

confidence: 99%

Analytical, numerical, and experimental investigation of a Luneburg lens system for directional cloaking

et al. 2019

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“…The general demonstration of the equivalence between classical and wave-mechanical Helmholtz-like equations and exact, trajectory-based Hamiltonian systems was given in Refs. [23] [24] [25] [26] [27], and led to extensive application both in relativistic electrodynamics and in the analysis of experimental arrangements and devices employed for light transmission and guiding [28] [29] [30]. Let us finally remind that the equivalence between the time-dependent Schrödinger equation and Hamiltonian Me-Journal of Applied Mathematics and Physics chanics was demonstrated in Ref.…”

Section: An Experimentally Tested Hamiltonian Description Of Wave-likmentioning

confidence: 99%

The Dynamics of Wave-Particle Duality

Orefice¹,

Giovanelli²,

Ditto³

2018

JAMP

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Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and interference process. In the case of Wave Mechanics, de Broglie's merging of Maupertuis's and Fermat's principles (see Section 3) provides, without resorting to the probability-based guidance-laws and flow-lines of the Bohmian theory, the simple law addressing particles along the Helmholtz rays of the relevant matter waves. The purpose of the present research was to derive the exact Hamiltonian ray-trajectory systems concerning, respectively, classical electromagnetic waves, non-relativistic matter waves and relativistic matter waves. We faced then, as a typical example, the numerical solution of non-relativistic wave-mechanical equation systems in a number of numerical applications, showing that each particle turns out to "dances a wave-mechanical dance" around its classical trajectory, to which it reduces when the ray-coupling is neglected. Our approach reaches the double goal of a clear insight into the mechanism of wave-particle duality and of a reasonably simple computability. We finally compared our exact dynamical approach, running as close as possible to Classical Mechanics, with the hydrodynamic Bohmian theory, based on fluid-like "guidance laws". Journal of Applied Mathematics and Physics redly leading to Bohm's Mechanics [2]-[7], with its probability-based guidance-laws and hydrodynamic flow-lines.

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“…The light branching is attributed to variations of the film's refractivity, which bends and bundles the light rays at favorable locations and form caustics [21]. Despite its complexity, branched flow is usually a linear phenomenon [22] and the distance d 0 from the source to the first branching point follows the scaling 18,23], where l c is the correlation length of the medium's unevenness, and v 0 is a strength parameter (to be defined later).…”

mentioning

confidence: 99%