Optical theorem in<i>N</i>dimensions

Boya, Luis J.; Murray, Robert

doi:10.1103/physreva.50.4397

Cited by 21 publications

(8 citation statements)

References 8 publications

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“…28 According to the optical theorem in two dimensions, 34 the total cross-section (which includes absorption and scattering) can be determined from the forward scattering amplitude f ð0Þ…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Paul

Urzhumov

Elsen

et al. 2012

Journal of Applied Physics

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Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display J. Appl. Phys. 111, 103119 (2012) Image acceleration in parallel magnetic resonance imaging by means of metamaterial magnetoinductive lenses AIP Advances 2, 022136 (2012) Inhomogeneous nanostructured honeycomb optical media for enhanced cathodo-and under-x-ray luminescence J. Appl. Phys. 111, 103101 (2012) Broadband Purcell effect: Radiative decay engineering with metamaterials Appl. Phys. Lett. 100, 181105 (2012) Additional information on J. Appl. Phys. Transformation optics (TO) is a powerful tool for the design of electromagnetic and optical devices with novel functionality derived from the unusual properties of the transformation media. In general, the fabrication of TO media is challenging, requiring spatially varying material properties with both anisotropic electric and magnetic responses. Though metamaterials have been proposed as a path for achieving such complex media, the required properties arising from the most general transformations remain elusive, and cannot implemented by state-of-the-art fabrication techniques. Here, we propose faceted approximations of TO media of arbitrary shape in which the volume of the TO device is divided into flat metamaterial layers. These layers can be readily implemented by standard fabrication and stacking techniques. We illustrate our approximation approach for the specific example of a two-dimensional, omnidirectional "invisibility cloak," and quantify its performance using the total scattering cross section as a practical figure of merit. V C 2012 American Institute of Physics. [http://dx

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Section: Simulation Results and Discussionmentioning

confidence: 99%

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Paul

Urzhumov

Elsen

et al. 2012

Journal of Applied Physics

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“…However, the need to evaluate and integrate the scattering amplitude over angle leads to a significant computational expense. A much simpler method is to apply the optical theorem [42,43], which states that the total cross section is proportional to the imaginary part of the scattering amplitude evaluated in the forward (k = k 𝑖 ) direction as…”

Section: Approachmentioning

confidence: 99%

“…Repeating the optical theorem derivation for the 2D case results in the same expression for the scattering cross-section as Eq. ( 10), with the volume elements replaced by area elements [42,43].…”

Section: Approachmentioning

confidence: 99%

“…In this Letter, we develop a more efficient optimization method for designing invisibility cloaks. Our inverse design approach is based on minimizing the forward scattering amplitude, which by the optical theorem is equal to the total cross section [42,43]. The use of the optical theorem circumvents the need to integrate the scattered fields over angle by evaluating the cross section from the forward scattering amplitude alone, and thus provides a simpler, more computationally efficient algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Inverse Design of Invisibility Cloaks using the Optical Theorem

Slovick¹,

Hellhake²

2021

Preprint

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We develop and apply an optimization method to design invisibility cloaks. Our method is based on minimizing the forward scattering amplitude of the cloaked object, which by the optical theorem, is equivalent to the total cross section. The use of the optical theorem circumvents the need to evaluate and integrate the scattering amplitude over angle at each iteration, and thus provides a simpler, more computationally efficient objective function for optimizing structures. We implement the approach using gradient descent optimization and present several gradient-permittivity cloaks that reduce scatter by metallic targets of different size and shape.

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“…Although a rectangular cloak is not exactly a 1D object, we may expect that FPR-like resonances could strongly reduce the forward-scattering amplitude (i.e., the shadow). By virtue of the 2D optical theorem [17], then, the total extinction cross section is also strongly suppressed.…”

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confidence: 99%

Low-loss directional cloaks without superluminal velocity or magnetic response

Urzhumov

Smith

2012

Opt. Lett.

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The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve (meta)materials with superluminal phase velocity [refractive index (RI) less than unity] and/or magnetic response. We introduce a new approximation applicable to certain device geometries in the eikonal limit: piecewise-uniform scaling of the RI. This transformation preserves the ray trajectories but leads to a uniform phase delay. We show how to take advantage of phase delays to achieve a limited (directional and wavelength-dependent) While TO is not the only methodology proposed for invisibility [7,8], so far it is the only known path to the cloaking of very large (relative to free-space wavelength λ 0 ) objects. To date, proposed and demonstrated TO cloaks based on passive, linear, reciprocal media require at least three [2,9-12] EM properties that are hard to find in natural substances. One key ingredient is the large and precisely controlled anisotropy of the refractive index [2,10] (RI). Implementations of TO recipes generally require anisotropic materials, with the exception of conformal maps (CM). The usefulness of CMs for cloaking designs is fundamentally limited by several factors, including the preservation of the conformal modulus of the transformed domain, lack of rotational symmetry [11,12], and the absence of useful CMs in three dimensions. In two dimensions, lacking radially symmetric CMs, the CM subset of TO can at best offer cloaking for one propagation direction, as was demonstrated by Leonhardt [13]. We refer to such devices as directional cloaks here. CM cloaks also suffer from other issues, such as the impossibility of conformally mapping a finite-area domain onto a smaller domain, which leads to an inevitable impedance mismatch at the finite radius cutoff [11,12]; such issues are easily avoided in nonconformal TO scenarios with anisotropic media.The second and more fundamental cloaking requirement is superluminal phase velocity, or RI n < 1. Generally, the requirement is n < n 0 , where n 0 is the RI of the immersion medium [14]; we consider only free space cloaking, n 0 1. This requirement persists even in CM-based cloaking scenarios [11][12][13]15]. To implement n < 1, at least one of the principal values of the ϵ and μ tensors of a nonbianisotropic medium would need to be less than unity. Transparent media with n < 1 are necessarily dispersive-otherwise they could be used to transmit information-carrying signals with superluminal speed, a clear contradiction to special relativistic causality. By virtue of Kramers-Kronig relations, one may deduce that effective media with ϵ < 1 (or μ < 1) must be lossy because of their dispersion. Photonic bandgap media operating beyond the effective medium regime in a high-order Bloch band have been proposed as superluminal velocity substrates for lossless, all-dielectric TO devices [16]; however, they still suffer from the disp...

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Optical theorem inNdimensions

Cited by 21 publications

References 8 publications

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Inverse Design of Invisibility Cloaks using the Optical Theorem

Low-loss directional cloaks without superluminal velocity or magnetic response

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