General relativity in electrical engineering

Leónhardt, Ulf; Philbin, T. G.

doi:10.1088/1367-2630/8/10/247

Cited by 627 publications

(665 citation statements)

References 74 publications

(134 reference statements)

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“…Interesting examples are optical attractors and photon traps that mimic celestial mechanics. [9][10][11] These optical analogs of celestial phenomena may find niche applications in light control, optoelectronics, and solar-energy harvesting. Their fabrications are enabled by the advances of nanofabrication techniques and transformation optics.…”

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Graded index photonic hole: Analytical and rigorous full wave solution

Liu

Lin

et al. 2010

Phys. Rev. B

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We present a rigorous full wave approach to the omnidirectional photonic hole ͑PH͒, an optical system inspired by celestial phenomena and characterized by a radially graded refractive index n͑r͒ϳ1 / r ␣/2 . It is analytically demonstrated that light capture is effective for ␣ Ն ␣ c = 2. Our analyses are corroborated by precise numerical simulations of steady-state and time-evolution behaviors. The simulations indicate that the optical energy entering the PH system can be kept in captivity for a time duration t d scaling as t d ϳ 1 / ͑␣ c − ␣͒ when ␣ approaches ␣ c . A crucial difference in the time evolution of fields is shown between the cases with ␣ close to and equal to ␣ c . DOI: 10.1103/PhysRevB.82.054204 PACS number͑s͒: 42.25.Ϫp, 41.20.Jb Nature has been a source of inspiration to many scientific and technological advances. For a long time, the natureinspired designs of optical systems are predominantly based on mimicking structures appearing in the diversity of the biological world, leading to a thriving area of biomimetic or bioinspired photonics. [1][2][3][4] Typical examples in this area include, among others, the study of structural color 5-7 and artificial compound eyes. 8 In addition to imitating terrestially occurring structures, the design of novel optical components is recently inspired by mimicking celestial phenomena. Interesting examples are optical attractors and photon traps that mimic celestial mechanics. 9-11 These optical analogs of celestial phenomena may find niche applications in light control, optoelectronics, and solar-energy harvesting. Their fabrications are enabled by the advances of nanofabrication techniques and transformation optics. 12,13 The former offers a wide range of possibilities to locally tailor the electromagnetic ͑EM͒ response 14-16 while the latter allows the transmutation of dielectric singularities into a manageable topological defect. 17,18 One intriguing astroinspired optical device is motivated by the black hole, a fascinating celestial phenomenon. It is characterized essentially by a radially graded refractive index n͑r͒ϳ1 / r ␣/2 . 10,11,19 In contrast to the bioinspired photonics that directly solves Maxwell's equations, the astroinspired optical design starts with the study of ray trajectories. In the ray tracing limit, it is shown for integer power index ͑PI͒ ␣ that ␣ Ն 2 constitutes the condition for the ray trajectories to fall into the core of the system, resulting in an optical attractor ͑OA͒ or "photonic black hole," 10,11,19 in the sense that all light satisfying certain criterions will be held in captivity inside the system. However, the critical PI ␣ c for light trapping has not yet been identified under arbitrary wavelength conditions, and interesting phenomena occurring when ␣ comes ͑close͒ to ␣ c remain unexplored.In this paper, we present the first rigorous full wave analysis in the astroinspired photonics 9-11 for the photonic hole ͑PH͒ system. Starting with an arbitrary real ␣, the critical PI ␣ c = 2 for the capture of light is derived a...

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“…In this paper, we present the first rigorous full wave analysis in the astroinspired photonics [9][10][11] for the photonic hole ͑PH͒ system. Starting with an arbitrary real ␣, the critical PI ␣ c = 2 for the capture of light is derived analytically based on wave optics as well as ray optics.…”

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confidence: 99%

Graded index photonic hole: Analytical and rigorous full wave solution

Liu

Lin

et al. 2010

Phys. Rev. B

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“…It is doubtless that if we can further dramatically reduce the overall size-especially the aperture-of the planar reflector, then the proposed method may be more attractive in practical applications. Fortunately, folded transformation [16] and negative refracting media can provide us with an effective approach to tackle this issue [17]. A few small-sized antennas have been designed using this method [18,19].…”

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confidence: 99%

Flattening of conic reflectors via a transformation method

Luo¹,

He²,

Zhu³

et al. 2011

Phys. Rev. A

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This paper presents a general and rigorous transformation method to tailor planar conic reflectors. The proposed method enables the designed reflectors to scatter or reflect incident light in the same manner as a conic reflector while the whole device as well as the reflector would maintain planar profiles. In order to reduce the overall size, especially the aperture of the reflector, we further apply a set of compressed and folded spatial mapping to the planar reflectors. Planar reflectors with reduced sizes are finally obtained which may be useful in several optical and electromagnetic applications.

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“…4 Let us define a physical space with a coordinate system ͑uЈ , vЈ , wЈ͒ that represents the two surfaces by the equations wЈ͑xЈ , yЈ , zЈ͒ = a and wЈ͑xЈ , yЈ , zЈ͒ = b, respectively. If we fill the volume between these two surfaces with metamaterial, an appropriate design of the metamaterial can map the actual fields on these two surfaces onto any other pair of surfaces in a virtual space, 12 with another coordinate system ͑u , v , w͒, so that the fields propagate in a physical medium with material constants ͑ u Ј , v Ј , w Ј ͒ and ͑ u Ј , v Ј , w Ј ͒ across two surfaces in the physical space as if they propagate across the two mapped surfaces in a virtual medium with ͑ u , v , w ͒ and…”

Section: A General Proceduresmentioning

confidence: 99%

“…III B and argue that the perfect lens design proposed in Ref. 12 does not provide magnification, but rather changes the depth of field or depth of focus only. Our magnifying superlens design, outlined in Sec.…”

Section: Introductionmentioning

confidence: 99%

Magnifying perfect lens and superlens design by coordinate transformation

2008

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The coordinate transformation technique is applied to the design of perfect lenses and superlenses. In particular, anisotropic metamaterials that magnify two-dimensional planar images beyond the diffraction limit are designed by the use of oblate spheroidal coordinates. The oblate spheroidal perfect lens or superlens can naturally be used in reverse for lithography of planar subwavelength patterns.

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General relativity in electrical engineering

Cited by 627 publications

References 74 publications

Graded index photonic hole: Analytical and rigorous full wave solution

Graded index photonic hole: Analytical and rigorous full wave solution

Flattening of conic reflectors via a transformation method

Magnifying perfect lens and superlens design by coordinate transformation

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