Graded index photonic hole: Analytical and rigorous full wave solution

Abstract

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...

Broadband omnidirectional absorption for linear liquid surface wave

“…It is noted that the mathematical velocity distribution of the LLSW OA is identical to those of the OAs for the EM wave and the acoustic wave [3][4][5][6][7]9]. It is noted that an EM OA is also constructed by applying radial depth distribution [7].…”

“…In order to illustrate the physical mechanism of the OA, the wave dynamics of the LLSW is analyzed by using the raytracing method, which yields highly accurate description when b ≫ λ with λ being the wavelength of LLSW. The ray trajectories in the guiding shell are governed by [5] …”

“…With the aid of artificial metamaterials, the omnidirectional absorber (OA) strongly interacts with the classic waves and absorbs the radiation for omnidirectional incidence. Previous studies have established the design principles such as the coordinate-transformation theory [1,8,[11][12][13][14][15][16] and the Hamiltonian theory [3][4][5][6], which have been used in the designs of OA for the electromagnetic (EM) wave [1][2][3][4][5][6][7], the acoustic wave [8,9] and the elastic wave [10]. The OA suggests a variety of potential applications such as wave shielding, energy absorption, and energy collection.…”

“…Recently, there has been an increasing interest in the omnidirectional absorption for types of classical waves by mimicking the celestial black hole [1][2][3][4][5][6][7][8][9][10]. With the aid of artificial metamaterials, the omnidirectional absorber (OA) strongly interacts with the classic waves and absorbs the radiation for omnidirectional incidence.…”

Refractive devices for acoustical and flexural waves.

“…This is the case of the "optical black-hole" introduced by Narimanov and Kildishev [30,52]. This work inspired several theoretical proposals for EM waves [21,56,81], as well as numerical realizations based on photonic crystals [40,43] and an experimental demonstration [13,89]. Following these results with electromagnetic metamaterials, "acoustic black holes" based on sonic crystals were also theoretically proposed [38] with a performance similar to that for electromagnetic waves.…”