There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was "hidden" inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space.

/pdf/metamaterial-electromagnetic-cloak-at-microwave-frequencies-1qj4zdgl8e.pdf

Metamaterial Electromagnetic Cloak at Microwave Frequencies

Conventional optical components rely on gradual phase shifts accumulated during light propagation to shape light beams. New degrees of freedom are attained by introducing abrupt phase changes over the scale of the wavelength. A two-dimensional array of optical resonators with spatially varying phase response and subwavelength separation can imprint such phase discontinuities on propagating light as it traverses the interface between two media. Anomalous reflection and refraction phenomena are observed in this regime in optically thin arrays of metallic antennas on silicon with a linear phase variation along the interface, which are in excellent agreement with generalized laws derived from Fermat’s principle. Phase discontinuities provide great flexibility in the design of light beams, as illustrated by the generation of optical vortices through use of planar designer metallic interfaces.

http://www.zenogaburro.it/papers/LightPropagation.pdf

Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction

Metamaterials are artificially fabricated materials that allow for the control of light and acoustic waves in a manner that is not possible in nature. This Review covers the recent developments in the study of so-called metasurfaces, which offer the possibility of controlling light with ultrathin, planar optical components. Conventional optical components such as lenses, waveplates and holograms rely on light propagation over distances much larger than the wavelength to shape wavefronts. In this way substantial changes of the amplitude, phase or polarization of light waves are gradually accumulated along the optical path. This Review focuses on recent developments on flat, ultrathin optical components dubbed 'metasurfaces' that produce abrupt changes over the scale of the free-space wavelength in the phase, amplitude and/or polarization of a light beam. Metasurfaces are generally created by assembling arrays of miniature, anisotropic light scatterers (that is, resonators such as optical antennas). The spacing between antennas and their dimensions are much smaller than the wavelength. As a result the metasurfaces, on account of Huygens principle, are able to mould optical wavefronts into arbitrary shapes with subwavelength resolution by introducing spatial variations in the optical response of the light scatterers. Such gradient metasurfaces go beyond the well-established technology of frequency selective surfaces made of periodic structures and are extending to new spectral regions the functionalities of conventional microwave and millimetre-wave transmit-arrays and reflect-arrays. Metasurfaces can also be created by using ultrathin films of materials with large optical losses. By using the controllable abrupt phase shifts associated with reflection or transmission of light waves at the interface between lossy materials, such metasurfaces operate like optically thin cavities that strongly modify the light spectrum. Technology opportunities in various spectral regions and their potential advantages in replacing existing optical components are discussed.

Flat Optics With Designer Metasurfaces

Exploiting the dependence of graphene conductivity on the electric bias field, we theoretically investigate the manipulation, routing, waveguiding and scattering of surface-plasmon polaritons along graphene at IR wavelengths, proposing a “flatland” paradigm for optical metamaterials.

Manipulating IR Surface Plasmon Polaritons on Graphene

Metasurfaces have paved the way for compact and flat electromagnetic systems with properties not readily available in nature. Graphene, naturally occurring two-dimensional material, may serve as a candidate for fully functional flatland photonics. Here we exploit the unique electronic properties of graphene and suggest a paradigm for a single-layer nonreciprocal graphene-based metasurface with extreme Faraday rotation. We propose a graphene meta-atom exhibiting an unprecedented magneto-optical activity - a near 90° Faraday rotation - at magnetic biasing as low as 0.35T, suggesting a platform for non-reciprocal light manipulation at the nanoscale.

Extreme magneto-optics with graphene metasurfaces

We present a metasurface-based platform that solves Fredholm integral equations of the second kind for free-space radiation. An inverse-designed metagrating is coupled to a semitransparent mirror providing feedback in order to perform an analog version of the Neumann series.

Inverse Designed Metagratings for Far-Field Integral Equations Solving

In this work we present and discuss the case of a reconfigurable, Mach–Zehnder interferometer-based photonic network, specially designed for implementing any arbitrary matrix operator. After a brief discussion on the available architectures we describe the main elements of the proposed architecture. Finally, using simulations we demonstrate a practical example where an $11 \times11$ MZI network is implement for the solution of differential equation.

Solving differential equations with reconfigurable Mach–Zehnder interferometer photonic networks

We present here the main features of cloaking based on plasmonic materials, together with some novel aspects of the exotic and anomalous features that such plasmonic shells may provide. In particular, in addition to scattering cancellation features, we discuss a special condition for which a suitably designed plasmonic metamaterial shell may produce an anti-resonant (very low) scattering, independently of the specific properties of the object placed inside it. Different from classic plasmonic cloaking, this condition may provide novel physical insights into the anomalous scattering properties of plasmonic shells, and it may lead to various interesting possibilities for applications.

Nader Engheta

Papers

Manipulating IR Surface Plasmon Polaritons on Graphene

Extreme magneto-optics with graphene metasurfaces

Inverse Designed Metagratings for Far-Field Integral Equations Solving

Solving differential equations with reconfigurable Mach–Zehnder interferometer photonic networks

Peculiar and anomalous cloaking features of plasmonic materials