On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Der speziellen Relativitatstheorie liegt folgendes Postulat zugrunde, welchem auch durch die Galilei-Newtonsche Mechanik Genuge geleistet wird: Wird ein Koordinatensystem K so gewahlt, das in bezug auf dasselbe die physikalischen Gesetze in ihrer einfachsten Form gelten, so gelten dieselben Gesetze auch in Bezug auf jedes andere Koordinatensystem K′, das relativ zu K in gleichformiger Translationsbewegung begriffen ist. Dieses Postulat nennen wir „spezielles Relativitatsprinzip“. Durch das Wort „speziell“ soll angedeutet werden, das das Prinzip auf den Fall beschrankt ist, das K′ eine gleichformige Translationsbewegung gegen K ausfuhrt, das sich aber die Gleichwertigkeit von K′ und K nicht auf den Fall ungleichformiger Bewegung von K′ gegen K erstreckt.

Die Grundlage der allgemeinen Relativitätstheorie

In this paper, we propose a switchable and tunable functional metamaterial device based on hybrid graphene-vanadium dioxide (VO2). Using the properties of the metal-insulator transition in VO2, the proposed metamaterials can enable switching between tunable circular dichroism (CD) and dual-band perfect absorption in the terahertz region. When VO2 is in the insulator state, a polarization-selective single-band perfect absorption can be achieved for circularly polarized waves, thus resulting in a strong CD response with a maximum value of 0.84. When VO2 acts as a metal, there is a tunable dual-band perfect absorption for the designed metamaterial device under the illumination of x-polarization waves. The operation mechanism behind the phenomena can be explained by utilizing the electric field distribution and the coupled mode theory. Moreover, the influences of the Fermi energy of graphene and geometrical parameters on the CD and absorption spectra are discussed in detail. Our proposed switchable and tunable metamaterial can provide a platform for designing versatile functional devices in the terahertz region.

An active tunable terahertz functional metamaterial based on hybrid-graphene vanadium dioxide.

Starting from the wave equation with a non-zero space curvature, a generalized coordinate-independent expression for the evolution of a light beam on a curved space is derived. By defining the propagation axes, the expression reduces to integrable Green functions without an inevitable singular point. With a Gaussian incident field, the stationary status and refocusing effect of the light field on different shapes of curved surfaces are discussed. Different from a constant diffusion behavior in a flat space, the field experiences a periodical diffraction and refocusing spontaneously with no additional optical elements. To be more specific, we noticed that the laser field on a curved surface experiences a fractional Fourier transform, with a propagation angle to be the transform order. We hope our theoretical results can provide some references for the practical application in a curved surface space.

Propagation and transformation of a light beam on a curved surface.

General relativity establishes the equality between matter-energy density and the Riemann curvature of spacetime. Therefore, light or matter will be bent or trapped when passing near the massive celestial objects, and Newton’s second law fails to explain it. The gravitational effect is not only extensively studied in astronomy but also attracts a great deal of interest in the field of optics. People have mimicked black holes, Einstein’s ring, and other fascinating effects in diverse optical systems. Here, with a gradient index lens, in the geometrical optics regime, we mimic the Schwarzschild precession in the orbit of the star S2 near the Galactic Center massive black hole, which was recently first detected by European Southern Observatory. We also find other series of gradient index lenses that can be used to mimic the possible Reissner–Nordstrom metric of Einstein’s field equation and dark matter particle motion. Light rays in such gradient lenses will be closed in some cases, while in other cases it would be trapped by the center or keep dancing around the center. Our work presents an efficient toy model to help investigate some complex celestial behaviors, which may require long period detection by using high-precision astronomical tools. The induced gradient lenses enlightened by the gravitational effect also enrich the family of absolute optical instruments for their selective closed trajectories.

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Mimicking the gravitational effect with gradient index lenses in geometrical optics

Whispering gallery mode (WGM) cavity is important for exploring physics of strong light-matter interaction. Yet it suffers from the notorious radiation loss universally due to the light tunneling effect through the curved boundary. In this work, we propose and demonstrate an optical black hole (OBH) cavity based on transformation optics. The radiation loss of all WGMs in OBH cavity is completely inhibited by an infinite wide potential barrier. Besides, the WGM field outside the cavity is revealed to follow $1/r^\alpha$ decay rule based on conformal mapping, which is fundamentally different from the conventional Hankel-function distributions in a homogeneous cavity. Experimentally, a truncated OBH cavity is achieved based on the effective medium theory, and both the Q-factor enhancement and tightly confined WGM field are measured in the microwave spectra which agree well with the theoretical results. The circular OBH cavity is further applied to the arbitrary-shaped cavities including single-core and multi-core structures with high-Q factor via the conformal mapping. The OBH cavity design strategy can be generalized to resonant modes of various wave systems, such as acoustic and elastic waves, and finds applications in energy harvesting and optoelectronics. 

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Conformal optical black hole for cavity

In this work, we proposed a black phosphorus (BP) achiral metasurface and theoretically study the chiroptical response arising from extrinsic 2D-chirality in the mid-infrared regime. The achiral metasurface is composed of a monolayer BP sheet sandwiched by a silver ring array and dielectric spacer stacking on a silver substrate. The giant circular conversion dichroism (CCD) of the achiral metasurface is allowed at oblique incidence for the cooperative interaction of BP anisotropic surface plasmon modes and localized surface plasmons in metal rings, and the integrated BP can dynamically modulate the chiroptical response by controlling the doping concentration of BP. Furthermore, we found that a multiband phenomenon for CCD response occurs when tuning the thickness of the spacer. The proposed hybrid achiral metasurface provides more flexible opportunities to realize active polarization modulator, biosensor and chiral detection.

Giant 2D-chiroptical response in an achiral metasurface integrated with black phosphorus.

In this Letter, we find that Morse potential (proposed about 90 years ago) could be connected to Coulomb potential (or Newton potential) and harmonic potential (or Hooke potential) by conformal mappings. We thereby design a new conformal lens from Morse potential, Eaton lens, and Luneburg lens and propose a series of generalized Eaton/Luneburg lenses. We find that this Morse lens is a perfect self-focusing asymmetric lens that differs from a Mikaelian lens. Our theory provides a new insight to Morse potential and other traditional potentials, and revisits their classical applications on designing lenses.

Morse lens [Invited]

Absolute optical instruments with rotation symmetry and corresponding absolute geodesic lenses have drawn considerable attention for their property of perfect imaging of light rays In this paper, we systematically explore a series of absolute geodesic lenses which is mapped from generalized Maxwell's fish-eye lenses with a rational number index {p} Moreover, we construct new types of duplex absolute geodesic lenses by splicing two different half absolute geodesic lenses, which is inspired by the work [Huiyan Peng, et al Phys Rev Applied13, 034050 (2020)] Also, we fabricate some samples of absolute geodesic lenses based on the 3D printing technique and observe light rays on them Our findings enlarge the family of absolute geodesic lenses and might find an application on classical imaging systems

Wen Xiao

Papers

Mimicking the gravitational effect with gradient index lenses in geometrical optics

Conformal optical black hole for cavity

Giant 2D-chiroptical response in an achiral metasurface integrated with black phosphorus.

Morse lens [Invited]

Observation of light rays on absolute geodesic lenses.