Effective manipulation of cavity resonant modes is crucial for emission control in laser physics and applications. Using the concept of parity-time symmetry to exploit the interplay between gain and loss (i.e., light amplification and absorption), we demonstrate a parity-time symmetry-breaking laser with resonant modes that can be controlled at will. In contrast to conventional ring cavity lasers with multiple competing modes, our parity-time microring laser exhibits intrinsic single-mode lasing regardless of the gain spectral bandwidth. Thresholdless parity-time symmetry breaking due to the rotationally symmetric structure leads to stable single-mode operation with the selective whispering-gallery mode order. Exploration of parity-time symmetry in laser physics may open a door to next-generation optoelectronic devices for optical communications and computing.

Piezoelectricity allows precise and robust conversion between electricity and mechanical force, and arises from the broken inversion symmetry in the atomic structure [1][2][3] . Reducing the dimensionality of bulk materials has been suggested to enhance piezoelectricity 4 . However, when the thickness of a material approaches a single molecular layer, the large surface energy can cause piezoelectric structures to be thermodynamically unstable 5 . Transition-metal dichalcogenides can retain their atomic structures down to the single-layer limit without lattice reconstruction, even under ambient conditions 6 . Recent calculations have predicted the existence of piezoelectricity in these two-dimensional crystals due to their broken inversion symmetry 7 . Here, we report experimental evidence of piezoelectricity in a free-standing single layer of molybdenum disulphide (MoS 2 ) and a measured piezoelectric coefficient of e 11 = 2.9 × 10 -10 C m −1 . The measurement of the intrinsic piezoelectricity in such free-standing crystals is free from substrate effects such as doping and parasitic charges. We observed a finite and zero piezoelectric response in MoS 2 in odd and even number of layers, respectively, in sharp contrast to bulk piezoelectric materials. This oscillation is due to the breaking and recovery of the inversion symmetry of the two-dimensional crystal. Through the angular dependence of electromechanical coupling, we determined the two-dimensional crystal orientation. The piezoelectricity discovered in this single molecular membrane promises new applications in low-power logic switches for computing and ultrasensitive biological sensors scaled down to a single atomic unit cell 8,9 .Since its discovery in 1880, piezoelectricity has found a wide range of applications in actuation, sensing and energy harvesting. The rapidly growing demand for high-performance and miniaturized devices in micro-electro-mechanical systems (MEMS) and electronics 10-12 calls for nanoscale piezoelectric materials, motivating theoretical investigations into novel low-dimensional systems such as nanotubes and single molecules 13,14 . Transition-metal dichalcogenides (TMDCs) are ideal candidates as low-dimensional piezoelectric materials because of their structural non-centrosymmetry 7 . Although there has been extensive research interest in the unique properties originating from such symmetry breaking, including circular dichroism and second harmonic generation (SHG) [15][16][17][18][19] , experimental quantitative determination of the intrinsic piezoelectric properties of these two-dimensional crystals has yet to be demonstrated. Here, we report the observation of piezoelectricity in freestanding monolayer MoS 2 membranes. Interestingly, we found that this molecular piezoelectricity only exists when there are an odd number of layers in the two-dimensional crystal where inversion symmetry breaking occurs. We observed an angular dependence of the piezoelectric response in agreement with the three-fold symmetry of the crystal, and based...

Metamaterial-based optical cloaks have thus far used volumetric distribution of the material properties to gradually bend light and thereby obscure the cloaked region. Hence, they are bulky and hard to scale up and, more critically, typical carpet cloaks introduce unnecessary phase shifts in the reflected light, making the cloaks detectable. Here, we demonstrate experimentally an ultrathin invisibility skin cloak wrapped over an object. This skin cloak conceals a three-dimensional arbitrarily shaped object by complete restoration of the phase of the reflected light at 730-nanometer wavelength. The skin cloak comprises a metasurface with distributed phase shifts rerouting light and rendering the object invisible. In contrast to bulky cloaks with volumetric index variation, our device is only 80 nanometer (about one-ninth of the wavelength) thick and potentially scalable for hiding macroscopic objects.

Recently, two-dimensional (2D) materials have opened a new paradigm for fundamental physics explorations and device applications. Unlike gapless graphene, monolayer transition metal dichalcogenide (TMDC) has new optical functionalities for next generation ultra-compact electronic and opto-electronic devices. When TMDC crystals are thinned down to monolayers, they undergo an indirect to direct bandgap transition 1, 2 , making it an outstanding 2D semiconductor [1][2][3][4][5] . Unique electron valley degree of freedom [6][7][8][9] , strong light matter interactions 10 and excitonic effects were observed [11][12][13] . Enhancement of spontaneous emission has been reported on TMDC monolayers integrated with photonic crystal 14,15 and distributed Bragg reflector microcavities 16,17 .However, the coherent light emission from 2D monolayer TMDC has not been demonstrated, mainly due to that an atomic membrane has limited material gain volume and is lack of optical mode confinement. Here, we report the first realization of 2D excitonic laser by embedding monolayer tungsten disulfide (WS 2 ) in a microdisk resonator. Using a whispering gallery mode (WGM) resonator with a high quality factor and optical confinement, we observed bright excitonic lasing in visible wavelength. The Si 3 N 4 /WS 2 /HSQ sandwich configuration provides a strong feedback and mode overlap with monolayer gain. This demonstration of 2D excitonic laser marks a major step towards 2D on-chip optoelectronics for high performance optical communication and computing applications.

Phase matching is a critical requirement for coherent nonlinear optical processes such as frequency conversion and parametric amplification. Phase mismatch prevents microscopic nonlinear sources from combining constructively, resulting in destructive interference and thus very low efficiency. We report the experimental demonstration of phase mismatch-free nonlinear generation in a zero-index optical metamaterial. In contrast to phase mismatch compensation techniques required in conventional nonlinear media, the zero index eliminates the need for phase matching, allowing efficient nonlinear generation in both forward and backward directions. We demonstrate phase mismatch-free nonlinear generation using intrapulse four-wave mixing, where we observed a forward-to-backward nonlinear emission ratio close to unity. The removal of phase matching in nonlinear optical metamaterials may lead to applications such as multidirectional frequency conversion and entangled photon generation.

Strongly anisotropic media where the principal components of electric permittivity or magnetic permeability tensors have opposite signs are termed as hyperbolic media. Such media support propagating electromagnetic waves with extremely large wave vectors exhibiting unique optical properties. However, in all artificial and natural optical materials studied to date, the hyperbolic dispersion originates solely from the electric response. This restricts material functionality to one polarization of light and inhibits free-space impedance matching. Such restrictions can be overcome in media having components of opposite signs for both electric and magnetic tensors. Here we present the experimental demonstration of the magnetic hyperbolic dispersion in three-dimensional metamaterials. We measure metamaterial isofrequency contours and reveal the topological phase transition between the elliptic and hyperbolic dispersion. In the hyperbolic regime, we demonstrate the strong enhancement of thermal emission, which becomes directional, coherent and polarized. Our findings show the possibilities for realizing efficient impedance-matched hyperbolic media for unpolarized light.

Metamaterials are artificially engineered materials that exhibit novel properties beyond natural materials. By carefully designing the subwavelength unit cell structures, unique effective properties that do not exist in nature can be attained. Our metamaterial research aims to develop new subwavelength structures with unique physics and experimentally demonstrate unprecedented properties. Here we review our research efforts in optical and acoustic metamaterials in the past 15 years which may lead to exciting applications in communications, sensing and imaging.

Metamaterials have extraordinary abilities, such as imaging beyond the diffraction limit and invisibility. Many metamaterials are based on split-ring structures, however, like atomic orbital currents, it has long been believed that closed rings cannot produce negative refractive index. Here we report a low-loss and polarization-independent negative-index metamaterial made solely of closed metallic nanorings. Using symmetry breaking that negatively couples the discrete nanorings, we measured negative phase delay in our composite 'chess metamaterial'. The formation of an ultra-broad Fano-resonance-induced optical negativeindex band, spanning wavelengths from 1.3 to 2.3 mm, is experimentally observed in this structure. This discrete and mono-particle negative-index approach opens exciting avenues towards symmetry-controlled topological nanophotonics with on-demand linear and nonlinear responses.