The extraordinary electronic properties of graphene provided the main thrusts for the rapid advance of graphene electronics. In photonics, the gate-controllable electronic properties of graphene provide a route to efficiently manipulate the interaction of photons with graphene, which has recently sparked keen interest in graphene plasmonics. However, the electro-optic tuning capability of unpatterned graphene alone is still not strong enough for practical optoelectronic applications owing to its non-resonant Drude-like behaviour. Here, we demonstrate that substantial gate-induced persistent switching and linear modulation of terahertz waves can be achieved in a two-dimensional metamaterial, into which an atomically thin, gated two-dimensional graphene layer is integrated. The gate-controllable light-matter interaction in the graphene layer can be greatly enhanced by the strong resonances of the metamaterial. Although the thickness of the embedded single-layer graphene is more than six orders of magnitude smaller than the wavelength (<λ/1,000,000), the one-atom-thick layer, in conjunction with the metamaterial, can modulate both the amplitude of the transmitted wave by up to 47% and its phase by 32.2° at room temperature. More interestingly, the gate-controlled active graphene metamaterials show hysteretic behaviour in the transmission of terahertz waves, which is indicative of persistent photonic memory effects.

Controlling the electromagnetic properties of materials, going beyond the limit that is attainable with naturally existing substances, has become a reality with the advent of metamaterials. The range of various structured artificial 'atoms' has promised a vast variety of otherwise unexpected physical phenomena, among which the experimental realization of a negative refractive index has been one of the main foci thus far. Expanding the refractive index into a high positive regime will complete the spectrum of achievable refractive index and provide more design flexibility for transformation optics. Naturally existing transparent materials possess small positive indices of refraction, except for a few semiconductors and insulators, such as lead sulphide or strontium titanate, that exhibit a rather high peak refractive index at mid- and far-infrared frequencies. Previous approaches using metamaterials were not successful in realizing broadband high refractive indices. A broadband high-refractive-index metamaterial structure was theoretically investigated only recently, but the proposed structure does not lend itself to easy implementation. Here we demonstrate that a broadband, extremely high index of refraction can be realized from large-area, free-standing, flexible terahertz metamaterials composed of strongly coupled unit cells. By drastically increasing the effective permittivity through strong capacitive coupling and decreasing the diamagnetic response with a thin metallic structure in the unit cell, a peak refractive index of 38.6 along with a low-frequency quasi-static value of over 20 were experimentally realized for a single-layer terahertz metamaterial, while maintaining low losses. As a natural extension of these single-layer metamaterials, we fabricated quasi-three-dimensional high-refractive-index metamaterials, and obtained a maximum bulk refractive index of 33.2 along with a value of around 8 at the quasi-static limit.

We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices n=2 and 3, exhibit strong localization of simple geometric shape, and we call them quasiscarred resonances in the sense that there is, unlike conventional scarring, no underlying periodic orbits. It is shown that the formation of a quasiscarred pattern can be understood in terms of ray dynamical probability distributions and wave properties like uncertainty and interference.

The use of wrinkling provides a generic route to stretchable metamaterials, with unprecedented terahertz tunability. The wrinkled metamaterial can be stretched reversibly up to 52.5%; the structural integrity can be maintained during at least 100 stretching/relaxing cycles. Importantly, the wrinkling of meta-atoms offers a deterministic way to achieve controlled broadening of electrical resonance.