|0⟩ |1⟩ |2⟩ 4 J J J J P P 5 C J C P C U L Figure 1: Topolectrical circuit model. a, Artistic view of two-photon excitations in the array of microresonators with tunneling couplings. The depicted state isâ † 1â † 3 |0 . b, Extended version of Bose-Hubbard model considered in the present article. Single-photon tunnelings J are shown by blue solid lines, direct two-photon tunnelings P are indicated by purple wavy lines. c, Top view of the equivalent two-dimensional topolectrical circuit with a voltage at the site (m, n) corresponding to probability amplitude βmn for one photon to be located at the m th resonator of the array with another one located at the n th resonator [cf. Eq. (2)]. Colored regions show characteristic voltage patterns for two-photon scattering states (green), doublons (red), and doublon edge state (blue). External voltage source applied for the system excitation and voltmeter are shown to the right. Side view of the diagonal (lower inset) and off-diagonal (upper inset) sites of the topolectrical circuit, where grounding elements are shown. d, The photograph of experimental setup having the size of 15 × 15 nodes. Inset shows the enlarged fragment of the circuit which includes two unit cells. d c b a J J P J P J J P J

The modern development of wireless power transfer (WPT) technologies brings various products that improve the lives of users. It has become an urgent demand to simultaneously charge multiple mobile devices operating under different WPT standards on a charging platform regardless of their position and orientation with respect to each other. Recent advances in metasurfaces make it possible to control the near electromagnetic fields with much more degrees of freedom in comparison to conventional resonators. Here, we develop a compact multi-mode metamaterial-inspired resonator formed as an array of sub-wavelength parallel strip conductors. This resonator aims to replace conventional flat coil resonators and offers multiple modes with different profiles of electromagnetic field distribution for various near-field WPT applications. The first three eigenmodes are numerically and experimentally studied, and their potential applications for design of multi-mode WPT systems capable of charging multiple receivers simultaneously are discussed.

Topological photonics provides exceptional opportunities to control electromagnetic waves with a great potential for applications. Most of the proposed photonic systems support topological edge states with fixed parameters, thus hindering their practical applications. The study of nonlinear and tunable effects in topological systems enlarges applications of topological phenomena. Here, we propose an approach for the manipulation of photonic topological edge states based on temperature tuning. We design and demonstrate experimentally topological zigzag arrays composed of high-index resonators. The resonators are fabricated from ferroelectrics that brings an opportunity to dynamically change their permittivity by heating. We study the emergence of topological edge states in zigzag arrays of ferroelectric particles supporting the Mie resonances and demonstrate the topological transition induced by heating individual resonators in the array.

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