Unidirectional emission of phase-controlled second harmonic generation from a plasmonic nanoantenna

Shaping the emission pattern of second harmonic (SH) generation from plasmonic nanoparticles is important for practical applications in nonlinear nanophotonics but is rendered challenging by the complex second-order nonlinear-optical processes. Here, we theoretically and experimentally demonstrate that a pair of V- and Y-shaped gold nanoparticles directs the SH emission perpendicularly to an incident light direction. Owing to spatial overlap of two orthogonal plasmonic dipole modes at the fundamental and SH wavelengths of the individual particles, surface SH polarizations induced by the fundamental field is efficiently near-field coupled to the SH plasmon mode, resulting in dipolar SH emission from the individual particles. Moreover, the phase of this emission can be tuned simply by altering the part of the Y-particle shape, which changes the SH plasmon resonance while keeping the fundamental resonance. Our approach is a promising platform for engineering not only directional nonlinear nanoantennas but also nonlinear metamaterials.

Nonreciprocal elasticity and the realization of static and dynamic nonreciprocity

The realization of the mechanical nonreciprocity requires breaking either the time-reversal symmetry or the material deformation symmetry. The time-reversal asymmetry was the commonly adopted approach to realize dynamic nonreciprocity. However, a static nonreciprocity requires—with no any other option—breaking the material deformation symmetry. By virtue of the Maxwell–Betti reciprocal theorem, the achievement of the static nonreciprocity seems to be conditional by the use of a nonlinear material. Here, we further investigate this and demonstrate a novel “nonreciprocal elasticity” concept. We investigated the conditions of the attainment of effective static nonreciprocity. We revealed that the realization of static nonreciprocity requires breaking the material deformation symmetry under the same kinematical and kinetical conditions, which can be achieved only and only if the material exhibits a nonreciprocal elasticity. By means of experimental and topological mechanics, we demonstrate that the realization of static nonreciprocity requires nonreciprocal elasticity no matter what the material is linear or nonlinear. We experimentally demonstrated linear and nonlinear metamaterials with nonreciprocal elasticities. The developed metamaterials were used to demonstrate that nonreciprocal elasticity is essential to realize static nonreciprocal-topological systems. The nonreciprocal elasticity developed here will open new venues of the design of metamaterials that can effectively break the material deformation symmetry and achieve, both, static and dynamic nonreciprocity.

Spectro-Spatial Wave Features in Nonlinear Metamaterials: Theoretical and Computational Studies

Considerable attention has been given to nonlinear metamaterials because they offer some interesting phenomena such as solitons, frequency shifts, and tunable bandgaps. However, only little is known about the spectro-spatial properties of a wave propagating in nonlinear periodic chains, particularly, a cell with multiple nonlinear resonators. This problem is investigated here. Our study examines both hardening and softening nonlinearities in the chains and in the local resonators. Explicit expressions for the nonlinear dispersion relations are derived by the method of multiple scales. We validate our analytical results using numerical simulations. The numerical simulation is based on spectro-spatial analysis using signal processing techniques such as spatial-spectrogram and wave filtering. The spectro-spatial analysis provides detailed information about the interactions of dispersive and nonlinear phenomena of waveform in both short- and long-wavelength domains. Furthermore, we validate and demonstrate the theoretically obtained bandgaps, wave distortion, and birth of solitary waves through a computational study using finite element software, ansys. The findings, in both theoretical and computational analyses, suggest that nonlinear resonators can have more effect on the waveform than the nonlinear chains. This observation is valid in both short and long wavelength limits.