Modeling of nonlinear response from metallic metamaterials by Maxwell-hydrodynamic equations

Abstract

In this work, the nonlinear response from metallic metamaterials is characterized by a finite-difference time-domain solution to the Maxwell-hydrodynamic equations. The spatial locations of E-fields (and electric currents) are interleaved with that of magnetic fields. The electron charge is at the center of Yee grids. The current continuity equation connects Maxwell and hydrodynamic equations. For conserving total charges within metallic metamaterials, an interpolation scheme for electron density is developed. Other interpolation schemes for the magnetic field and electron velocity are also implemented, which is critical for capturing conservation laws of second harmonic radiation. The linearly and circularly polarized plane-wave sources with controlled central frequency, bandwidth, and amplitude are introduced by pure scattered field technique. For different harmonic radiation, perfectly matched layer is adopted to absorb outgoing waves at a broadband; and near-to-far-field transformation is employed to obtain far-field data. Different from existing methods, our model accurately captures the conservation laws of the second harmonic radiation from complex-shaped metallic metamaterials with versatile incident waves. Charge conservation, angular momentum conservation, and parity conservation are fully demonstrated by different numerical examples. Through exploring the conservation laws, a nonlinear Yagi-Uda nanoantenna is proposed to direct second harmonic radiation from a centrosymmetric nanoparticle. By tuning the spacing and dimensions of two lossless dielectric elements, which function respectively as a compact director and reflector, the second harmonic radiation can be deflected 90 degrees with reference to the incident pump direction. Our works pave a new way toward nonlinear signal detection, sensing, and manipulation.