Bridging Microscopic Nonlinear Polarizations toward Far-Field Second Harmonic Radiation

Since the first observation of second harmonic generation (SHG), there have been extensive studies on this nonlinear phenomenon not only to clarify its physical origin but also to realize unconventional functionalities. Nonetheless, a widely accepted model of SHG with rigorous experimental verification that describes the contributions of different underlying microscopic mechanisms is still under debate. Here, we examine second harmonic far-field radiation patterns over a wide angle from metallic structures with different resonances, to reveal the structure-dependent contributions from distinct nonlinear polarizations. By comparing the measured SHG radiation patterns of 82 antennas with different SHG models, we demonstrate the critical role of the surface-parallel and bulk nonlinear polarizations in the far-field SHG patterns, and thus show that the common belief of the dominant contribution of the surface-normal component in SHG should be corrected. A virtual multi-resonator SHG model inside a single physical resonator is introduced to explain and control the interplay between different nonlinear polarizations and their structure-dependent excitations. Our findings offer a new strategy for the design of highly efficient and directional nonlinear metamaterials.