  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.
