Bridging Microscopic Nonlinear Polarizations toward Far-Field Second Harmonic Radiation

TL;DR

This study investigates the microscopic mechanisms behind second harmonic generation (SHG) in metallic structures, revealing the importance of surface-parallel and bulk nonlinear polarizations, and introduces a model for improved design of nonlinear metamaterials.

Contribution

It provides the first comprehensive experimental comparison of SHG models across various structures, highlighting the roles of different nonlinear polarizations and proposing a virtual multi-resonator model.

Findings

Surface-parallel and bulk polarizations significantly influence far-field SHG patterns.

Common assumptions about surface-normal dominance in SHG are challenged.

A new multi-resonator model enables better control of nonlinear responses.

Abstract

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.