A complete phase diagram for dark-bright coupled plasmonic systems: applicability of Fano’s formula

Wanxia Huang,Jing Lin,Qiong He,Meng Qiu,Shiyi Xiao,Lei Zhou,Tong Liu

doi:10.1515/nanoph-2020-0007

Abstract

Abstract Although coupled plasmonic systems have been extensively studied in the past decades, their theoretical understanding is still far from satisfactory. Here, based on experimental and numerical studies on a series of symmetry-broken nano-patch plasmonic resonators, we found that Fano’s formula, widely used in modeling such systems previously, works well for one polarization but completely fails for another polarization. In contrast, a two-mode coupled-mode theory (CMT) can interpret all experimental results well. This motivated us to employ the CMT to establish a complete phase diagram for such coupled plasmonic systems, which not only revealed the diversified effects and their governing physics in different phase regions, but more importantly, also justifies the applicabilities of two simplified models (including Fano’s formula) derived previously. Our results present a unified picture for the distinct effects discovered in such systems, which can facilitate people’s understanding of the governing physics and can design functional devices facing requests for diversified applications.

Highlights

Plasmonic resonances in nano-metallic particles, caused by collective oscillations of free electrons inside the particles associated with electromagnetic (EM) waves, have attracted intensive attention recently
Scientists have proposed several simplified models, such as Fano’s formula [33, 34] and the independent-oscillator model [35,36,37,38], to understand the rich physics discovered in different systems
We start by studying a series of gold nano-square-resonators with broken symmetries experimentally, and show that while Fano’s formula can explain the spectra obtained under one incident polarization well, it completely fails for those obtained under another polarization

Summary

Introduction

Plasmonic resonances in nano-metallic particles, caused by collective oscillations of free electrons inside the particles associated with electromagnetic (EM) waves, have attracted intensive attention recently. We start by studying a series of gold nano-square-resonators with broken symmetries experimentally, and show that while Fano’s formula can explain the spectra obtained under one incident polarization well, it completely fails for those obtained under another polarization (see Section 2) To understand such intriguing results, we employ a two-mode coupledmode-theory (CMT) [39,40,41,42,43] to re-examine the problems, and find that the CMT can explain all experimental findings well (see Section 3). Based on the two-mode CMT, we establish in Section 4 a complete phase diagram for such dark-bright coupled systems, which provides a unified picture to understand all the fascinating optical effects discovered, but more importantly, reveals the applicable regions of those simplified models derived previously.

Experimental studies on a series of examples: issues arising

The root-mean square error is defined as

Re-explain the experimental results by the CMT

Generic phase diagram derived from CMT

Conclusions