Manipulating Nonlinear Plasmonics by Fundamental Conservation Laws

Plasmonically-Powered Processes, 25-30 June 2017 in Chinese University of Hong Kong, Hong Kong

Manipulating Nonlinear Plasmonics by Fundamental Conservation Laws W. E. I. Sha1, X. Y. Z. Xiong1, L. J. Jiang1, M. Fang2, Z. Huang2, A. Al-Jarror3, N. C. Panoiu3, W. C. Chew1 1Department of EEE, The University of Hong Kong, Hong Kong 2Key Laboratory of Intelligent Computing & Signal Processing, Anhui University, China 3Department of EEE, University College London Introduction

Charge & Energy Conservation

Unique combination of surface-sensitive second harmonic (SH) generation and strong field enhancement in plasmonic structures opening up new possibilities in Centrosymmetric Centrosymmetry  Ultrasensitive shape characterization material broken at surfaces  Nonlinear plasmonic sensing  All optical signal processing P b u lk ≈ 0 Psurface ≠ 0  High-sensitivity detectors

Second & third harmonic generation from a gold nanosphere • Electron density fluctuates at each point, the total charge is conserved

https://doi.org/10.2528/PIER16100401

Yee's grids for the FDTD method

• Energy conservation SH Martin, et. al., Nano Lett. (2013)

Mesch, et. al., Nano Lett. (2016)

SH Generation

TH

All optical chip, IBM (2011)

Motivation Weak nonlinear SH process requires strong field enhancement and efficient radiation mechanisms; however, this is full of challenges:  Conventional plasmonic enhancement rules breakdown  Difficult to control the radiation of SH wave: multipole emission nature  Complicated relation between particle shape and resonance  Lack of commercial software SH field

FH field

Nonlinear nanoantenna design by breaking parity symmetry • Compact nonlinear Yagi-Uda nanoantenna SH

Parity Conservation

E k

PNL

https://doi.org/10.1103/PhysRevA.94.053825 https://doi.org/10.1038/srep18872

Parity Conservation

PNL

Phase Retardation

FH

Cancelation PNL

PNL

Zero SH field inside the gap

Net PNL

 Parametric nonlinear process governed by fundamental conservation laws Charge • Energy • Parity • Angular Momentum

Method (1)

( ) =0 ( ) () ∇ × ∇ × E − μ ε Ω (1 + χ ( Ω ) ) E ( ) = ε μ Ω χ ( ) : E ( ) E( )

∇ × ∇ × E (ω ) − μ 0ε 0ω 2 1 + χ (1) (ω ) E (ω ) = i μ 0ω J (ω ) + ε 0 μ 0ω 2 χ ( 2 ) : E ( Ω ) E(ω )* 2

Ω

1

0 0

Cavity: light harvester, concentrator, and reflector Strong gap plasmonic enhancement Unidirectional radiation by symmetry broken Near field distribution

• Coupled-wave Equations for SHG

Ω

• Particle-in-Cavity Nanoantenna (PIC-NA)

2

0

2

ω

(2)

ω

0

Undepleted-pump Approximation

• Self-consistent Boundary Element Method (BEM) Initially set PS(ω ) to be zero, Iteratively solve (1) and (2) to capture mutual coupling. (ω , e )

(ω ,inc )

 π 0 = −n × H 0  (ω , m ) (ω ,inc )  π 0 = n × E0 Linear Source (Ω)

( Ω ,e )

 π0 = −iΩPt  ( Ω ,m ) 1 = ε 0 n × ∇ S PnS  π0 S

Nonlinear Source

E(0

ω,inc)

V1 V2

S− S+ E(ω,sca) 1

J(2 ) ω

(ω,tot )

E2

Angular Momentum Conservation

https://doi.org/10.1103/PhysRevB.95.165432

General Angular Momentum Conservation Law

J1(

ω)

(ω)

M2

M1(

ω)

n Love’s Equivalent Principle

( 2)

with PS = ε 0  χ ⊥⊥⊥nnn + χ ⊥( 2) ( nt1t1 + nt 2t 2 ) + χ(⊥2) ( t1nt1 + t 2nt 2 )  : E(2ω )E(2ω )

N-fold rotational symmetry

• Self-consistent Maxwell-Hydrodynamic Model Maxwell

Hydrodynamic

Supports Two systems are coupled through the polarization term

AoE/P-04/08