Several Quantum-Optical Analogies in

Coupled Nanoantenna, Waveguide and

Metasurface

Jun-Jun Xiao

Harbin Institute of Technology, Shenzhen Graduate School

Xili, Shenzhen 518055, Guangdong Province, China

E-mail: eiexiao@hitsz.edu.cn

IAS Winter School & Workshop on Advanced Concepts in Wave Physics: Topology and Parity-Time Symmetries, HKUST (2016.01.10-15)

Fano resonance

Toroidal moment

EIT

Optical topology

Insulator

……

….

Tamma et al., Nanoscale 5, 1592 (2013)

Zhang et al., Phys. Rev. Lett. 101, 047401 (2008)

Kaelberer et al., Science 330, 1510 (2010)

Bliokh et al., Nat. Photonics 9, 796 (2015)

Quantum-Optical Analogues

Bloch oscillation

Spin-dependent

optics

PT-symmetry

optics

Anderson localization

Zeno resonance

Gauge field optics

Outline

• Bloch oscillation in coupled nanoparticles and waveguides

− Wave-packet oscillation in time domain

− Bloch oscillation in spatial domain

• Fano resonance and EIT in nanoantenna and plasmonic waveguides

– Multiple Fano resonances by different order of electric antenna modes

– Magnetic and toroidal cavity modes in MDM nanodisk

– Double-EIT in plasmonic slot waveguides

– Controllable Fano/EIT in plasmonic-dielectric hybrid antenna

• PT-symmetry optics in coupled waveguides

• Absence of EP in finite-size waveguide array of apparently balanced gain/loss

• Summary

I. Bloch Oscillation, Fano Resonance & EIT

Zheng et al., J. App. Phys. 106, 113307 (2009)

Wave oscillation in graded nanoparticle chain

~ 11.8 ps

Bloch oscillation in graded waveguide array

Zheng et al., Phys. Rev. A 81, 033829 (2010)

Equation of motion:

Bloch Oscillation Breathing-like Oscillation

Miroshnichenko et al. Rev. Mod. Phys. 82., 2010

Joe et al. Phys. Scr. 74, 2006.

Classical analogy of Fano resonance & EIT

2 2

2 2

1 2 2 2 2 2

1 1 2 2

Af f i f

cf f i f f f i f

1. At the Fano dip resonance, the

“bright mode” is suppressed

2. Fano dip shows up near the

“dark mode” intrinsic frequency

3. Cross the Fano dip, “bright mode”

has abrupt phase variation

1| |C

Interference between

“bright” and “dark”

modes

U. Fano, Phys. Rev. 124, 1866 (1961)

Fano resonance induced by antenna modes

-- Reversal of optical binding force

E k

H

Homodimer:

---no Fano resonance

---no force reversal

Heterodimer:

----ED-EQ Fano resonance

----Reversal of binding force

Q. Zhang et al, Opt. Express 21, 6601 (2013)

E k

H

attraction

repulsion

Anti-bonding mode is completely dark

Multipole Fano resonances induced multiple BF reversals

Q. Zhang et al, Opt. Lett. 38, 4240 (2013)

Composite spoof localized surface plasmon (LSP)

R 33 mm

2 /d R N

0.15a d

1 0.4r R

2 0.5r R

20N

1 2 9.0g gn n

The spoof LSP resonance modes in the

composite resonator are derived from those

generated by the substructures

Spatially compact while spectrally efficient

Fano resonance in 2D composite spoof LSPs Complex resonance frequencies for the two

substructures are calculated

(1)2 0

(1) '

0

( )

( )

nn g

n

H k R fS n

H k R g

The relatively broad D-modes of

the two substructures interact with

each other and give rise to Fano-

like asymmetric line shape in the

spectrum

Qin, Xiao and Zhang et al., Opt. Lett. 41, 60 (2016)

A. Pors et al., Phys. Rev. Lett. 108, 223905 (2012)

Multimode competition and spectrum squeezing

1 7.787gn

At this particular point, two dipole

and one quadrupole resonance of

the two substructures come into

play, the effect of the quadrupole

resonance cannot be neglected

Fano resonance for 3D complex spoof LSPs (finite thickness)

1 0.3r R

2 0.4r R

0.3a d

t R

1 2.9gn

2 2gn

Transmission of slot waveguides with stub + resonators

Double EIT: Four-level atomic system

Z. Liu et al., Plamonics 10, 1057 (2015)

00 0 0 1 1

11 1 1 1 0 2 2

22 2 2 2 1

( )

( )

( )

j

e e

daj a e S j a

dt

daj a j a j a

dt

daj a j a

dt

0

j

eS S e a

St

S

Coherent plasmonic wave interference

CMT vs. FEM

22

0 0

1( )

e

e

ST

S j A

2

1 1 1/ [ ( ) ]A j B

2

2 2 2/ [ ( ) ]B j

EIT by interactions between Bragg gap and ‘polariton’ gap

Z. Liu et al., J. Opt. 18, 015005 (2016)

0Ti

e i

di

dt

aΩ Ξ Ξ a Γ S

i i i S C S Β a

1 2T

mi i i ia a aa

2 22 1 1

12 1 1

1

1

S S St r r

S S St r

M

12

1 1 e

iSt

S i

det 0BiK Le M IDispersion:

Transmission:

3 2 22

3 2 2

exp( ) 0

0 exp( )

S S Si

S S Si

M

2 1( )nM M M

222

1T M

Coupled mode theory

1

1 1

,e

e

Sr

S i

Single resonances case

Two-resonances case

Three-resonances case

2

2

1 10 2

21

2

1 ,e

e

St

Si

ii

2

2

10

1

1 .e

e

St

Si

i

1

2

10

1

,e

e

Sr

Si

i

1

2

1 10 2

21

2

.e

e

Sr

Si

ii

Plasmonic slot waveguide realization

Stopped by ‘polariton’ gap

II. Toroidal resonance and its interactions with other modes

Q. Zhang et at., ACS Photonics 2, 60 (2015)

Q. Zhang et al., J. Opt. Soc. Am. B 5, 1103 (2014)

E

K

H

Metal-Dielectric-Metal

Magnetic and toroidal cavity modes

anti-parallel going currents

Ez

Hx,y

EIT and Fano resonance induced by coupling between antenna mode and cavity modes

Delicately designed dipole antenna

Metal: Ag ------ antenna mode

Dielectric: ------ cavity mode

(different angular momentum)

load

90 , 50 , 20L nm R nm and d nm

Envelope: broad dipole resonance

sub-peak first dip second dip

Q. Zhang et al., Sci. Rep. 5, 17234 (2015)

=1load

=3load

=6load

=12load

=18load

Multipole decomposition in spherical basis

12

1 0 0(1) 2

0

2

1 0 0(1) 2

0

ˆ, sin

2 1 1

ˆ, sin

2 1 1

l

lm lm s

l

l

lm lm s

l

i kra Y d d

h kr E l l l

i krb Y d d

h kr E l l l

r E r

r H r

2 2

21

2 1l

s lm lm

l m l

C l a bk

(1)

lh spherical Hankel function

,lmY Spherical Harmonics

wave impendence in background

Multipole decomposition in Cartesian basis

4 4 5 6 6 6 62 22 2 2* *

03 3 4 5 5 5 5

2 2 4 2 2( Im( ) Re( )) / (8 )

3 3 3 3 20 20 15

e mIc c c c c c c

2

mP M P T T Q Q Μ R

3

3

2 3

3

3

2 3 2

1

1

2

1( ) 2

10

1 2( )

3

1

3

1[ ]

2

e

m

m

P J d ri

M d rc

T r r J d rc

Q r J J r d ri

Q r r d rc

R d r rc

r J

r J

r J

r J r J

r J

Note :

The SI form is just obtained by multiplying I in CGS

form by 0

1

4

2

0

2 I0SCS

ZC

E

2

0

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ( ) ( ) ( ) [ ( )] ( )4 2 2

ikre mk e ik ik

E ikr

n P n M n n T n n n Q n n Q n

Multipole scattering decomposition: benchmark

High dielectric sphere benchmark

ED: electric dipole a1 MD: magnetic dipole b1 EQ: electric quadrupole a2 MQ: magnetic quadrupole b2 MH: magnetic hexapole b3

Numerical vs. Mie theory R 65

22

nm

E k

TM

D=250 nm

Pure silver disk w/o gap layer

EQ

ED

EH

Multipole scattering decomposition: Application

Two families of resonances: AM and CMs Dipole-toroidal Fano resonance suppresses the

bright electric antenna mode

Moments identified by multipole decomposition

Different far field scattering patterns

Coexistence of scattering suppression and enhancement

Spin-dependent emission control

Coupled oscillator model: bright + sub-bright + dark modes

( , , ) ( ) ( ) im

z gspE z a z f k e

( , , ) ~ ( ) ( )zE z AF z G

2( ') '

02 ( )i m me d m m

Tunable by geometry and loaded material

L = 90 nm, d = 20 nm , d = 20 nm 12

Adv. Mat. 2012, 24, OP136-OP142 ACS Nano, 2015, 10.1021/acsnano.5b01591

III. Absence of Exceptional Points in Coupled Waveguides

PT-symmetry and mode coalescence in 2D coupler

In optics

*n r n r

balanced gain/loss contrast 1 121 1

12 12 20

e

e

n ia ai d

n ia ak dz

2 2

12 1coupled en n

Non-Hermitian Hamiltonian

x -a a b -b

1n i1n i

0n

PT-symmetry and EP in 2D waveguide coupler

（1, 1） （1, -1）

( 1. ei0.52 ,1) (1. e i2.62 ,1)

Exceptional point (EP)

(1. ei1.57,1)

(2.62 ei1.57,1) (0.38 ei1.57,1) Complex conjugate

Real

Increasin

g

PT-symmetry in two coupled 3D waveguides

1 1

1 1

2 20

2 2

0 0

0 0

0 0

0 0

e L

e T

L e

T e

n ia a

n ib bi d

n ia ak dz

n ib b

0

p e p p p

p p e p p

a n i a ai dH

b n i b bk dz

p : Coupling strength for the longitudinal (p = L) and transverse (p = T) cases

, 3.5

1.5

0.2

0.5

A B

b

n ig

n

R m

d m

PT-symmetry in four coupled waveguides

1

1

1

e T

e T

iH

i

n

n

2

2

2 e

L

T

en iH

in

(TB, TB)

(LB, TB)

With EPs and phase transition

No EPs No phase transition Band 1,7

Band 3,4

Lattice symmetry Mode symmetry PT symmetry

Z. Z. Liu et al., (under review)

Phase rigidity

( ) ( )

1

( ) ( ) ( ) ( )

L R

k k

k R R R R

k k k k

r

0L R

l kkla

'R

kkl la

( )R

k ( )L

k normalized right (left) eigenvector

0L

l the original state

l the unit vector

Ding, Ma, Xiao, Zhang and Chan

arXiv:1509.06886 (2015)

Photonic cavity and magnetic resonance modes

Nanoantenna and optical-matter interaction

Metal-dielectric artificial metasurfaces

Magnetically controllable directional metasurface

Spoof SPP resonator and waveguide

Our Interests

• Financial Support

– NSFC(11004043, 11274083)

– 973 Program (2012CB921501)

– Guangdong Province NSF (2015A030313748)

– Shenzhen Municipal Science & Technology Plan (JCYJ20150513151706573, JSGG20150529153336124)

– Shenzhen Oversea Talent Plan (KQCX20120801093710373)

• Group Member (Ph.D Candidates)

• Collaborators

– Prof. K. W. Yu, Chinese University of Hong Kong

– Prof. D. Z. Han, Chongqing University

– Prof. L. Gao, Soochow University

– Prof. W. G. Liang, Fujian Inst. Res. Stuct. Matt.

– Prof. K. Y. Tao, Shenzhen University

Acknowledgements

X. M. Zhang Z. Z. Liu F. F. Qin Q. Zhang

Master Students

5-year development plan of HIT@Shenzhen

Expanding…

哈尔滨工业大学（深圳） with PG & UG