Optics, Plasmonics and Excitonics: Connecting Fundamental Theory to

Experiments and Applications

Emerging Topics in Optics University of Minnesota April 24, 2017

George C. SchatzNorthwestern University

Metal nanoparticle optical property research

Teri Odom, Rick Van Duyne,Chad Mirkin,Emily Weiss, M. Ratner, Stephen Gray (Argonne)

Electrodynamics:Shengli Zou (Central Florida)Marty Blaber (Seagate)Montacer Dridi (France)Kevin KohlstedDaniel Park, Mike Ross, Marc BourgeoisDanqing Wang, Weijia WangWendu Ding, Liang-Yan Hsu

Outline

1. Optical properties of isolated particles2. Plasmon resonances for 1D and 2D

nanoparticle arrays; lattice-plasmons and plasmon lasers

3. Plasmon resonances for 3D superlatticecrystals: plasmon-photonic interactions and metamaterials properties.

4. Plasmon-mediated exciton transport

1.7 nm

350 400 450 500 550 600 650 700

Wavelength (nm)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Extin

ctio

n (O

ptic

al D

ensi

ty)

3.5 nm

5.2 nm

20 nm

60 nm100 nm

160 nm

Spectra of dispersed colloidal gold for selected diameters (data from Turkevich (1954), Doremus (1964))

Colloidal Gold

Extinction = absorption + scattering(color of solution=color of light not absorbed or scattered)

Michael Faraday, 1856

E-field

e- cloud

Metalsphere

Plasmon excitation: collective excitation of the conduction electrons

osp 2

e

1shape / surroundings 2 cchemical properties 4 ne

m

+ χελ = = π

π

Plasmon (Bohm, Pines, 1952):

n=electron densityχ = shape factor (2 for sphere, >2 for spheroid)εo = dielectric constant of surroundings

Charge cloud of conduction electrons

Nuclear framework of particle

Mie Extinction for 13 nm Au spheres

0.0

0.2

0.4

0.6

0.8

1.0

Extin

ction

Effi

cienc

y

200 300 400 500 600 700 800

wavelength(nm)

2

pe

4 nemπ

ω =Langmuir plasma frequency (1929):

Spectrum of Colloidal Silver

The Plasmonic Periodic Table

Blaber, et al. J. Phys: Condens. Matter, 2010. 22, 143201.

Mie Extinction for 13 nm Au spheres

0.0

0.2

0.4

0.6

0.8

1.0

Extin

ction

Effi

cienc

y

200 300 400 500 600 700 800

wavelength(nm)

20 nm

Extinction for 20 nm spheres

Extinction Cross Section = (long wavelength limit)

ε = dielectric function of metal = ε1 + iε2

2 322 2

1 2

382

( radius )( )

επλ ε ε+ +

Mie Theory (1908)

real

imaginary

Dielectric constants of Au

200 300 400 500 600 700 800

wavelength (nm)

-15.0

-10.0

-5.0

0.0

5.0

Real

or Im

agina

ry pa

rt of

diele

ctric

cons

tant

ε1

ε2

(Lorenz-Mie-Debye) Theory

G. Mie, Annalen der Physik, 26, 597-614, 1908

Gustav Mie1868-1957

Size-Tunable Surface Plasmon Resonanceswidth95 120 145 145 145150150

Wavelength (nm)400 500 600 700 800 900

Nor

mal

ized

Ext

inct

ion

lmax565 638 720 747 782497446

height48 46 59 55 50627012042

426shape

Ag/mica

Computational Electrodynamics Methods for Nanoparticles

Grid or Finite element methods:•Discrete Dipole Approximation•Finite Difference Time Domain Method•Whitney-form Finite Element Method

Beyond Conventional Maxwell:•Nonlocal dielectric functions•Coupled QM + EM

1H Et µ∂

= − ∇×∂

1E H Jt ε∂

= ∇× −∂

( ) ( ) ( )20p p p p

d J t J t E tdt

γ ω ε+ =

Discrete Dipole Approximation

ik ri i 0 ij j

i jP E e A P

≠

= α −

∑

k=ω/c, rij=|ri-rj|, and rij= (ri-rj)/rij

Solve using iteration with complex conjugate gradient and FFT

( )ijikr

ij2 2ij j ij ij j ij j ij ij j3 2

ij ij

1 ikreA P k r (r P ) r P 3r r Pr r

− = × × + −

E H Jt

ε ∂= ∇× −

∂

H Et

µ ∂= −∇×

∂

1/2 1/21/2, , 1/2, ,

1/2, ,

n nx i j k x i j k

i j k

E Et

ε+ −

+ ++

−=

∆1/2, 1/2, 1/2, 1/2, 1/2, , 1/2 1/2, , 1/2

n n n nz i j k z i j k y i j k y i j kH H H H

y z+ + − + + + + −− −

−∆ ∆

1, 1/2, 1/2 , 1/2, 1/2

, 1/2, 1/2

n nx i j k x i j k

i j k

H Ht

µ+

+ + + ++ +

−=

∆

1/2 1/2 1/2 1/2, 1/2, 1 , 1/2, , 1, 1/2 , , 1/2

n n n ny i j k y i j k z i j k z i j kE E E E

z y

+ + + ++ + + + + +− −

−∆ ∆

Finite-difference Time-Domain Method

05

101520

300 400 500 600 700 800 900 100005

101520 76 nm 12 nm 16 nm

100 nm16 nm a

bExtinction Efficiency

Wavelength, nmMirkin, et al, Figure 5

0

300 400 500 600 700 800 900 10000

5

10

15

20

76 nm 12 nm

16 nm

b

Wavelength, nm

300 400 500 600 700 800 9000.00

0.05

0.10

335 nm

~480 nm

~670 nm

Extin

ctio

n (a

.u.)

Wavelength, nm

Silver prisms (15x75 nm) Measured spectrum

Calculated Spectrum

Induced polarization at 670 nm

y

2.667

1020

3040

45.3

4.64710203040

46.84

Y ax

is

Z axis

2.667

1020

3040

45.3

4.64710203040

46.84

R. Jin, Y. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, J. -G. Zheng, Science, 294, 1901-1903 (2001).

Modeling the Spectra of Silver Bipyramids using EM

400 600 800Wavelength (nm)

Zhang, Li, Wu, Schatz, and Mirkin Angew. Chem. Int. Ed., 48, 7787, (2009)

Simulations

Extin

ctio

n

400 600 800

Experiments and simulations are in good agreement with each other.

Wavelength (nm)

Extin

ctio

n

ExperimentsAg right bipyramid

Au rod-sheath

a = 106, 131, 165, 191 nmb

a

a = 2b

~ 1 nm precision required for theory-experiment match !!McMahon, Wang, Sherry, Van Duyne, Marks, Gray, and Schatz , JPCC, 113, 2731-2735 (2009)

90 nm Ag cube on glass: Plasmon is “split” into a blue component on the top and a red component on the bottom

Precision test of electrodynamics for silver cubes

LSPR Control by Molecular Adsorbates:Alkanethiols

Ag

Wavelength (nm)400 600 800 1000

Extin

ctio

n

0.08

0.16

0.24564

Van Duyne et al., J. Am. Chem. Soc., 123, 1471-1482 (2001).

CH

3

CH

3

CH

3

Ag

CH (CH ) SH3 2 15

D l max = +40 nm

604

5000 nm

Δλmax

D. L. Jeanmaire and R. P. Van Duyne, J. Electroanal. Chem. 84, 1-20 (1977)

Nanoparticles

Nanoparticles

ωexωex - ωvib

Normal Raman Spectrum (NRS) 2.5 M Pyridine

Surface - Enhanced RamanSpectrum (SERS): enhancement factor = 106

Surface Pyridine

Surface Enhanced Raman Spectroscopy (SERS)

Plasmon enhancement factors (electromagnetic mechanism):

Absorption =~|E(ω)|2

SERS enhancement =~|E(ω)|2|E(ω’)|2~ (|E|4)ave~106-12

When molecule is in direct contact with surface there are also chemical enhancements in SERS

Arrays of Au, Ag Nanoparticles: Optical properties strongly determined by structure

300 400 500 600 700 800 9000

3

6

9

D/2r=521.51.251.01singleEx

tinct

ion

Effic

ienc

y

Wavelength (nm)

a

Extinction Spectra of Nanoparticle Chains

parallel

E0

Coupled multipole results for 100 30 nm spheres, parallel polarization

Parallel polarization leads to red shifts

320 340 360 380 400 4200

3

6

9

12

c perpendicular

E0

Perpendicular polarization leads to blue shifts

5.02.01.51.251.01single

E0

400 50 nm particles

Width=4 meV

Width=0.001meV

Shengli Zou, Nicolas Janel, and George C. Schatz, J. Chem. Phys. 120, 10871-10875 (2004).

Infinite array of 50 nm particles

Narrow lineshapes for one-dimensional arrays of silver particles spaced by the wavelength

Particle arrays made using optical lithography show sharp lattice plasmon resonances

W. Zhou and T. Odom, Nature Nano, 6, 423 (2011), A. Yang, T. B. Hoang, M. Dridi, C. Deeb, M. H. Mikkelsen, G. C. Schatz, T. W. Odom, Nature Comm 6, 6939 (2015)

Particle arrays made using lithography show interaction of lattice mode with a gap plasmon

Q-Y Lin et al (M. Ross, GCS, C. A. Mirkin) Nano Lett, 15, 4699 (2015)

Experiment Theory

Al nanoparticle arrays show both dipole and quadrupole lattice plasmons

A. Yang, A. J. Hryn, M. R. Bourgeois, W-K Lee, J. Hu, G. C. Schatz, T. W. Odom, PNAS 113, 14201-6 (2016)

Background and Motivations 26

Plasmonic LasersGain medium near plasmonic structure results in enhanced stimulated emission

Oulton,R. F. et al. (X Zhang), Nature, 461, 629-632 (2009)

Noginov, M. A. et al.(Shalaev, Stockman) , Nature, 460, 1110–1168 (2009)

Laser dye around spherical gold particle

CdSe nanowire near flat silver surface

Nature Nano 8, 506-511 (2013)

Coupling QM to EM at the rate constant level

1)Quantum treatment of dye molecules

2)Classical electrodynamics for nanoparticle array

Model components:

Nature Nano 8, 506-511 (2013)

Measured and calculated dispersion behavior

Measured and calculated extinction

Coupling QM to EM at the rate constant level

3) Coupling of molecular polarization to field

22

2

( ) ( ) ( ) ( ) ( )a aa a a a

d P t dP t P t N t E tdt dt

ω ω κ+ ∆ + = ∆

2)Rate equations (derivable from Bloch equations) determine state populations, including amplified spontaneous and stimulated emission

1) Maxwell’s equations determine fields

Nature Nano 8, 506-511 (2013)

3 3 3

32 30

1 a

a

dN N N dPEdt dtτ τ ω

= − − + ⋅ ⋅

32 2

32 21

1 e

e

N dPdN N Edt dtτ τ ω

= − + ⋅ ⋅

1 2 1

21 10

1 e

e

dPdN N N Edt dtτ τ ω

= − − ⋅ ⋅

0 31

10 30

1 a

a

dN N dPN Edt dtτ τ ω

= + − ⋅ ⋅

(S5)

Coupling QM to EM at the rate constant level

Results:(1) Emission shows threshold behavior

(2)Population inversion distribution show plasmon enhancement

Nature Nano 8, 506-511 (2013)

(3)Population inversion is pinned above the lasing threshold <50 nm from particles

New work shows that lasing can be tuned by changing dye/refractive index with liquid gain materials

A. Yang, T. B. Hoang, C. Deeb, M. Dridi, M. Mikkelsen, GCS, T. Odom, Nature Comm., 6, 6939 (2015)

experiment theory

Laser emission: experiment

Laser emission: theory

DNA-linked Nanoparticle Superlattices

S. Y. Park, A. K. R. Lytton-Jean, B. Lee, S. Weigand, GCS, C. A. Mirkin, Nature, 451, 553 (2008).

2.55Å/bp 3.40Å/bp

# DNA/nanoparticle

Calculate for loading on each particle, then take smaller value

What crystal lattices occur when particles have different sizes and DNA loadings? Geometrical model: lattice is determined by crystal that has the largest DNA hybridization

Science, 334, 204-8 (2011)

Science, 334, 204-8 (2011)

FCC

CsC

lC

r 3Si

NaC

l

BC

CAlB

2C

s6 C

60Sim

ple Cubic

M. Jones, R. MacFarlane, B. Lee, J. Zhang, K. Young, A. Senesi, C. Mirkin, Nat. Mat 9, 913 (2010).R, H, Macfarlane, B. Lee, M. R. Jones, N. Harris, G. C. Schatz, C. A. Mirkin, Science, 334, 204-8 (2011).

DNA-linked nanoparticle superlattices:Extension to Nonspherical Particles

Experimental Studies for Disks show Plasmon Hybridization and Fano Interference effects

• High energy anti-bonding mode

• Bonding mode with a net dipole

M. O‘Brien, M. R. Jones, K. L. Kohlstedt, GCS and CAM, Nano Lett, 15, 1012 (2015)

For Au 3D superlattice material, effective medium approximation leads to red shifts in extinction spectra with

increasing crystal size

A. Lazarides and G. C. Schatz, J. Phys. Chem. 104, 460-7 (2000)M. B. Ross, J. C. Ku, B. Lee, C. A. Mirkin and G. C. Schatz, J. Phys. Chem. C 120, 816-830 (2016)

38

Silver Superlattices show collective metallic response

BCC: Ag 20 nm diameter20 nm edge to edge

DielectricLSPR

Metallic

Kaylie L. Young, Michael B. Ross, Martin G. Blaber, Matthew Rycenga, Matthew R. Jones, Chuan Zhang, Andrew J. Senesi, George C. Schatz, and Chad A. Mirkin, Adv. Mat. 26, 653-659 (2013).

Re ε

Ag superlattice aggregates: theory vs expt

Kaylie L. Young, Michael B. Ross, † Martin G. Blaber, Matthew Rycenga, Matthew R. Jones, Chuan Zhang, Andrew J. Senesi, George C. Schatz, and Chad A. Mirkin, Adv. Mater., 26, 653-659 (2013).

red: 17.1% Ag

green: 3.7% Ag

blue: 1.5% Ag

Metallic Dielectric

DNA-linked nanoparticle superlattice crystals

Auyeung, et al., Nature 2014, 505, 73.scale bar: 5 um

Plasmonic/Photonic Crystals made by DNA Nanoparticle Assembly Show Strong

Coupling of Plasmons and Fabry-Perot Modes

D. J. Park et al. “Photonic Crystals Realized through DNA Programmable Assembly” Proc. Natl. Aca. Sci., 2014, doi: 10.1073/pnas.1422649112.

Theory – 2D slab (EMT) Theory – 2D BCC slab (FDTD)

ExperimentFabry-Perot Modes(Scale bar 1 μm )

Volume Fraction ~1% Volume Fraction ~10%

g

e

SurfacePlasmon

CavityModes

ω

PS

600

Ag/Au Alloy and Bimetallic Superlattice Thin FilmsM. Ross, J. Ku, B. Lee, C. A. Mirkin and G. C. Schatz, Adv. Mat., 28, 2790(2016)

Atomic vs nanoscale alloying leads to different results: reflects charge transfer at the atomic level that doesn’t occur for nanoparticles.

Ag/Au Alloy and Bimetallic Superlattice Thin Films

Reflectivity is asymmetric as a result of the combination of gradient with lossy material.

M. Ross, J. Ku, B. Lee, C. A. Mirkin and G. C. Schatz, Adv. Mat., 28, 2790(2016)

Silver on left Gold on left

Expt Theory

Magneto-Plasmonics Provide New Opportunities for Designing Light-Matter Interactions

Combination: plasmonic sensitivity and optical control with magneto-responsive character

Magnetic materials provide asymmetric and magneto-responsive optical properties:Kerr RotationKerr EllipticityFaraday Rotation

Plasmonic systems provide exquisitely tunable optical properties

Magnetic thin film Au Ag

Model System: TMOKE in Co-Superlattice Thin Films

Superlattice modulates intensity and phase of light reaching the magnetic layerManifests as changes in:

• Overall reflectance of multilayer structure• Enhancement and control of TMOKE response• Unusual positive TMOKE parameter for metallic Ag superlattice

Transverse Magneto Optical Kerr Effect

Michael B. Ross, Marc R. Bourgeois, Chad A. Mirkin and George C. Schatz, J. Phys. Chem. Lett. 7, 4732-38 (2016).

Conclusions1. Solutions of Maxwell’s equations for isolated silver and gold nanoparticles

accurately match observed extinction spectra.

2. Arrays of nanoparticles which satisfy Bragg scattering conditions lead to lattice plasmon modes with narrow lines that are of interest in subwavelength lasers.

3. 3D arrays with well defined crystal habits lead to interesting plasmonicFabry-Perot modes. There are also unique metamaterials properties associated with these materials.

4. We have developed a FDTD-based approach to describe plasmon-mediated exciton transport.