Emerging Topics in Optics University of Minnesota April 24, 2017 Optics, Plasmonics and Excitonics: Connecting Fundamental Theory to Experiments and Applications

George C. Schatz Northwestern University Metal nanoparticle optical property research

Electrodynamics: Shengli Zou (Central Florida) Marty Blaber (Seagate) Montacer Dridi (France) Teri Odom, Rick Van Duyne, Kevin Kohlsted Chad Mirkin, Daniel Park, Mike Ross, Marc Bourgeois Emily Weiss, M. Ratner, Danqing Wang, Weijia Wang Stephen Gray (Argonne) Wendu Ding, Liang-Yan Hsu Outline

1. Optical properties of isolated particles 2. Plasmon resonances for 1D and 2D nanoparticle arrays; lattice-plasmons and plasmon lasers 3. Plasmon resonances for 3D superlattice crystals: plasmon-photonic interactions and metamaterials properties. 4. Plasmon-mediated exciton transport Colloidal Gold

Michael Faraday, 1856

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

0.8 60 nm 0.7 100 nm 20 nm 0.6 5.2 nm 0.5 160 nm

0.4

0.3

Extinction (Optical Density) (Optical Extinction 0.2 3.5 nm

0.1 1.7 nm 0.0 350 400 450 500 550 600 650 700

Wavelength (nm)

Extinction = absorption + scattering (color of solution=color of light not absorbed or scattered) Plasmon excitation: collective excitation of the conduction electrons

E-field Metal sphere Nuclear framework of particle

Charge cloud of conduction electrons e- cloud

4π ne2

Mie Extinction for 13 nm Au spheres

1.0

0.8

0.6

ω= Efficiency Extinction 0.4

0.2

0.0 200 300 400 500 600 700 800 Langmuir plasma frequency (1929): p wavelength(nm) me Plasmon (Bohm, Pines, 1952):

shape / surroundings 1+ χεo λ=sp =π2c chemical properties 4π ne2

n=electron density me χ = shape factor (2 for sphere, >2 for spheroid)

εo = dielectric constant of surroundings Spectrum of Colloidal Silver The Plasmonic Periodic Table

Blaber, et al. J. Phys: Condens. Matter, 2010. 22, 143201. Mie Theory (1908) (Lorenz-Mie-Debye) Theory G. Mie, Annalen der Physik, 26, 597-614, 1908

π 23ε Extinction Cross Section = 8 ( radius ) 3 2 22 (long wavelength limit) λε()12++2 ε

ε = dielectric function of metal = ε1 + iε2

Mie Extinction for 13 nm Au spheres

1.0

0.8

0.6

Extinction Efficiency Extinction 0.4

0.2

0.0 200 300 400 500 600 700 800 wavelength(nm) Extinction for 20 nm spheres Gustav Mie1868-1957

Dielectric constants of Au

5.0

imaginary

0.0

real

-5.0 Real or Imaginary part of dielectric constant dielectric of part Imaginary or Real

-10.0

-15.0 200 300 400 500 600 700 800 wavelength (nm) 20 nm

ε2

ε1 Size-Tunable Surface Plasmon Resonances 120 150 150 95 120 145 145 145 width 42 70 62 48 46 59 55 50 height

n shape

o i 426 446 497 565 638 720 747 782 t lmax

c

n

i Ag/mica

t

x

E

d

e

z

i

l

a

m

r o

N

400 500 600 700 800 900 Wavelength (nm)

Computational Electrodynamics Methods for Nanoparticles

∂ 1  ∂ 1 d   E= ∇× HJ − HE=− ∇× Jt( ) +=γ Jt( ) ωε2 Et( ) ∂t ε ∂t µ dt p pp p0

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 Discrete Dipole Approximation

 P=α− Eeik r A P i i 0 ∑ ij j Solve using iteration with ≠ ij complex conjugate gradient and FFT

eikrij 1− ikr A P= k22 r ×× (r P ) +ij  r P − 3r r P ij j 32ij ij j ij j ij( ij j ) rrij ij

k=ω/c, rij=|ri-rj|, and rij= (ri-rj)/rij Finite-difference Time-Domain Method

∂   ε E=∇× HJ − ∂t ∂  µ HE= −∇× ∂t

EEnn+−1/2 − 1/2 HHnn−− HH nn ε x i++1/2, jk , x i1/2, jk , = zijk++1/2, 1/2, zijk −+1/2, 1/2, − yijk ++1/2, , 1/2 yijk +−1/2, , 1/2 i+1/2, jk , ∆t ∆∆yz

HHnn+1 − En+1/2 −− EE nn ++1/2 1/2 E n +1/2 µ x ij,++ 1/2, k 1/2 xij , ++ 1/2, k 1/2 = y ij,+ 1/2, k + 1 y ij,+ 1/2, k− z ij,++ 1, k 1/2 z ijk, ,+ 1/2 ij,++ 1/2, k 1/2 ∆t ∆∆zy Silver prisms (15x75 nm) Measured spectrum R. Jin, Y. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, J. -G. Zheng, ~670 nm Science, 294, 1901-1903 (2001). 0.10

~480 nm

0.05 Extinction (a.u.)

335 nm

0.00 300 400 500 600 700 800 900 Wavelength, nm y 3 . 5

20 100 nm 15 a 16 nm

10 y c

n 5 e i c i f f E

0

20n o i t c

n 12 nm i 76 nm

t b

15x

E 16 nm

10

5

0 300 400 500 600 700 800 900 1000 Wavelength, nm

Mirkin, et al, Figure 5 4 Calculated Spectrum

0 0 4 20

0 76 nm 12 nm 3 15 b s i 16 nm x a

Y 0 2 10 0 1 5 7 6 6 . 4 0 0 0 0 7 2 8 4 3 2 1 4 . 6 6 . 4 Z axis 4 0

Induced polarization at 670 nm 300 400 500 600 700 800 900 1000

Wavelength, nm

Modeling the Spectra of Silver Bipyramids using EM

Ag right bipyramid Experiments Simulations b a = 106, 131, 165, 191 nm

a a = 2b Extinction Extinction

400 600 800 400 600 800 Wavelength (nm) Wavelength (nm) Au rod-sheath

Experiments and simulations are in good agreement with each other.

Zhang, Li, Wu, Schatz, and Mirkin Angew. Chem. Int. Ed., 48, 7787, (2009) Precision test of electrodynamics for silver cubes

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

~ 1 nm precision required for theory-experiment match !!

McMahon, Wang, Sherry, Van Duyne, Marks, Gray, and Schatz , JPCC, 113, 2731-2735 (2009)

LSPR Control by Molecular Adsorbates: Alkanethiols

5

0

0.24 0 Ag 0

n 564 604 m

n CH3 (CH 2 ) 15 SH

o

i

t

3 3 3

c

H H H n 0.16

i

C C C

t

x

E

Ag

Δλ 0.08 Dl maxmax = +40 nm 400 600 800 1000 Wavelength (nm) Van Duyne et al., J. Am. Chem. Soc., 123, 1471-1482 (2001). Surface Enhanced Raman Spectroscopy (SERS)

Normal Raman Spectrum (NRS) 2.5 M Pyridine

Surface - Enhanced Raman Surface Pyridine Spectrum (SERS): enhancement factor = 106

ωex Nanoparticles ωex - ωvib

Nanoparticles

D. L. Jeanmaire and R. P. Van Duyne, J. Electroanal. Chem. 84, 1-20 (1977) Plasmon enhancement factors (electromagnetic mechanism):

Absorption =~|E(ω)|2

2 2 4 6-12 SERS enhancement =~|E(ω)| |E(ω’)| ~ (|E| )ave~10

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 Extinction Spectra of Nanoparticle Chains

9 Parallel polarization leads to red shifts a y c

n 6 e

c i Coupled multipole results for 100 i

f D/2r=5 f

E 2

n 1.5 30 nm spheres, parallel polarization

o parallel i 1.25 c t n i 3 1.01 x t single E

0 300 400 500 600 700 800 900 E0 Wavelength (nm) Perpendicularpolarization leads to blue shifts

12 0 6 9 3 320 single 1.01 1.25 1.5 2.0 5.0 340 360

380 400 c 420 perpendicular E 0 400 50 nm particles Narrow lineshapes for one-dimensional arrays of silver Width=4 meV particles spaced by the wavelength Infinite array of 50 nm particles

Width=0.001meV E0

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

Experiment Theory

Q-Y Lin et al (M. Ross, GCS, C. A. Mirkin) Nano Lett, 15, 4699 (2015) 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) Plasmonic Lasers Gain medium near plasmonic structure results in enhanced stimulated emission

CdSe nanowire near flat silver surface

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

Laser dye around spherical gold particle

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

Background and Motivations 26 Nature Nano 8, 506-511 (2013) Coupling QM to EM at the rate constant level Nature Nano 8, 506-511 (2013) Model components:

1)Quantum treatment of dye molecules 2)Classical electrodynamics for nanoparticle array

Measured and calculated dispersion behavior Measured and calculated extinction Coupling QM to EM at the rate constant level Nature Nano 8, 506-511 (2013)

1) Maxwell’s equations determine fields (S5)

dN N N1 dP 3=−− 33 + ⋅⋅E a dt ττ ω dt 2)Rate equations (derivable from 32 30  a Bloch equations) determine state dNN N 1 dP 22=3 − + ⋅⋅E e populations, including amplified dt ττ32 21  ωe dt spontaneous and stimulated dN N N 1 dP 1= 21 − − ⋅⋅E e emission dt ττ21 10  ωe dt

dNN N1 dP 03=1 + − ⋅⋅E a dt ττ10 30  ωa dt

3) Coupling of molecular polarization to field

 dPt2 () dPt ()  aa+∆ω + ωκ2 P() t = ∆ NtEt () () dt2 a dt aa a Coupling QM to EM at the rate constant level Nature Nano 8, 506-511 (2013)

Results: (1) Emission shows threshold behavior

(3)Population inversion is pinned (2)Population inversion above the lasing threshold <50 distribution show plasmon nm from particles enhancement New work shows that lasing can be tuned by changing dye/refractive index with liquid gain materials Laser emission: experiment

experiment theory

Laser emission: theory

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

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

Calculate for loading on 2.55Å/bp 3.40Å/bp each particle, then take smaller value

Science, 334, 204-8 (2011) Science, 334, 204-8 (2011) BCC FCC AlB CsCl 2 Cs Si 3 6 C Cr 60 Simple Cubic Simple NaCl DNA-linked nanoparticle superlattices: Extension to Nonspherical Particles 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) . 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) Silver Superlattices show collective metallic response

Re ε

Dielectric LSPR

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

BCC: Ag 20 nm diameter 20 nm edge to edge

38 Ag superlattice aggregates: theory vs expt

Metallic Dielectric

red: 17.1% Ag

green: 3.7% Ag

blue: 1.5% Ag

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). 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

S P Volume Fraction ~1% Volume Fraction ~10%

Surface Cavity 600 Plasmon Modes ω e

g Theory – 2D slab (EMT) Experiment (Scale bar 1 μm ) Theory – 2D BCC slab (FDTD) 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. Ag/Au Alloy and Bimetallic Superlattice Thin Films

M. 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

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

Silver on left Gold on left

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

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

Magnetic thin film Au Ag Plasmonic systems provide Magnetic materials provide asymmetric and magneto-responsive optical properties: exquisitely tunable optical Kerr Rotation properties Kerr Ellipticity Faraday Rotation

Combination: plasmonic sensitivity and optical control with magneto-responsive character Model System: TMOKE in Co-Superlattice Thin Films

Superlattice modulates intensity and phase of light reaching the magnetic layer

Manifests as changes in: Transverse Magneto Optical Kerr • Overall reflectance of multilayer structure Effect • Enhancement and control of TMOKE response • Unusual positive TMOKE parameter for metallic Ag superlattice

Michael B. Ross, Marc R. Bourgeois, Chad A. Mirkin and George C. Schatz, J. Phys. Chem. Lett. 7, 4732-38 (2016). Conclusions 1. 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 plasmonic Fabry-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.