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= Extinction Efficiency 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 32ij 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 Science, Science, J. Schatz, G.C. Kelly, K. L. A. Mirkin, C. Cao, Y. Jin, R. Silver prisms Induced polarization 670 nm at 46.84 294 40 1901 , - 1903 (2001). 1903 30 Z y a x i s (15x75 nm) (15x75 20 10 4.647 2.667 10 20 30 40 45.3 Y axis - G. Zheng, G. Zheng, 15 10 20 15 10 Extinction20 Efficiency 5 0 5 0 Mirkin, et al, Figure 5 Mirkin, et 300 16 nm 16 nm 76 nm 400 100 nm 500 Wavelength, nm 12 nm 600 700 800 900 b a 1000 15 10 20 0 5 0 Extinction (a.u.) 300 16 nm 16 0.00 0.05 0.10 300 335 nm 76 nm Measured spectrum 400 CalculatedSpectrum 400 500 ~480 nm ~480 Wavelength, nm Wavelength, 500 12 nm12 Wavelength, nm 600 600 ~670 nm ~670 700 700 800 800 900 900 b 1000 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 i c Coupled multipole results for 100 i f D/2r=5 f E 2 n 1.5 30 nm spheres, parallel polarization o parallel i t 1.25 c n i 1.01 t 3 x single E 0 300 400 500 600 700 800 900 E0 Wavelength (nm) Perpendicular polarization leads to blue shifts 12 c 5.0 perpendicular 9 2.0 1.5 1.25 1.01 6 single 3 0 320 340 360 380 400 420 E0 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.