Coupling of Plasmon resonances/ Fano Resonances

1. Coupling of Plasmon resonances/Fano Resonances Tomáš Šikola Institute of Physical Engineering, Brno University of Technology

2. Localized Surface Plasmons in Metallic Nanoparticles Closely spaced nanoparticles (Dimer) – the most fundamental system of two interacting objects. Its behaviour can be explained by the Hybridization Model • Bright Modes: lower energy • (directly excited by incident light) • Bonding symmetricallyaligned plasmons - • couplings occur for longitudinal polarization • Finite dipole moments • The strongest plasmonic couplings + - + - • Dark Modes: higher-energy • (weak interaction with the incident light) • Antibondingmodes with their antisymmetric • alignment of nanoparticle dipoles • No net dipole moment • Single nanoparticles: • quadrupolar and highermultipolar modes • Nanoparticlechains and higher-order multipoles: • coupled modes with vanishing dipole • moments in nanoparticle pairs • propagating modes in nanoparticle • chains and higher-order multipoles P. Nordlander at al., NanoLett., 2004, 4, 899

3. Generation of LSP by an Electron Beam Au nanoparticle with a citrate coating Polar Mie resonance (I, blue) and bulk plasmon modes (II, red) Experimental EELS data of a single silver nanoparticle of diameter approximately 24 nm, showing plasmon energies as a function of electron probe position. The spectra were obtained by positioning the electron probe at 2 nm intervals. Ai Leen Koh, ACS Nano,

4. Generation of LSP by an Electron Beam (EELS) Antibonding mode EELS Modelling Antibonding mode Dipolar peak Higher order peaks Quadrupole peak Bulk mode Dark mode Bright mode Contributions from the electron field at the edge (blue curve) and the intersection (red curve) of a dimer Experimental EELS data set of a symmetrical silver nanoparticle dimer, showing plasmon energies as a function of electron probe position. The spectra are obtained at regular intervals of 4 nm. Ai Leen Koh, ACS Nano,

5. Localized Surface Plasmons in Metallic Nanoparticles • Complex Plasmonic Nanostructures: • Serve as model systems for a variety of coherent phenomena arising from • the physics of coupled oscillators (classical oscillators at the nanoscale) • Symmetry breaking: • Provides a mechanism for enhancing the coupling of • plasmon modes • Allows the modes that only weakly couple to the radiation continuum • to couple directly to incident electromagnetic radiation • Structures with broken symmetry: • Fano resonances arising due to the interaction • of narrow dark (subradiant) modes with broad bright (superradiant) • modes • This coupling leads to a plasmon-induced transparency of • nanostructures (for strong interactions and near-degenerate energy • levels)  qualitative similarity with elmg. induced transparency (EIT)

6. Electromagnetically Induced Transparency(EIT) • Effect known in atomic physics: • The EIT phenomenon appears as a dip in the absorption spectra • Physical model: • Incident light couples to a bright • strongly damped oscillator (mode) • being coupled in turn to a dark weakly damped oscillator (mode) • Dispersive coupling between the • two modes  a strong dependence • on the frequency in a narrow • interval arround the dark mode • frequency  a strong modulation of • the absorption spectrum Coupling frequency C.L. GarridoAlzar, Am. J. Phys., 70(1) 2002

7. Analogy between Plasmon Modes and Classical Oscillators • Plasmonic Nanostructures: • Physically realizable coupled oscillator systems on the nanoscale Plasmon modes of a composite nanostructure expressed by PH Normal modes of a system of damped oscillators • Energies and linewidths of individual nanoparticleplasmons given by: • Nanoparticle geometry and size • Interactions between plasmon modes depends on: • Mutual relative positions of individual nanoparticles

8. Localized Surface Plasmons in Metallic Nanoparticles • The dark (subradiant) modes and higher order resonances are of fundamental interest: • Waveguiding deeply under the diffraction limit • Reduced radiative losses(development of plasmonicnanolasers) • Metamaterials with high-quality-factor resonances • Highly tunablesubradiant ring/disk plasmon cavities • Importance in biosensing and plasmonicnanolasing applications • How to generate dark and higher-order modes? • Optical excitations by breaking the symmetry • on individual nanoparticles so as to modify the selection • rules for plasmon interaction modes • Using electron beams

9. A metallic nanostructure: a disk inside a thin ring Concentric ring/disk cavity (CRDC): Highly tunable metallic nanostructure • Interaction between a dipolar disk and ring • PH: • LE dipolar bonding resonance (DBR) – • subradiant • (dipolar moments of the disk and ring • aligned oppositely) • HE dipolar antibonding resonance (DAR) - superradiant • (both dipolar moments in phase) FDTD calculations Red shift of DBR with increasing D

10. Extinction spectra for Ag concentric ring/disk cavity (CRDC) and NCRDC CRDC NCRDC • Major effects with growing symmetry breaking: • Red shift of DBR (interaction of the dipolar ring mode with • higher multipolar modes) • AssymetricFano resonance in the broad DAR (interaction • of the bright antibondingdipolar disk mode with the • dark quadrupole ring mode) FDTD calculations

11. Plasmon Hybridization for the NCRDC Multipolar resonances induced by parallel light incidence Higher angles - phase retardation higher order multipolar hybridized modes Note: The quadrupole resonances of individual thin disks and resonances cannot be excited for perpendicular incidence!

12. Plasmon Hybridization for the NCRDC Very high LSPR sensitivities of the subradiant (DBR) and Fano resonances to the surroundings sensing Large Red Shifts

13. A metallic nanostructure: a disk inside a thin ring • Broad superradiant and very narrow subradiant modes • The increased interaction between the plasmon resonances (modes) of the ring • and the disk with breaking symmetry (NCRDC) larger field enhancement • (e.g. 260 for DBR and 60 for DAR) caused by (1) the narrowing of the • junction between the inner ring and outer disk surface and (2) admixture of • higher multipolarplasmon modes • Symmetry braking coupling between plasmon modes of different multipolar • order tunable Fano resonances • NCRDC may serve as a highly efficient LSPR sensors

16. Experimental and simulated EEL Spectra

17. 3. Far-Field Illumination and Near-field Detection Amplitude and phase of recorded field distributions ES(x, y) = AS(x, y) exp [i (ω0t + φS(x, y) + βS)] ER = AR exp [i (ω0t + δωt + βR)] I = |AS(x, y)|2 + |AR|2 + + 2AR · AS(x, y) cos [−δωt + φs(x, y) + βS − βR] Signal Amplitude Phase L. Novotny and B. Hecht: Principles of Nano-optics, Cambridge University Press, 2006

18. 3. Far-Field Illumination and Near-field Detection • Aperture probe: • Lower collection efficiency – higher • signals needed • Tip influence on the NF signal • but: • better light confinment ( 50 nm, min.  20 nm (2 x skin-effect depth in metal • coating) • Scattered field rejected • No need for evanescent field • excitation (any field can be used for • excitation – e.g. focused laser beam) Collection mode near-field optical microscopy L. Novotny and B. Hecht: Principles of Nano-optics, Cambridge University Press, 2006

19. 3. Far-Field Illumination and Near-field Detection Collection mode near-field optical microscopy ‘Double-slit experiment’ R. Zia and M. Brongersma

20. Application of SPP – PLASMONICS (Going beyond diffraction limit) Optical integratedcircuits of subwavelength dimensions a b • Waveguide based on surfcaeplasmonpolaritons. • Gold stripe on a glass substrate - 40 nm thick, 2.5m wide (SEM). • Surface plasmonpolaritons propagating on the gold stripe surface (PSTM) • Barnes et al., Nature (2004)

21. Two-Photon Induced Photoluminiscence (TPA) through interband transitions in Au: Nonlinear spectroscopy  E4 preferentially sensitive to the most intense fields (i.e. close to the metal) Tunable Ti: saphire laser (150 fs pulses, 700 – 780 nm, 30 W)Tightly focused beam (immersion oil 100 x objective , NA=1,25 (spot size 350 nm) Detector: Avalanche photodiode Substrate: Glass coated by ITO (10 nm)

22. 1. Far-field Illumination and Detection Spot size: Numerical aperture Spatially filtered light  = 500 nm. NA = 1.4 x = 220 nm Single-photon counting avalanche diode L. Novotny and B. Hecht: Principles of Nano-optics, Cambridge University Press, 2006

23. 1. Far-field Illumination and Detection The Confocal Principle L. Novotny and B. Hecht: Principles of Nano-optics, Cambridge University Press, 2006

24. 1. Far-field Illumination and Detection The Nonlinear Excitation and Saturation L. Novotny and B. Hecht: Principles of Nano-optics, Cambridge University Press, 2006

25. Two-Photon Induced Photoluminiscence Weaker field modulation: Multipolar resonance involved

26. Two-Photon Induced Photoluminiscence

27. Both thermal (T and HSD) and optical measurements (two-photon luminiscence of Au): Thermal Imaging Method: Fluorescence Polarization Anisotropy (FPA) Fluorescence molecules dispersed in glycerol . Speed of rotation of molecules increases with temperature  reduced degree of polarization of the emitted fluorescence Ti:Sapphire (IR) laser: cw mode - heating plasmonicstriutures , pulse mode - two-photon lumniscence of Au (TPL) Excitation of fluorescence molecules T (r) map: unfocused IR laser, blue beam scanned, HSD - h (r) map: blue and IR beam scanned and overlapped, stage scanned

28. Mapping Heat Origin in Plasmonic Structures Poisson Equation: Temperature ‘Heat source’ density Thermal Conductivity Simplification: • G (r; r’ ) is the scalar thermal Green function associated to PE, generalized Green dyadic tensor

29. Mapping Heat Origin in Plasmonic Structures

30. A general rule: In plasmonic structures the heat origin does not match the optical hot spots !

31. Mapping Heat Origin in Plasmonic Structures