Coupling of Plasmon resonances/Fano Resonances

Tomáš Šikola

Institute of Physical Engineering, Brno University of Technology

Localized Surface Plasmons in Metallic NanoparticlesClosely 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 symmetrically aligned plasmons - couplings occur for longitudinal polarization • Finite dipole moments• The strongest plasmonic couplings

Dark Modes: higher-energy(weak interaction with the incident light)

• Antibonding modes with their antisymmetric

alignment of nanoparticle dipoles • No net dipole moment

Single nanoparticles: • quadrupolar and higher multipolar modes

Nanoparticle chains 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., Nano Lett., 2004, 4, 899

+ - + -

Generation of LSP by an Electron Beam

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.

Au nanoparticle with a citrate coating

Polar Mie resonance (I, blue)and bulk plasmon modes (II, red)

Ai Leen Koh, ACS Nano,

Generation of LSP by an Electron Beam (EELS)

Ai Leen Koh, ACS Nano,

Experimental EELS data set of a symmetrical silver nanoparticledimer, showing plasmon energies as a function of electron probe position.The spectra are obtained at regular intervals of 4 nm.

Contributions from the electron field at the edge (blue curve) and the intersection (red curve) of a dimer

Bright mode

Dark mode

Bulk mode

EELS Modelling

Dipolar peak

Quadrupole peak

Higher order peaks

Antibonding mode

Antibonding mode

Localized Surface Plasmons in Metallic NanoparticlesComplex 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)

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. Garrido Alzar, Am. J. Phys., 70(1) 2002

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 nanoparticle plasmons given by:• Nanoparticle geometry and size

Interactions between plasmon modes depends on:• Mutual relative positions of individual nanoparticles

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 plasmonic nanolasers)• Metamaterials with high-quality-factor resonances • Highly tunable subradiant ring/disk plasmon cavities• Importance in biosensing and plasmonic nanolasing 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

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 calculationsRed shift of DBR with increasing D

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) • Assymetric Fano resonance in the broad DAR

(interaction of the bright antibonding dipolar disk mode with the dark quadrupole ring mode)

FDTD calculations

Plasmon Hybridization for the NCRDC

Note: The quadrupole resonances of individual thin disks and resonances cannot be excited for perpendicular incidence!

Multipolar resonances induced by parallel light incidence

Higher angles - phase retardation higher order multipolar hybridized modes

Plasmon Hybridization for the NCRDC

Very high LSPR sensitivities of the subradiant (DBR) and Fano resonances to the surroundings sensing

Large Red Shifts

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 multipolar plasmon modes• Symmetry braking coupling between plasmon modes of different multipolar

order tunable Fano resonances• NCRDC may serve as a highly efficient LSPR sensors

Experimental and simulated EEL Spectra

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

3. Far-Field Illumination and Near-field DetectionCollection mode near-field optical microscopy

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)

L. Novotny and B. Hecht: Principles of Nano-optics,Cambridge University Press, 2006

3. Far-Field Illumination and Near-field DetectionCollection mode near-field optical microscopy

‘Double-slit experiment’

R. Zia and M. Brongersma

Application of SPP – PLASMONICS (Going beyond diffraction limit)

Optical integrated circuits of subwavelength dimensions

Waveguide based on surfcae plasmon polaritons.

(a) Gold stripe on a glass substrate - 40 nm thick, 2.5m wide (SEM).

(b) Surface plasmon polaritons propagating on the gold stripe surface (PSTM)

Barnes et al., Nature (2004)

a b

Two-Photon Induced Photoluminiscence (TPA) through interband transitions in Au:

Nonlinear spectroscopy E4 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)

1. Far-field Illumination and Detection

Spot size:

Numerical aperture

= 500 nm. NA = 1.4 x = 220 nm

Spatially filtered light

Single-photon counting avalanche diode

L. Novotny and B. Hecht: Principles of Nano-optics,Cambridge University Press, 2006

1. Far-field Illumination and Detection

The Confocal Principle

L. Novotny and B. Hecht: Principles of Nano-optics,Cambridge University Press, 2006

1. Far-field Illumination and Detection

The Nonlinear Excitation and Saturation

L. Novotny and B. Hecht: Principles of Nano-optics,Cambridge University Press, 2006

Two-Photon Induced Photoluminiscence

Weaker field modulation: Multipolar resonance involved

Two-Photon Induced Photoluminiscence

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

Both thermal (T and HSD) and optical measurements (two-photon luminiscence of Au):

Excitation of fluorescence molecules

Ti:Sapphire (IR) laser: cw mode - heating plasmonic striutures , pulse mode - two-photon lumniscence of Au (TPL)

T (r) map: unfocused IR laser, blue beam scanned, HSD - h (r) map: blue and IR beam scanned and overlapped, stage scanned

Mapping Heat Origin in Plasmonic Structures

Poisson Equation:

Thermal Conductivity

Temperature

‘Heat source’ density

Simplification:

G (r; r’ ) is the scalar thermal Green function associated to PE, generalized Green dyadic tensor

Mapping Heat Origin in Plasmonic Structures

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

Mapping Heat Origin in Plasmonic Structures