Understanding Nanoplasmonics Greg Sun University of Massachusetts Boston
Nanoplasmonics Space 100pm 1nm 10nm 100nm 1μm 10μm 100μm 1ns 100ps 10ps Photonics 1ps 100fs 10fs 1fs Time
Surface Plasmons Surface plasmon polaritons (SPPs): W.Barnes, et.al., Nature 424. 824 (2003) Localized surface plasmons(lsps): E 3
Applications: Light Manipulation Beyond the diffraction limit Manipulate optics at the Nanoscale << Planar waveguide Nanoantennas Plasmonic imaging 2n Slot waveguide Faster chips A cloaking device H.A. Atwater, Scientific American 15. 562(2007) 4
Application: Field Enhancement H.A. Atwater et.al., Nature Materials 9, 205 (2010) J.A. Schuller et.al., Nature Materials 9, 103 (2010) R.F.Oulton et.al., Nature 461, 629 (2009) 5
Optical Enhancement and Field Concentration Optical absorption (Detectors and solar cells) Optical emission (Electroluminescence from LEDs) Photoluminescence (Fluorescence in sensing) Luminescence quenching Raman scattering (Molecular sensing) Nanofocusing (Nanolens) Hotspots in complex metal nanostructrues 6
Objectives Analytical approach based on clear underlining physics Understanding of the enhancement mechanisms Why sizes of the nanoparticles matter How to optimize nanostructures Limitations on attainable enhancement Why some processes get enhanced more than others 7
Terrylene molecule Au
Laser scattering from Ag colloid sample Laser scattering filtered Filtered photos taken from a Ag colloid sample incubated with 2X10-11 M R6G Enhancement factor of 10 14-10 15 yields Raman vibrational signals that are more intense and more stable, and leads to single molecule detection.
The Drude Model (free electrons) Optical field Electron displacement Polarization nee P nex 0 1 E 2 m j 0 Dielectric function Plasma frequency p : 2 2 p j
Metal Properties Re(ε): polarization Im(ε): absorption 2 2 p p ' 1 1 2 2 2 '' 2 2 p p 2 2 3 UV transparency of metals: Gold: ω p =1.37 10 16 Hz ( =137.60nm) = 6.46*10 12 s -1 Silver: ω p =1.40 10 16 Hz ( =134.64nm) = 4.35*10 12 s -1 if Q ' '' 11
The Electro-Static Approximation Infinitesimal (Hertzian) dipole antenna: H E 1 j 0r j 0 1 ˆ ILe 4 j 4 0 j r 0 0 ILe sin 0 j 1 cos r 2 ˆ r r 2 0 j 0 1 2sin ˆ 2 3 r r r r r 2 Far field Near field Very near field Deep subwavelength scale: H 0
Surface Plasmon Modes Electro-Static model z r Electric potential y l - Legendre polynomials - mode index Dipole polarization Molecule d a Metal sphere x
SP Field and Resonance Continuity of the normal electric displacement: a Mode frequency: r SPP Au sphere in GaN Small B-field for Subwavelength scale H = 1 Z 2πa λ D E, U H = 2πa λ D 2 U E
Mode Volume Definition: Effective mode volume U l = 1 2 Φ l σ l d 2 r = 1 2 ε 2 0ε D E max,l V eff,l V eff,l = 4πa3 (l + 1) 2 ε D Mode volume decreases with the mode order excellent energy confinement for enhancement, but Smaller particles better energy confinement
SP Charges and Dipoles + + + + + + - - + + - - - - - - - - + - - + + l = 1 l = 2 l = 3 All l 2 modes have zero dipole - Uncoupled to radiation mode
SP Mode Decays Radiative decay rate for dipole mode γ rad = 1 U 1 du 1 dt rad = 2ω 1 3ε D 2πa λ 1 Nonradiative rate for all modes 3 Larger nanoparticles - better antennae Metal loss Total decay rate Only dipole mode decays radiatively
Absorption Enhancement Optical excitation in Radiative decay rad ex 1st step nrad d 2nd step
Absorption Enhancement Far field Without the metal sphere, the incident power φ θ a is focused onto a spot With metal, the incident light couples into dipole mode U 1 = 1 2 ε 2 0ε D E max,1 V eff,1 Near field a E foc confined in the effective mode volume V eff,1 = πa3 ε D E max,1 w 0 Absorption enhancement factor F a = E 2 max,1 2 E foc a a + d 6
Optical Excitation-SP Coupling Far field φ θ a Optical excitation into SP mode can be determined as reciprocal process of the radiation into a solid cone Ω. SP amplitude excitation rate da 1 dt ex = κ in s + with in-coupling coefficient κ in = Ω γ rad θ a 2 3γ rad 2 a 3/2
Absorption Enhancement Factor Rate equation for the mode amplitude A 1 = U 1 = 1 2 ε 0ε D V eff,1 E max,1 da 1 dt = j ω ex ω 1 A 1 γ rad + γ nrad + γ abs 2 A 1 + κ in s + Excitation detuning Steady state solution at resonance SP decay In-coupling F A = E max,1 E foc 2 a a + d 6 = 2 Q 1 + Q 1 abs 1 + Q rad 2 a + d a 6 Q = ω γ Q abs = ω γ abs Q rad = ω γ rad
Absorption Enhancement Result Ag sphere embedded in GaN Q 40 Absorption enhancement favors closely spaced weak absorbers Appl. Phys. Lett. 94, 071103 (2009)
Emission Enhancement Phonons or other non-radiative states Radiation EL 2nd step Metal loss d 1st step Electrically excited molecule
Purcell Factor Radiative decay rate 3D photon states 1 τ rad = 2π ħ r E 2 ρ f ħω Density of final states Dipole emission matrix element Nonradiative states High density SP states Purcell factor: F p,l = τ SP 1 1 τ rad = ρ SP ρ rad λ 3 d V eff,l a a + d 2l 2 l + 1 2 λ d 3 a 3 a a + d 2l 2
Bottlenecking Density of states Nonradiative processes Radiation
Was the bottleneck removed? Purcell factor Dense Surface Plasmon Radiation Nonradiative processes Nonradiative decay
Emission Enhancement Factor Original radiative efficiency Efficiency with SP Coupling into SP mode a Purcell factor enhanced by SP out-coupling efficiency η dp = γ rad γ rad + γ nrad Emission enhancement factor F e = 1 + η dp F p,1 1 + η η rad l=1 F dp > η rad p,l
Emission Enhancement Result Size dependence Optimal enhancement vs. efficiency Ag/GaN Q 40 Emission enhancement is significant for closely placed molecules with low efficiency Appl. Phys. Lett. Vol.93, 021120 (2008)
Fluorescence (PL) Enhancement Absorption Decay Emission Two sequential enhancement: absorption and emission Appl. Phys. Lett. 94, 101103 (2009)
Fluorescence (PL) Result Ag/GaN Both absorption and emission contribute to PL enhancement Both excitation and emission frequencies need to be close to SP resonance
Efficiency Dependence Enhancement is strong for molecules that are weak absorbers and inefficient emitters placed near metal nanoparticles the reason for the observation of SERS
a NP d Quenching for small d
Properties of Higher Order Modes Au NP In GaN Effective mode volume V eff,l = 4πa3 (l + 1) 2 ε D Total decay rate
Purcell Effect of SP Modes a Au d Purcell factor F p,l l + 1 2 λ d 3 a 3 a a + d 2l 2
Au sphere in GaN Quenching Ratio f q = l=2 F p,l F p,1
Enhancement Optimization a Au d Efficiency η SP = 1 τ nrad τ 1 rad + F p,1 τ 1 rad η dp + 1 + l=1 1 F p,l τ rad G. Sun, J. B. Khurgin, and C. C. Yang Appl. Phys. Lett. 95, 171103 (2009) Quenching ratio due to nonradiative higher order modes Closer not necessarily better!
Emission Optimization
Single Particle Dilemmas Dipole mode Particle size Effective mode volume V eff,l = 4πa3 (l + 1) 2 ε D Good antenna Good cavity SP modes Higher order modes Dipole mode Smaller mode volumes, but uncoupled to external fields Couples to external fields, but with large mode volume
Coupled Metal Nanoparticles Higher order modes coupling Optical exciation Dipole mode
Excitation of Higher Order Modes High order modes Coupling between dipole and higher order modes
Optical Excitation Far field θ a φ Near field E foc w 0 Energy couples into the dipole mode of each sphere according to its radius
Mid Gap Enhancement Narrow gaps favor two uneven spheres larger one acts as antenna while smaller one as resonator. Wide gaps favor even spheres of optimal size spheres are only weakly coupled.
Nano Dimer Au/GaN Mid gap Resonance splitting Peak is shifted toward lower frequency because of coupling. Splitting
Dimer vs. Single Sphere Single sphere Improvement over single sphere is about a factor of 2~3. For absorption and emission ( E 2 ), additional factor of ~10. For SERS ( E 4 ), an additional factor of ~100. Appl. Phys. Lett. 97, 263110 (2010)
Nano Lens a 1 a 2 Energy gets coupled in through the large sphere and subsequently being focused by the small sphere.
Nano Lens Optimization a 1 a 2 Appl. Phys. Lett. 98, 153115 (2011) Energy gets coupled in through the large sphere and subsequently being focused by the small sphere.
Best of Both Worlds The effective mode volume of the nanolens is only slightly greater than that of the small sphere. The radiative decay rate of the nanolens is slightly smaller than that of the large sphere.
Hot Spots in Complex Structures Following the energy flow can lead to quick estimate of field enhancement. J.A. Schuller et.al., Nature Materials 9, 103 (2010)
Raman Scattering Phonon Incident photon Scattered photon 1923 Theoretical prediction by the Austrian physicist A.Smekal 1928 Experimental discovery - by the Indians C.V. Raman and K.S. Krishnan in Kalkutta - by the Russians G. Landsberg et L. Mandelstam à Moscou 1930 Nobel price: Sir C.V. Raman
Raman vs. PL Incident photon PL enhancement up to 10 3 with quenching observed Raman enhancement up to 10 14 without quenching whatsoever
The PL Picture Optical excitation SP Mode at excitation frequency Radiation 3 2 ω ex ω s SP Mode at Stokes frequency l = 3 l = 2 Metal loss Metal loss Metal loss 1 Nonradiative decay l = 1 Metal loss PL Emission
The Raman Picture Optical excitation SP Mode at excitation frequency Metal loss Radiation 2 1 ω ex Molecular vibration ω s Stokes processes SP Modes at Stokes frequency l = 3 l = 2 l = 1 Raman Emission Metal loss Metal loss Metal loss
Spontaneous Raman Scattering Rate Excitation detuned from molecular absorption γ RM = 2π ħ d m E ex 2 ħ 2 ω ex ω m 2 H ev 2 ħ 2 ω S ω m 2 d m 2 ω S ε 0 ρ ω S Electron-vibrational coupling detuned from molecular resonance Density of states at Stokes emission
Raman vs. PL F RM ω ex, ω S = E max,1 E foc 4 E SP E foc 2 a a + d 6 1 + η dp F P,1 ω S E SP E foc 2 F PL = F a F e Absorption enhancement F A = E max,1 E foc 2 a a + d 6 1 1 + γ abs / γ abs + γ 2 Emission enhancement The Raman enhancement is PL in the limit of Zero absorption cross section σ abs 0 Zero radiative emission efficiency η rad 0
Raman vs. PL
Resonance Raman
Resonance Raman Spontaneous scattering rate γ RM = 2π 2 2 d m E ex H ev ħ ħ 2 2 γ m ħ 2 ω S ω 2 m d m 2 ω S ε 0 ρ ω S SP enhanced De-coherence γ m,sp = 1 T 2 + 1 2τ rad l=1 F P,l ω ex Enhancement F RR ω ex, ω S = 1 + 1 + η out F P,1 ω S T 2 2τ rad l=1 F P,l ω ex 2 E max,1 ω ex E foc 2 a a + d 6 Resonance Raman gets quenched too!
Resonance vs. NR. Raman
Conclusions Strong improvement for weak absorbers and inefficient emitters (Best enhancement for Raman) Luminescence and resonance Raman quenching effects due to dark (higher order) SP modes. Optimization of nanoparticle size compromise between a good antenna and cavity. Additional enhancement achievable in complex metal nano clusters. Analytical model developed with clear physics allowing for fast result and optimization.