Measurement of the Complex Dielectric Constant of a Single Gold Nanoparticle Nick Vamivakas Journal Club Patrick Stoller, Volker Jacobsen, Vahid Sandoghdar Optics Letters 31, (2006) Primary Reference:

Problem Optically characterize plasmon resonances in “small” diameter gold nanoparticles (few nm) Why is this hard? strength Rayleigh scattered light ~ diameter 6 Boyer, et al Science > absorption ~ diameter 3 photothermal effect leads to measurable index contrast One approach:

Solution Homodyne the pump laser with the Rayleigh scattered light Measure the intensity of the total field on the detector |E| 2 Interference cross-term scales with D 3 !!! pump, E o scatter, E s dipole diameter D Schematically |E| 2 = |E in e -iπ/2 +E in |α|e -iФ | 2 = |E in | 2 (1+|s| 2 -2|α|sinФ) where α ~D 3 and is particle polarizability

Technique: Differential Interference Contrast λ/4 f λ/4 s λ/4 NW f WsWs NW s WfWf NW W E1E1 E2E2 Polarizing Elements Axes Field Vectors E1E1 E2E2 W s =B Wollaston projects channels 1 and 2 onto A and B axis circular linear elliptical linear W f =A A = E 1 -E 2 B = E 1 +E 2

Differential Interference Contrast with Spectral Information Folded version of the previous DIC E 1 =E o α(λ)=E o |α(λ)|exp(iarg[α(λ)]) where polarizability is E 2 =E o r exp(-iπ/2) α(λ) = ε m (πD 3 /2) [ε g (λ)-ε m ] / (πε g (λ)+2ε m )] E1E1 E2E2 Guoy phase 63x, 1.4NA (ε m =2.3) w/ oil immersion |E 1 -E 2 (λ)| 2 |E 1 +E 2 (λ)| 2 spectral detector

Differential Interference Contrast with Spectral Information Folded version of the previous DIC Show X(λ) = (2/ε m πD 3 )α(λ) E1E1 E2E2 Define diameter independent 63x, 1.4NA w/ oil immersion |E 1 -E 2 (λ)| 2 |E 1 +E 2 (λ)| 2 spectral detector (ε m =2.3) X re (λ) = F(A-B) and X im (λ) = G(A-B,A+B) Which can further be related to ε re,g and ε im,g

The Dielectric Function D=15nm (a) and (b) show X re (λ) and X im (λ), solid is fit using quasi- static approx and bulk gold dielectric from literature (c) and (d) calculate ε re,g and ε im,g from X re (λ) and X im (λ) ; solid is measured bulk gold dielectric TEM to rule out particle ellipticity induced deviation

The Average Dielectric Function 13 10nm particles and 15 15nm particles dashed lines incorporate surface damping into ε im,g good agreement in region of plasmon resonance ( nm) but disagreement below 510nm between bulk and sphere in ε im,g (speculate on broadening)

Conclusion Measured dielectric function of 10 and 15nm gold nanoparticles interferometrically in DIC microscope Quasi-white light source and spectral detection accessed all wavelength channels simultaneously Observed plasmon resonance in these diameter nanoparticles spectrally similar to that of bulk gold

Wollaston and Nomarski Wedges