Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

agents [34]. The short-wavelength band at around 520 nm corresponds to theoscillation of the electrons perpendicular to the major rod axis. It is referred toas the transverse plasmon absorption [36]. This feature is relatively insensitiveto the nanorod aspect ratio and coincides spectrally with the surface plasmonband in spherical nanoparticles. The other absorption band is shifted to alonger wavelength and is due to oscillations of free electrons along the majorrod axis. This band is referred to as the longitudinal surface plasmonabsorption [36]. Figure 3b shows a plot of the maxima of the transverse(squares) and longitudinal (circles) surface plasmon modes as a function ofthe rod aspect ratio. These data nicely illustrate the strong dependence of thelongitudinal plasmon maximum on the aspect ratio, which provides a meansto spectrally tune the optical absorption of metal nanoparticles.As an extension to Mie’s theory, Gans [37] applied the theoreticaltreatment developed for spherical particles to cylinders (rods). Within thedipole approximation, the optical absorption spectrum of a collection ofrandomly orientated gold nanorods with aspect ratio R is given by r ext ¼ x 3c e3=2 m V X j1=P 2 j e 2 2; ð4Þe 1 þ ½ð1 P j Þ=P j Še m þ e22where P j are the depolarization factors for the three axes,P A ¼ 1 e2 1e 2 2e ln 1 þ e 1ð5Þ1 eP B ¼ P C ¼ 1 P A; ð6Þ2A, B, and C are the axes lengths (A > B = C, R = A/B), andsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B 2rffiffiffiffiffiffiffiffiffiffiffiffiffiffi1e ¼ 1 ¼ 1AR 2ð7ÞGans’ theory accurately reproduces the red shift of the longitudinalsurface plasmon absorption with increasing nanorod aspect ratio. The redshift of the surface plasmon absorption in spherical nanoparticles is also welldescribed by Mie’s theory for larger nanoparticles (>20 nm). When the dipoleapproximation is no longer valid, the plasmon resonance depends explicitlyon the particle size, as x is a function of the particle radius r [see Eqs. (1) and(2)]. As the particle size increases, higher-order modes become more important,as the light cannot polarize the nanoparticles homogeneously. Retar-Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.