Size Dependence of the Optical Response

The peak positions of the hard-wall jellium model are slightly blue-shifted compared to the experimental data [8, 27, 36-39]. Agreement can be obtained by using a soft-wall jellium model [16, 36], or, more correctly, by pseudopotential perturbation theory [38, 39]. 

For the small cluster sizes (n = 3-9), single, well-separated resonances are observed, which could be well fitted by Gaussians. As discussed above (see Section 5.3.1), the peaks are interpreted as vibrationally broadened electronic transitions of an Na molecule [17, 30, 40]. 

The number of electronic lines increases with cluster size and in the size range n = 10 to 15 the lines begin to overlap. For even bigger clusters, single electronic resonances can no longer be resolved. Instead broad peaks are seen which can be characterized by one, two or three Lorentzian peaks, which were accordingly fitted by 

The larger the cluster size, the stronger is an additional broad absorption on the high-energy side of the optical spectrum. This can have one of two origins (1) it could 

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Ballesteros, J.M., Solis, J., Serna, R., Afonso, C.N. Nanocrystal size dependence of the third-order nonlinear optical response of Cu Al2O3 thin films. Appl. Phys. Lett. 74, 2791-2793 (1999)... 

Ma, G., Sun, W., Tang, S.-H., Zhang, H., Shen, Z., Qian, S. Size and dielectric dependence of the third-order nonlinear optical response of Au nanocrystals embedded in matrices. Opt. Lett. 27, 1043-1045 (2002)... 

Of particular interest are the size resolution of the counter, or its ability to distinguish between neighboring particle sizes, and the limit of detection, or smallest size to which the counter responds. The size resolution depends on the relationship between pulse height and particle size, the response cioTe, For piuticles of given optical properties, this relationship is detennined by the geometry of the illumination and light collection systems. Particle shape and refractive index also influence the relationship. 

In the second part of this work we review our theoretical and experimental works to obtain enhanced two-photon cross-sections by using the super-linear response of centrosymmetric monomers that are coherently coupled. In this alternative approach, the nonlinear material consists of an assembly of nonsubstituted /r-electron systems that are coupled by dipole-dipole interactions. The monomer two-photon term is a pure transition dipole term ( UQ,jU,2). Typical materials can be molecular aggregates, nanocrystals, oligomers, and dendrimers. The dipole-dipole interactions determine the size dependency of optical properties, and in particular of two-photon cross-sections. 

It should be noted that optical humidity sensors as a rule use similar effects, which were discussed above (Russell and Flecher 1985 Ballantine and Wohltjen 1986 Boltinghouse and Abel 1989 Wang et al. 1991 Kharaz and Jones 1995 Ando et al. 1996 Zhou et al. 1998 Skrdla et al. 1999 Alvarez-Herrero et al. 2004). The water adsorption in a porous matrix produces a variation in the optical response of the device, because the refractive index of the layer changes when the hydration of sensing material takes place and the pores are filled or emptied. The water adsorption isotherms and, therefore, the sensor response depend on the size and shape of the pores. One can find in Posch and Wolfbeis (1988), Otsuki and Adachi (1993), Papkovsky et al. (1994), Costa-Femandez et al. (1997), Costa-Femandez and Sanz-Medel (2000), Choi and Tse (1999), Choi and Shuang (2000), and Bedoya et al. (2001, 2006) a description of optical humidity sensors used and other principles. 

Size and shape dependency is very important property in SPR [33, 34] of metal NPs observed in the range between 10 and 100 nm. The optical response of the SP absorption in these metal NPs can be demonstrated by the electron dynamics (electron-electron and electron-phonon scattering). It is found that the electron-phonon relaxation processes in NPs, which are smaller than the electron mean free path (MFP), are independent of their size or shape (Fig. 13.8). 

Detection has been one of the main challenges for analytical microsystems, as very sensitive techniques are needed as a consequence of the ultrasmall sample volumes used in micron-sized environments. Electrochemical detection (ED) is a very suitable detection principle to be coupled in microchips because it presents the inherent ability for miniaturization without loss of performance and its high compatibility with microfabrication techniques. Similarly, it possesses high sensitivity, its responses are not dependent on the optical path length or sample turbidity, and it has low power supply requirements which are its additional advantages [5-9]. 

Moreover, in considering the effects of the size in the optical response of a metallic nanoparticle, we must put in evidence that in the case of particles with dimensions comparable or smaller than the mean free path of its oscillating electrons (i.e. for gold and silver particles of radius o < 10 nm) the dielectric function of the particles becomes strongly size-dependent and the additional surface damping must be considered for a correct treatment of the resonances intensity. 

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