Mode localization in self-affine fractal interfaces observed by near-field microscopy

Abstract

Near-field optical microscopy with simultaneous topographic imaging shows that for a given excitation wavelength the electromagnetic optical fields excited in a self-affine film are highly localized at ''hot spots'' whose dimensions are often smaller than the wavelength. The pattern of hot spots varies greatly with excitation wavelength and does not correlate simply with the film topography. This observation is consistent with a recent theory of the optical response of self-affine fractal objects and also indicates that the locus of optical effects such as surface-enhanced Raman does not reside in special surface sites such as interstices. Additionally, we show that the conclusions of the theory, which was based on a quasilocal approximation, are qualitatively valid for self-affine films considerably larger than the exciting optical wavelength. ͓S0163-1829͑98͒01223-5͔ INTRODUCTIONSurface-enhanced Raman spectroscopy ͑SERS͒ and other surface-enhanced optical effects have been known for some 20 years. 1 It is recognized that the sometimes enormous increase in signal intensity comes about to a large extent from the increase in the magnitude of both the incident and the scattered electromagnetic fields resulting from the excitation of surface plasmon polaritons in the active system. These resonances lead to particularly large effects when one deals with small metal particles of an appropriate metal whose geometry is auspicious for field enhancement, i.e., particles with high local curvatures, or with assemblies of small metal particles where the interaction between the individual dipolar surface plasmons of the particles couple to produce normal modes. Recently a great deal of attention has been given theoretically to such assemblies, especially to assemblies with fractal character. 2 This is because many of the most efficient SERS-active systems are found to be fractal clusters of adsorbate-covered colloidal particles, and because the optical response of fractal aggregates have been shown to manifest a number of surprising physical attributes. In brief, for a periodic or compact assembly of identical coupled dipolar oscillators the spatial extent of the normal modes will span the entire assembly. That is, in general, in any normal mode, every oscillator is significantly excited. This will be true of both two-dimensional and three-dimensional clusters of oscillators. In contrast, it has been suggested that fractal clusters of oscillators will possess many normal modes that are significantly localized with respect to the dimension of the entire cluster 2 and that of the exciting wavelength. Moreover, it has been suggested that the pattern of localized excitation will vary substantially with the exciting wavelength and the polarization of the exciting fields. In a fractal cluster the individual oscillating elements are arranged in such a manner that they possess dilation symmetry so that magnification of portions of the cluster on a sufficiently broad range of length scales is self-similar. The localization results from...

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