ELSEVIER Physica A 241 (1997) 249-258 Nonlinear optics of fractal nanomaterials: Small-particle composites and self-affine thin films Vladimir M. Shalaev a,*, E.Y. Poliakov a, V.A. Markel a, R. Botet b a Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA b Laboratoire de Physique des Solides, Centre d'Orsay, 91405 Orsay, France Abstract Fractal nanostructured materials, such as nanocomposites and self-affine thin films, are shown to possess giant optical nonlinearities. The enhancement results from the sub-wavelength local- ization of dipolar modes and strong local field fluctuations. PACS: 78.90.+t; 42.65.An; 61.43.Hv; 42.70.Nq; 42.65.Hw Keywords: Optics; Fractals; Composites; Films Optical phenomena experience giant enhancements in metal nanocomposites and rough thin films consisting of small nm-sized particles and roughness features, re- spectively. The enhancement is associated with excitation of surface plasmons which are collective modes and depend strongly on the morphology (geometrical structure) of the material. Fractal structures are prevalent in composites and cold-deposited thin films. The emergence of fractal geometry was a significant breakthrough in the de- scription of irregularity. Fractal objects do not possess translational invariance and, therefore, cannot transmit running waves. Accordingly, collective excitations, such as surface plasmons, tend to be localized in fractals [1]. Formally, this is a consequence of the fact that plane running waves are not eigenfunctions of the operator of dilation symmetry characterizing fractals. Fractal aggregates of small particles embedded in a three-dimensional host are self- similar (scale-invariant), within a certain interval of sizes. Unlike fractal assembles of particles, a self-affine surface reveals a scale-invariance if different scaling factors are applied in the (x, y )-plane of the surface and in the normal, z-direction. We studied * Corresponding author. Tel: (505) 646-1932; fax: (505) 646-1934; e-mail: vshalaev@nmsu.edu. 0378-4371/97/$17.00 Copyright @ 1997 Elsevier Science B.V. All rights reserved PII S0378-4371 (97)00092-7