Fractal Nanoparticle Plasmonics: The Cayley Tree

There has been strong, ongoing interest over the past decade in developing strategies to design and engineer materials with tailored optical properties. Fractal-like nanoparticles and films have long been known to possess a remarkably broad-band optical response and are potential nanoscale components for realizing spectrum-spanning optical effects. Here we examine the role of self-similarity in a fractal geometry for the design of plasmon line shapes. By computing and fabricating simple Cayley tree nanostructures of increasing fractal order N, we are able to identify the principle behind how the multimodal plasmon spectrum of this system develops as the fractal order is increased. With increasing N, the fractal structure acquires an increasing number of modes with certain degeneracies: these modes correspond to plasmon oscillations on the different length scales inside a fractal. As a result, fractals with large,N exhibit broad, multipeaked spectra from plasmons with large degeneracy numbers. The Cayley tree serves as an example of a more general, fractal-based route for the design of structures and media with highly complex optical line shapes.