Carving Plasmon Modes in Silver Sierpiński Fractals

The surface plasmon resonance (SPR) modes of the first three generations of a Sierpiński fractal triangle are investigated using electron energy loss spectroscopy (EELS) complemented with finite difference time domain simulations. The Sierpiński fractal geometry is created in a subtractive manner, by carving triangular apertures into the triangular prism of the previous fractal generation. The ability of the fractal antenna to efficiently utilize space in coupling to long wavelength excitations is confirmed on the single nanostructure level via redshifting of the primary dipole mode as the fractal generation is increased. Through application of the Babinet principle, it is demonstrated that this spectral shift is caused by coupling of two degenerate orthogonal dipolar modes of a single triangle with two degenerate orthogonal dipole modes of the triangular aperture occupying the center of the first generation fractal. It is also shown that the spectral position and strength of the dipole mode can be tuned by altering the size of the central aperture, and thus the capacitance of the equivalent circuit, and the width of the conductive channels joining different fractal building blocks, thereby altering the circuit inductance. Importantly, placing the aperture on a node of the SPR mode causes a shift in energy of this mode without changing the charge configuration; placing the aperture on an antinode of the SPR mode causes no shift in energy, but changes the field configuration, as revealed through EELS measurements. These fractal-specific properties provide new strategies to design, predict, and effectively exploit highly tunable SPR modes using simple building blocks.