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.