When photons impinge on a metal nanoparticle surface the conduction band electrons are excited and oscillate coherently, generating what is known as surface plasmons. The optical properties of plasmonic nanostructures can be engineered to their specific applications by tuning their size, shape, and material. This thesis presents two advancements in the field of plasmonics, the first is a fundamental advancement in the design of multiply resonant plasmonic nanoparticles through simple design principles, and the second is a demonstration of the analytical power that rotational spectroscopy can bring to the study of gas phase plasmonic photocatalysis. Initially this thesis will focus on the role of self-similarity for the design of plasmon resonance lineshapes. Fractal-like nanoparticles and films have long been known to possess a remarkably broadband optical response and are potential nanoscale components for realizing spectrum-spanning optical effects. By computing and fabricating simple Cayley tree nanostructures of increasing fractal order N, we are able to identify the principle behind how the multi-modal 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, multi-peaked 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 lineshapes. In the latter half of this thesis, frequency modulated rotational spectroscopy is presented as an alternative methodology to study plasmonic photocatalysis. This technique is compelling for its unambiguous recognition specificity and extremely sensitive (ppm or better) real-time quantitative measurement of molecular species, validated by the accurate measurement of the natural abundance of molecular isotopomers. The decomposition of the toxic industrial compound carbonyl sulfide (OCS) and the production of carbon monoxide (CO) by exciting chemically synthesized aluminum nanocrystals serves as a model experiment to showcase the power of this technique. Two measures of reaction efficiency, collision efficiency and external quantum efficiency, enabled by this technique are quantitatively described.