The reflectance and transmittance spectra of a set of thin gold films on sodium alginate are measured and simulated in the framework of the generalized transfer matrix method. In the simulation, the dielectric function for the nano-particles (NP) was modified from that of gold bulk by using a variable damping energy. A Lorentz oscillator was used to describe the localized surface plasmon resonance. The results elucidate the structural arrangement of the deposited material on the specific substrate. The collision frequency obtained from the simulation indicates that the aggregation of the NPs at the nanoscopic level correlates with the electrical properties. The intense surface plasmon resonance remains visible for film thicknesses up to 10 nm, in spite of the increasing loss of particle separation. In addition to the attained results, the developed methodology can be usefully applied on other case studies for a thorough characterization of the formation of the growing NP films on the specific substrate.