Despite numerous advances in the field, the exact mechanism behind neural communication remains elusive. This work is an attempt to answer the question of whether the propagation of an action potential along a neuron axon involves a localised phase transition of the neuron membrane. The work consists of the development of optical techniques for the study of supported lipid bilayers as models for the cell membrane. The final aim of the work was to perform simultaneous optical and electrophysiological measurements on the membranes of living neurons in order to answer the aforementioned question. We first present the scientific theory required to understand this work, as well as a brief summary of cell membrane biology. We then describe in detail the Hodgkin-Huxley and Heimburg-Jackson models of action potential propagation and examine how well each model is able to explain the vast body of experimental findings of mechanical, optical, thermodynamic and chemical phenomena concomitant with the action potential. From this examination we determine the properties required of a technique capable of observing action potentials in a way which can determine whether or not they involve a phase transition of the cell membrane. Two such techniques are inferferometric reflectometry and stimulated Raman scattering. We then describe the procedures which were used to prepare the samples we performed experiments on, as well as the optical and electrophysiological experimental setups and methodology we used in our experiments. Afterwards, we explain the theoretical work we have done for interferometric reflectometry, followed by our attempts at reducing experimental noise and a discussion of our experimental results with this technique and of electrophysiology experiments. We finally describe our data analysis procedure for stimulated Raman scattering microscopy and discuss our results with this technique.