Correcting the formalism governing Bloch Surface Waves excited by 3D Gaussian beams

Due to the growing number of publications and applications based on the exploitation of Bloch Surface Waves and the numerous errors and approximations that are used to evaluate their properties, we judge important for the successful interpretation and understanding of experiments to implement an adapted formalism allowing to extract the relevant information. Through comprehensive calculations supported by an analytical development, we establish generalized formula for the propagation length and the Goos-Hanchen shift, which are different from what is usually employed in the literature. The relative errors in the estimation of these two quantities are evaluated to vary between 50% and 200%. The effect due to a slight deviation of the angle of incidence or of the beam-waist position with respect to the structure are studied showing high effects on the Bloch Surface Waves properties. This formalism is adapted to any polarization-dependent Lorentzian-shape resonant structures illuminated by a polarized Gaussian beam. Theoretical models capable of accurately capturing the behaviour of plasmonic, Bloch surfaces waves are vital for the interpretation of experimental results. Here, the authors demonstrate the importance of extrinsic factors in determining the Goos-Hanchen shift in a generalised model of the propagation length.