Self-mixing in VCSELs for multi-parametric sensing applications: Theory and experiment

We consider a multi-transverse mode Vertical Cavity Surface Emitting Laser (VCSEL) subject to optical feedback. When the field profile can be described in terms of few Gauss-Laguerre modes we show that the self-mixing interferometric signal exhibits features peculiar of the spatial distribution and/or polarization state of the re-injected field. Based on these results we provide both theoretically and experimentally the proof-of-principle of an operational scheme for a sensor that can be used to simultaneously measure target translations along the optical axis and target rotations in the orthogonal plane.