In this work we investigate moderately underexpanded n-hexane jets in a supercritical environment with respect to the injectant. At supercritical chamber pressure and constant nozzle pressure ratio of NPR approximate to 5.6, we systematically increase the reduced injection temperature from (T) over bar (inj) = 1.06-1.18. Our experiments comprise multiphase and single-phase injections. The latter expand close to the Widom line. Using a combined method of shadowgraphy and elastic light scattering (ELS), we study the structural evolution of the jets. Surprisingly, our measurements reveal ELS signals even for the supercritical single-phase jets. The measurements show periodic structures in signal intensity, which can be spatially associated with the train of shock cells in the moderately underexpanded jets that subsequently compress and expand the fluid. With chamber conditions close to the Widom line this implies that the fluid state is alternately brought across the Widom line and hence experiences repetitive changes in fluid properties. In this transition, the fluid exhibits changes in structural and thermophysical properties that can be associated with density fluctuations. The latter lead to an increase in scattering cross-section and, therefore, promote additional Rayleigh scattering contributions. The explanation of the scattering signal for our single-phase injections is therefore ascribed to the interaction of fluid dynamical processes within the jet and thermodynamic peculiarities across the Widom line. In each shock cell the fluid experiences a transition in fluid behavior attributed to density fluctuations. The resulting increase in scattering cross-section allows the detection of Rayleigh scattering, even with nonintensified optical CMOS sensors.