Separation of kinetic rate orders in extreme ultraviolet transient grating spectroscopy

We present an Extreme Ultraviolet (EUV) transient grating (TG) experiment of the spinel Co3O4 compound using tuneable incident energies across the Co M2,3-edge and a 395 nm probe pulse, detecting both the first and the second diffraction orders. While the first diffraction order shows a monotonous behaviour as a function of time, with a sharp response at t=0, followed by a weak sub-picosecond component and a nearly constant signal thereafter, the time dependence of second diffraction order varies dramatically with the incident energy as it is tuned across the Co M-edge, with the appearance of a component at t>1 ps that grows with increasing energy. The results are rationalised in terms of the deviations of the initial grating from sinusoidal to non-sinusoidal, namely a flattening of the grating pattern, that introduces new Fourier components. These deviations are due to higher order, three-body terms in the population relaxation kinetics. These results highlight the use of the response of the second diffraction order in EUV TG as a tool to identify higher order terms in the population kinetics.