Even more pronounced effects can be expected for bilayers. Calculated mode profiles for the dynamic magnetization and the total field are shown in Fig. 9 for the 10 nm Co bilayer. The left panels of this figure are for the Si/Py/Co structures with the Co layer facing the transducer. The right panels are for Si/Co/Py with the Py layer facing the transducer. The fundamental mode displays a highly inhomogeneous dynamic magnetization across the Py, and has a minimum at the interface (see Fig. 9a and c). This minimum is due to partial dynamic pinning of magnetization at the Py/Co interface. The first high order SSWM is also strongly affected by pinning, and can be decomposed into a combination of the Co fundamental mode and the 1st Py SSWM. The broadband FMR response of a resonant mode can be approximated by an overlap integral composed of the SSWM amplitude and h$_{tx}$ ( y ). The total microwave magnetic field in a bilayer is also described by a linear function with a discontinuity at the magnetic interface where the slope scales with layer conductivity. The effect is seen in the profiles shown in the panels b and c of Fig. 9. Comparing the left and the right panels, one sees that the overlap integral of the fundamental mode profile with the total field is clearly dependent on the layer ordering. Note however that the overlap integral for the first SSWM is only weakly dependent on the layer ordering. We conclude from this that the coupling of the fundamental mode to the total field is efficient for Si/Co/Py structures, and it should be the dominant feature in an absorption spectrum. The response of the fundamental mode in the Si/Py/Co bilayers is weakened and becomes comparable with the response of the 1st exchange mode (whose response is much less dependent on the layer ordering). It is also worth noticing that in Figs. 3 and 5 we do not convert the values of the measured sample response S 21( H ) /S 21$_{0}$( H ) into the scalar magnetic permeability as is often done [4]. The reason for this is as follows. First, the permeability one obtains in this way is an effective scalar permeability but not the tensor of the microwave magnetic permeability [26]. Secondly, the effective permeability value which is extracted from the experimental data is found to a constant [3, 27]. This constant depends on the geometry of the stripline waveguide and should be obtained from theory which should be constructed separtely for each type of transducer. On the contrary, the values of the measured S 21( H ) /S 21$_{0}$( H ) allow extraction of a physically meaningful parameter of the transducer complex radiation resistance Z$_{r}$ = 2 z$_{0}$l ln(( S 21 /S 21$_{0}$)), where z$_{0}$ is the characteristic impedance of the transducer and l is the 15