  We report on the use of Z-scan technique with a beam composed with two modes,
to probe the nonlinear optical properties of phosphate glasses doped with
Er$^{3+}$-Yr$^{3+}$ and silver nanoparticles. Understanding the linear and
nonlinear properties of these materials is crucial to evaluate if they are
candidates to be used as gain media in lasers or optical amplifiers.
Experiments are carried out by implementing the open-aperture Z-scan technique
with bimodal laser pumping ($LG_{00}$ and $LG_{20}$) at 908.6 nm. The analysis
is performed using a simplifiedmodel that incorporates nonlinear absorption and
saturation intensity of the samples. The advantage of using a beam with a
bimodal structure is that it allows us to evaluate the energy transfer between
the modes, which is relevant since the optical active media act as an
intermediary. This process is incorporated through an effective
phenomenological parameter in the model that we use in our analysis.
