Theoretical analysis of the photon avalanche dynamics in Ho3+-Yb3+ codoped systems under near-infrared excitation

The photon avalanche upconversion mechanism in a ${\mathrm{Ho}}^{3+}\text{−}{\mathrm{Yb}}^{3+}$ system under near infrared excitation is discussed. Two looping cycles in the excitation process provide the necessary population of the ${}^{5}I_7$ intermediate level of ${\mathrm{Ho}}^{3+}$ ions to achieve the avalanche regime. The first one takes place between ${\mathrm{Ho}}^{3+}$ ions, while the second one occurs between ${\mathrm{Ho}}^{3+}$ and ${\mathrm{Yb}}^{3+}$ ions. We present a simplified model of the process, which only takes into account the ground, intermediate and emitting levels of ${\mathrm{Ho}}^{3+}$ and the ground and excited levels of ${\mathrm{Yb}}^{3+}$ ions. The rate equations of the system have been solved, and the photon avalanche regime has been interpreted in terms of gain and loss of the population of the intermediate level. The model predicts a reduction of the avalanche pump power threshold when the ${\mathrm{Yb}}^{3+}$ concentration increases which is in good agreement with experimental data.