Nonlinear properties of upconversion YVO₄:Yb³⁺, Er³⁺ nanoparticles

Nonlinear character of upconversion processes can be revealed via a measurement of power dependent steady-state emission intensity depicted in the ln-ln plot, where a slope indicates the degree of nonlinearity. As a rule observed values of the slope for YVO₄ : Yb, Er nanoparticles are less than 2 that interprets as a saturation effect due to high pump laser intensity. Here we based on a numerical analysis show that a life time of the Er³+ ion metastable state ⁴I_11/2 is also responsible for deviation of the slope from 2 even in the case when Yb³⁺-Er³⁺ upconversion system is far away from saturation mode.