Numerical Rate Equation Modeling of a ${\sim {\hbox {2.1}}-}\mu{\hbox {m}}-{\rm Tm}^{3+}/{\rm Ho}^{3+}$ Co-Doped Tellurite Fiber Laser

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Judd–Ofelt analysis is performed on measurements of bulk samples of <formula formulatype="inline"><tex Notation="TeX">${\rm Tm}^{3+}$</tex> </formula>- and <formula formulatype="inline"><tex Notation="TeX">${\rm Ho}^{3+}$</tex> </formula>-doped tellurite glass from which the host-dependent Judd–Ofelt intensity parameters are extracted. These have then been used to calculate the radiative rates and branching ratios in this particular material system. A rate-equation approach is then used to model an experimentally realized <formula formulatype="inline"><tex Notation="TeX">${\sim {\hbox {2.1}}}\,\mu{\hbox {m}}\,{\rm Tm}^{3+}/{\rm Ho}^{3+}$</tex></formula> codoped tellurite fiber laser and extract values of the energy transfer and upconversion rate parameters in <formula formulatype="inline"><tex Notation="TeX">${\rm TeO}_{2}-{\rm ZnO}-{\rm Na}_{2}{\rm O}$</tex></formula> (TZN) glass. Excellent agreement is found between simulated and experimental data, which indicates the validity of the approach. </para>