# Continuous-Wave and Mode-Locked Operation of an In-Band Pumped Tm,Ho,LuCaGdAlO4 Laser
## 1 Introduction
Traditionally, Tm\({}^{3+}\),Ho\({}^{3+}\) co-doped materials are pumped around 0.8 \(\upmu\)m (the \({}^{3}\)H\({}_{6}\)\(\rightarrow\)\({}^{3}\)H\({}_{4}\) Tm\({}^{3+}\) transition in absorption); see Figure 1. This wavelength range can be readily addressed by high-brightness tunable Ti:Sapphire lasers and high-power spatially multimode AlGaAs semiconductor laser diodes. After excitation to the \({}^{3}\)H\({}_{4}\) state, Tm\({}^{3+}\) ions can experience two subsequent multiphonon non-radiative (NR) relaxation steps ending in the metastable (long-living) \({}^{3}\)F\({}_{4}\) state. Another route to populate this manifold is the cross-relaxation (CR) process for adjacent Tm\({}^{3+}\) ions, \({}^{3}\)H\({}_{4}\) + \({}^{3}\)H\({}_{6}\)\(\rightarrow\)\({}^{3}\)F\({}_{4}\) and \({}^{3}\)F\({}_{4}\), which enhances the pump quantum efficiency for Tm\({}^{3+}\) ions by up to 2 (two-for-one process). Due to the nearly resonant energetic position of the \({}^{3}\)F\({}_{4}\) Tm\({}^{3+}\) and \({}^{5}\)I\({}_{7}\) Ho\({}^{3+}\) multiplets (the barycenter of the former multiplet exhibits a slightly higher energy), a bidirectional Tm\({}^{3+}\)\(\leftrightarrow\) Ho\({}^{3+}\) energy transfer is observed. The lifetimes of the two involved excited states are represented by a single thermal equilibrium value and their populations are linked. Usually, the Ho:Tm co-doping ratio is selected between 1:10 to 1:5 to ensure efficient population of the upper laser level \({}^{5}\)I\({}_{7}\) Ho\({}^{3+}\) manifold. Compared to single Ho\({}^{3+}\) doping, the Tm\({}^{3+}\),Ho\({}^{3+}\) co-doping brings the advantage of easier pumping (namely, more accessible pump sources and higher pump absorption efficiencies). Its main limitation is the relatively high heat loading causing more severe thermal problems and thermal roll over in the output dependences and leading eventually to thermal fracture/laser ceasing, thus limiting the output power that can be extracted. The main sources of heat generation in Tm,Ho lasers pumped at 0.8 \(\upmu\)m are (i) NR relaxation from the \({}^{3}\)H\({}_{4}\) and \({}^{3}\)H\({}_{5}\) Tm\({}^{3+}\) levels (which is especially significant for oxide crystals with high phonon energies), (ii) energy-transfer upconversion (ETU) from the \({}^{3}\)F\({}_{4}\) Tm\({}^{3+}\) and \({}^{5}\)I\({}_{7}\) Ho\({}^{3+}\) excited states, and (iii) energy losses associated with the bidirectional Tm\({}^{3+}\)\(\leftrightarrow\) Ho\({}^{3+}\) energy-transfer. The two relevant ETU processes are \({}^{3}\)F\({}_{4}\)(Tm) + \({}^{3}\)F\({}_{4}\)(Tm) \(\rightarrow\)\({}^{3}\)H\({}_{4}\)(Tm)\({}^{3}\)H\({}_{6}\) + \({}^{3}\)H\({}_{6}\)(Tm) and \({}^{3}\)F\({}_{4}\)(Tm) + \({}^{5}\)I\({}_{7}\)(Ho) \(\rightarrow\)\({}^{3}\)H\({}_{6}\)(Tm) + \({}^{5}\)I\({}_{5}\)(Ho). Both of these ETU processes are followed by multiple NR relaxation steps contributing to heat generation. Compared to the traditional Tm\({}^{3+}\)-ion pumping near 0.8 \(\upmu\)m, direct excitation of Tm\({}^{3+}\) ions at \(\sim\)1.7 \(\upmu\)m to the \({}^{3}\)F\({}_{4}\) state (\({}^{3}\)H\({}_{6}\)\(\rightarrow\)\({}^{3}\)F\({}_{4}\), in-band or resonant pumping) can partially release the heat load. This mainly happens through suppression of the NR relaxation path from the \({}^{3}\)H\({}_{4}\) and \({}^{3}\)H\({}_{5}\) excited-states of Tm\({}^{3+}\)[24]. The pump sources that address the spectral range of 1.7 \(\upmu\)m are Raman-shifted Erbium fiber lasers and short wavelength Tm fiber lasers. They benefit from good beam quality (nearly diffraction limited pump beams) offering good prospects for reducing the laser threshold, boosting the laser efficiency and eventually power scaling of Tm,Ho lasers (as compared to traditional AlGaAs diode lasers). In the present work, we demonstrate the potential of the Tm in-band pumping scheme for tunable and ML Tm,Ho lasers benefiting from the combined gain bandwidths of the two active ions and the reduced heat load.