# Continuous-Wave and Mode-Locked Operation of an In-Band Pumped Tm,Ho,LuCaGdAlO4 Laser
## 5 Conclusions  
In-band pumping is a widespread method for pumping Ho lasers nowadays, thanks to the availability of well-developed Tm lasers operating at slightly shorter wavelengths and, in particular, commercial Tm-fiber lasers. While in-band pumping of Tm lasers has been, in general, also well-known, more sophisticated pump sources are needed, which are not readily available. In-band pumping has been employed also for Tm,Ho co-doped materials in the past; however, the main purpose was to increase the efficiency and the output power [24; 27; 28]. The main interest in the present study was to combine its potential with the utilization of the combined gain profile of the two ions, both for extended tunable operation and spectral support of shorter pulse durations in ML lasers. Using a home-made Raman shifted Er-fiber laser, we achieved a CW tuning range of 160 nm and a ML laser pulse duration of 218 fs. The latter is the first demonstration of a ML in-band pumped Tm,Ho laser, and thus represents an initial result. Based on our previous experience with utilization of the Kerr effect in the laser crystal for Kerr-lens mode locking assisted by a SESAM, we expect substantially shorter pulses in the range of 50 fs after optimization of the present set up. Concerning the material point of view, we also plan to study samples with increased Lu content as already demonstrated in the CW regime [22]. It should be outlined that the flipping of the polarization in such materials observed in CW operation and related to the close gain cross sections for the two principal polarizations offers another possibility for engineering of the actual gain profile in terms of full range, flatness, and smoothness by combining the two polarizations using a special crystal cut. We also plan to fully exploit the power scaling potential of the in-band pumping scheme by implementing more powerful pump sources in the future. Conceptualization, W.C. and R.T.M. ; methodology, W.C., R.T.M., U.G. and L.W. ; software, L.W. and W.C.; validation, W.C. and V.P. ; formal analysis, H.Z. and W.C.; investigation, H.Z., W.X. and C.C. ; resources, Z.P., P.L., X.M., R.T.M., U.G. and W.C.; data curation, H.Z., W.X., P.L., X.M. and C.C. ; writing--original draft preparation, H.Z., W.X. and W.C.; writing--review and editing, V.P. ; visualization, H.Z. and W.X. ; supervision, W.C., R.T.M., L.W., U.G. and V.P. ; project administration, V.P. and U.G. ; funding acquisition, R.T.M. All authors have read and agreed to the published version of the manuscript. We gratefully acknowledge support from the National Natural Science Foundation of China (Grants # 52072351, 61975208, 61905247, U21A20508); the Sino-German Scientist Cooperation and Exchanges Mobility Program (DFG Grant M-0040); MCIN/AEI/ 10.13039/501100011033 Grants PID2022-141499 OB-I00 and PID2019-108543 RB-I00; and the French Agence Nationale de la Recherche (ANR) SPLENDID2 (ANR-19-CE08-0028). The authors confirm that the data supporting the findings of this study are available within the article. Figure 8: Radio-frequency (RF) spectra of the ML Tm,Ho,LuCALGO laser: **(a)** fundamental beat note measured with a resolution bandwidth (RBW) of 300 Hz and **(b)** a 1-GHz frequency span recorded with a RBM = 100 kHz. As established later, the decreasing intensity of the higher harmonics in **(b)** was, in fact, an artifact due to the low battery level of the detector used (ET-5000, EOT). **Acknowledgments:** We gratefully acknowledge support from the Imperial College European Partners Fund and the Institute of Security Science and Technology Champions Fund. We thank [PERSON], Reflektron Ltd., Muotialankuja 5 C5, Tampere 33,800, Finland, for the provision of different GaSb-based SESAMs. We acknowledge also support from the Qilu Young Scholar Program of Shandong University and the Taishan Scholar Foundation of Shandong Province, as well as from the \"RELANCE\" Chair of Excellence project funded by the Normandy Region. **Conflicts of Interest:** The authors declare no conflict of interest.