Minimize quantum-defect heating in thulium-doped silica fiber amplifiers by tandem-pumping

In this paper, we propose a simple model to investigate the quantum defect between pump and signal photons in thulium-doped fiber amplifiers. The achievable quantum defects are limited by several factors, i.e., pump and signal wavelengths, fiber length, area ratio between inner cladding and core, and gain and absorption at signal and pump wavelengths, respectively. Through the proposed model, we find that the quantum defect can reach as low as 1%-level. We also find that the smaller area ratio between inner cladding and core, the lower quantum defect can be obtained. The ultimate pumping approach will be core pumping. This can be realized through tandem pumping the thulium-doped fiber by the other fiber source at shorter wavelength with high brightness. Finally, it is necessary to optimize the pump and signal wavelengths and match the fiber length to obtain the lowest quantum defect.