Using excellent host of Gadolinium Vanadate (GdVO<sub>4</sub>), Tm<sup>3+</sup>:GdVO<sub>4</sub> laser has many advantages, such as high heat conductivity, little thermal effect, large stimulated emission cross-section, and low laser oscillation threshold. And due to its stronger and broader absorption spectrum in the 800 nm region, highly-efficient AlGaAs laser-diode (LD) can be adopted as pump source. In this paper, the properties of various kinds of Tm<sup>3+</sup>-doped laser crystals are compared in the first place. Then by describing the energy transmission process of Tm<sup>3+</sup>-doped system at the 2 μm band and establishing
the quasi-three-level rate equation, we obtain the expression of threshold pump power and slope efficiency. Moreover,
considering thermal lens effect of GdVO<sub>4</sub>, the three-mirror folded resonator is analysed using the method of transmission
matrix and optimized numerically. A low-threshold, high-power, and good-stability LD double-end pumping
Tm<sup>3+</sup>:GdVO<sub>4</sub> solid-state laser is designed by the guidance of the optimized resonator parameters. We obtained a
fundamental mode 1920 nm laser output.
An approximate explicit solution for Raman fiber lasers with arbitrary cascades is obtained. The solution is deduced
without using depleted pump approximation. The proposed analytical solution shows excellent agreement with numerical
simulation. Furthermore, optimal design of the cascaded Raman fiber lasers is carried out analytically. The optimal
values of fiber length, reflectivity of output fiber Bragg grating and power conversion efficiency are obtained under
different pump power. The optimal fiber length and reflectivity of output FBG decrease with increasing pump power.
There exists a certain tolerance of the optimal cavity parameters, in which the conversion efficiency decreases only
slightly. In addition, by the proposed solution one can readily determine whether pump power is depleted.