Analytical Investigation On Thermal Effects In Short Cavity Er³⁺/Yb³⁺ Co-doped Phosphate Fiber Laser

Short cavity narrow-linewidth single-frequency fiber laser has a potential use in optical communication and sensor fields, e. g. laser ranging, laser ladar, high resolution sensors, wavelength division multiplexing and military and security. Thermal effects induced by laser operation seriously influence the output power, linewidth, central frequency and polarization of laser, and thus resulting in a limited application of the short-cavity single-frequency fiber laser. Up to now, there is no research on thermal effects in short-length fiber laser to be reported. The existing models of two-dimensional (2D) radial heat flux hypothesis for long cavity fiber laser can not be used. In order to improve the performance of single-frequency fiber laser, especially reduce thermal phase noise, optimize rare-earth ions doping concentration, resonator cavity configuration, and pump scheme, it is necessary to theoretically investigate the thermal effect in short cavity fiber laser.In this paper, we established a three dimensional (3D) heat analytical model for short cavity configuration, in which the Er3+/Yb3+ co-doped phosphate fiber drawn in our institute was chosen as gain medium. The generalized orthogonal eigenfunctions expansion technique was used to calculate the analytical solutions of temperature field in fibers and the extra thermal load induced by the energy transfer upconversion (ETU) was investigated. The calculated results demonstrate that the maximum temperature of cavity can be reduced by 14.0% if the longitudinal heat conduction is considered based on our 3D model when the laser cavity of 1 cm length is pumped by the power of 100 mW. Moreover, owing to the upconversion, it is shown that 4.2% extra heat is generated in the active fiber, and therefore the influence of ETU on heat load should be considered in rare-earth heavily doped fiber.Then, on the basis of analytical results of 3D temperature model, the 3D thermal stress field was deduced through solving the Navier-Cauchy displacement equations. Meanwhile, the fundamental thermal phase noise was investigated based on the classical Langevin diffusion equation describing local function of the temperature. The thermal stresses and their distributions calculated by our model significantly differ from those of the model of plain strain approximate. These indicate that our 3D heat analytical model are more accurate to deal with short-length fiber laser than 2D radial heat flux approximation and plain strain approximation.At last, the transient heat conduction and thermal effects in pulse end-pumped fiber laser were modeled and analytically solved. For the arbitrary temporal shape of pump pulse, a 3D temperature expression is derived via an integral transform method, and the thermal stress field is deduced through solving the Navier displacement equations. The results show that pulse shape has an important influence on the peak thermal stress and transient phase shift induced by heating of the fiber.