Thermodynamic Analysis of End-Pumped Fiber Lasers Subjected to Surface Cooling

In this paper, the temperature distribution is derived analytically within a fiber laser end pumped by a top-hat beam subjected to an external convection at the cladding surface. The temperature distribution is obtained through considering the radial heat conduction and neglecting the axial heat conduction due to large aspect ratio. An expression for the volumetric entropy generation rate within the fiber laser is also derived, which is directly proportional to the temperature gradients and inversely proportional to the temperature. Based on the temperature distribution, the maximum pump power is obtained just before the thermal damage. The temperature distribution is compared with 2-D temperature distribution and the results are in good agreement. The effect of laser absorption coefficient and Biot number on the temperature and volumetric entropy generation rate are presented graphically. The results show that volumetric entropy generation rate decreases as the Biot number decreases because of lower temperature gradients at the cladding surface. The volumetric rate is always maximum at the fiber core and cladding interface. The results are presented in dimensionless form, so that they can be applied to any end-pumped laser rod, crystalline or glassy.