Analysis of heat generation and thermal lensing in erbium 3-μm lasers

The influence of energy-transfer upconversion (ETU) between neighboring ions in the upper and lower laser levels of erbium 3-μm continuous-wave lasers on heat generation and thermal lensing is investigated. It is shown that the multiphonon relaxations following each ETU process generate significant heat dissipation in the crystal. This undesired effect is an unavoidable consequence of the efficient energy recycling by ETU in erbium 3-μm crystal lasers, but is further enhanced under nonlasing conditions. Similar mechanisms may affect future erbium 3-μm fiber lasers. In a three-dimensional finite-element calculation, excitation densities, upconversion rates, heat generation, temperature profiles, and thermal lensing are calculated for a LiYF₄:Er³⁺ 3-μm laser. In the chosen example, the fraction of the absorbed pump power converted to heat is 40% under lasing and 72% under nonlasing conditions. The heat generation in a LiYF₄:Er³⁺ 3-μm laser is 1.7 and the thermal-lens power up to 2.2 times larger than in a LiYF₄:Nd³⁺ 1-μm laser under equivalent pump conditions, thus, also putting a higher risk of rod fracture on the erbium system.