Transversal mode competition in erbium-doped Ti:LiNbO3 waveguide lasers

Theoretical modeling of erbium-doped LiNbO₃ waveguide lasers has been developed considering the competition between q-TM and q-TE signal modes. Two different approaches have been used: the first is based on the mean field approximation for signal and pump power and for population inversion, the second takes into account the longitudinal distribution of the pump power and of the population densities. Our formulation takes into account, for the first time, the competition between orthogonally polarized modes, evaluating the transversal overlap between the fields and the population inversion, the effects of double pass for the pump, the signal and pump saturation effects, the stimulated emission also at pump wavelength, the wavelength dependent cross sections and mirror reflectivities. A diffused dopant distribution in depth and uniform in lateral direction have been used. A q-TM or q-TE pump mode around 1.48 μm has been considered. The threshold pump power optimization has been performed changing the dopant profile diffusion depth and maximum surface concentration. The results show how, above threshold, various types of output power characteristics, experimentally found, are due to the different transversal saturation of q-TM and q-TE lasing modes