Theoretical study of annealed proton-exchanged Nd:LiNbO3 channel waveguide lasers with variational method

The controllable fabrication parameters, including anneal time, initial exchange time, channel width, dependences of TM₀₀ mode size, corresponding effective refractive index, effective pump area, and coupling efficiency between pump and laser modes in z-cut annealed proton-exchanged (APE) Nd:LiNbO₃ channel waveguide lasers were studied by using variational method. The effect of channel width on the surface index increment and the waveguide depth was taken into account. The features of mode size and effective refractive index were summarized, discussed, and compared with previously published experimental results. The effective pump area, which is directly proportional to threshold pump power, increases strongly, slightly, and very slightly with the increase of anneal time, channel width, and initial exchange time, respectively. However, the coupling efficiency, which is directly proportional to slope efficiency, remains constant (around 0.82) no matter what changes made to these parameters. The variation of the coupling loss between an APE channel waveguide and a fiber with these parameters for both laser (1085 nm) and pump (815 nm) wavelengths was also calculated. The calculated results indicate that the coupling loss decreases rapidly, slightly and very slightly with the increase of anneal time, channel width and initial exchange time, respectively