Analytical modelling of end thermal coupling in a solid-state laser longitudinally bonded by a vertical-cavity top-emitting laser diode

The intrinsic features involving a circularly symmetric beam profile with low divergence, planar geometry as well as the increasingly enhanced power of vertical-cavity surface-emitting lasers (VCSELs) have made the VCSEL a promising pump source in direct end bonding to a solid-state laser medium to form the minimized, on-wafer integrated laser system. This scheme will generate a surface contact pump configuration and thus additional end thermal coupling to the laser medium through the joint interface of both materials, apart from pump beam heating. This paper analytically models temperature distributions in both VCSEL and the laser medium from the end thermal coupling regarding surface contact pump configuration using a top-emitting VCSEL as the pump source for the first time. The analytical solutions are derived by introducing relative temperature and mean temperature expressions. The results show that the end contact heating by the VCSEL could lead to considerable temperature variations associated with thermal phase shift and thermal lensing in the laser medium. However, if the central temperature of the interface is increased by less than 20 K, the end contact heating does not have a significant thermal influence on the laser medium. In this case, the thermal effect should be dominated by pump beam heating. This work provides useful analytical results for further analysis of hybrid thermal effects on those lasers pumped by a direct VCSEL bond.