We present a study of the single pass SHG conversion as a function of the Rayleigh length (RL) and beam diameter (BD) using a monolithic distributed Bragg reflector (DBR) tapered laser. The DBR tapered laser has a 6th order surface grating and a ridge waveguide. Single longitudinal mode emission at 978nm with a side-mode suppression ratio of more than 40dB and at an output power of 2.7W at 15°C have been obtained in continuous wave operation. The beam was collimated using an aspheric and a cylindrical lens and focused using a variety of lenses with various focal lengths. The resulting caustics were acquired using a camera and used for SHG in a 5cm periodically poled LiNbO3 (PPLN) crystal. This allowed an investigation of the dependency of the SHG conversion efficiency on the RLs and BDs. We obtained 330mW of output power at 488nm using the optimal focus length. The experiments showed that an optimum conversion requires longer focal length's then forecasted by Boyd-Kleinman's theory, which is explained due to the partial coherence. We developed an extension of that theory to account for that partial coherence, which bases in principle on a mismatch related general Agrawal's nonlinear integration kernel. We use this theory to explain the dependence of the SHG efficiency from the beam propagation factor M2.
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