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The intracavity use of newly developed low-birefringence synthetic diamond for thermal management in compact solid-state lasers is examined both experimentally and theoretically. A comparison - using single-crystal natural diamond as a base line - is made between synthetic, single-crystal diamond types: chemical vapor deposition and high pressure/high temperature grown diamond. The synthetic diamond samples are shown to possess significantly lower birefringence than often occurs in natural single-crystal diamond while maintaining the excellent thermal management properties and low insertion loss of natural diamond. Low threshold, high efficiency laser operation is demonstrated in polarization sensitive cavities incorporating intracavity synthetic diamond using both doped-dielectric and semiconductor gain elements. In addition, finite element analysis is used to demonstrate the potential of diamond to reduce thermal distortion and stress in doped-dielectric disk lasers. A 15 W Nd:GdVO4 disk laser utilizing diamond is demonstrated. These results highlight the potential of low birefringence synthetic diamond for intracavity thermal management applications in solid-state lasers.