Theoretical approach on the critical depth of cut of single crystal MgF₂ and application to a microcavity

Optical microcavity, which can localize light at a certain spot for a short period of time, has a wide range of applications, such as optical signal processing and optical frequency combs. Single crystal CaF₂ has excellent optical properties and many research on the manufacturing process to create a microcavity has been done. However, due to its unstable thermal conditions, stable oscillation of Kerr comb could not be done. Single crystal MgF₂, which also has excellent optical properties, has stable thermal conditions suitable to create a microcavity. Like CaF₂, MgF₂ microcavity can only be manufactured by ultra-precision cylindrical turning, yet its appropriate processing conditions is not known. In this study, a method to derive the critical depth of cut theoretically in ductile mode machining was proposed in consideration of specific cutting energy, mechanical properties and slip system of workpiece, and tool geometry. The critical depth of cut calculated by the proposed method roughly agreed with the experimental value on the MgF₂ plane. Unlike CaF₂, MgF₂ has an optical anisotropy; therefore, in order to create a microcavity where the refractive angle is constant, the resonance part needs to be made on a cylinder with (001) plane as end face. Therefore, a microcavity was fabricated according to the critical depth of cut on a cylinder with (001) as end face derived from the proposed method, and the surface integrity was evaluated from the viewpoint of microcavity performance.