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In this paper, we introduce a new type of Finsler metrics, called$(\alpha_1,\alpha_2)$-metrics. We define the notion of the good datum of ahomogeneous $(\alpha_1,\alpha_2)$-metric and use that to study the geometricproperties. In particular, we give a formula of the S-curvature and deduce acondition for the S-curvature to be vanishing identically. Moreover, weconsider the restrictive Clifford-Wolf homogeneity of left invariant$(\alpha_1,\alpha_2)$-metrics on compact connected simple Lie groups. We provethat, in some special cases, a restrictively Clifford-Wolf homogeneous$(\alpha_1,\alpha_2)$-metric must be Riemannian. An unexpected interestingobservation contained in the proof reveals the fact that the S-curvature mayplay an important role in the study of Clifford-Wolf homogeneity in Finslergeometry.

$(\alpha_1,\alpha_2)$-Spaces and Clifford-Wolf Homogeneity