The reflection and refraction of a high-frequency electromagnetic field in the presence of an arbitrarily curved dielectric interface is considered. The fields are expanded in asymptotic series of k−1, known as Luneburg-Kline expansions. Based on a ray method [Lee, 1975], the zero- and first-order terms of k−1 of the reflected and transmitted fields at the interface have been evaluated by Ansorge . Associated with the fields at the interface, effective surface current densities can be used to evaluate the fields at points away from the interface. This can be done analytically by means of the stationary phase method. In this paper the first-order terms of the reflected far field in the case of plane wave incidence and the transmitted far field in the case of homogeneous spherical wave incidence are given. The results allow a better description of the polarization state of reflected and transmitted fields then zero-order terms do alone, which is shown for some typical examples in frequency and time domain.