Asymptotic approximations are obtained for the reflected and refracted fields that result when an arbitrary monochromatic electromagnetic wave is incident on a plane interface separating two linear, homogeneous, isotropic dielectrics. The results are the first one or two terms in the asymptotic expansion of the fields valid as the point of observation moves away from the interface a distance large compared to the wavelength in any fixed direction apart from certain specified critical angles. The approximations are obtained from the exact solutions by applying the method of stationary phase extended to allow for the nonstandard form of the integrands in the integral representations of the fields. Although the method is applicable only when the medium containing the point of observation is nonabsorbing, the results probably have more general applicability.
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