Reflection of Waves in a Slowly Varying Medium

Short wave asymptotic methods fail to give information on the wave reflection caused by slow, analytic variations of refractive index. Recently, Meyer [8] established that the reflection coefficient is exponentially small and obtained a first estimate for it. Here a simpler method is described which yields much simpler analytic forms and which permits in principle higher order approximations to be obtained. Explicit answers are given in a form which is easily applicable to a large class of problems. A general proof that the problem is well posed is included, since Meyer’s proof does not cover parametric ranges which might be of interest.