Interferometric studies in curved thin films

Abstract

If we consider the general case of two intersecting spherical surfaces of different radii of curvature, then as each of the radii of curvature increases without limit along the line joining the centre of the corresponding sphere to a fixed point on the line of intersection, the two intersecting surfaces tend in the limit to two planes forming a wedge. If one of the radii of curvature increases without limit and the other remains constant, the first surface tends to a plane and we have the case of an interferometer consisting of a plane and a spherical surface. A lens-plate interferometer is a special case when the plane is tangential to the spherical surface. An arbitrary surface and a plane could be considered to be an extension of the previous simple case. If the two spherical surfaces are concentric, we have a spherically curved thin film of uniform thickness, a central section through which is identical with the section perpendicular to the axis of a cylindrically curved thin film. As the radii of curvature increase without limit, the interferometer tends to two planeparallel surfaces. By evaporating a highly reflecting semi transparent metallic film on Both components of these interferometers, multiple beam interference fringes are obtained. Their intensity distribution approaches a Fabry-Perot distribution with the result that there is extreme sharpness of the fringes.Localization arises from the difference in angles of emergence of the beams leaving the two sides of the interferometer. This depends on the difference in angles of incidence at the first and second surfaces of the interferometer. In the case of a wedge, for incident parallel light, the angles of incidence at the first and second surfaces are constant and their difference is equal to the wedge angle. The interferometer gap t varies along the wedge. It satisfies the linear relation t = y tan where y is the distance measured from the apex along one of the components. In the case of a lens-plate interferometer, a slight variation in the angle of incidence occurs along the curved surface. The interferometer gap t is related to y by the second order equation t2- 2Rt = y2. For cylindricallycurved thin films, the angles of incidence at bothsurfaces vary from nearly while theirdifference as well as the interferometer gap remain constant. Tolansky (1) applied and developed multiple bean interference to both the cases of a lens-plate and an arbitrary surface plate interferometers. The latter is case of Fizeau fringes.The present work deals with the theory of formation and properties of localized fringes obtained by cylindrically curved thin films. Their application to isotropic, uniaxial and biaxial media is considered in detail.