Inhomogeneous lens stuctures for integrated optics
The thesis is concerned with the design, analysis, fabrication am evaluation of integrated optic lenses which are inhomogeneous either in physical shape or in refractive index profile. The thesis has nine chapters. Chapter one, the introduction, illustrates the importance of these lenses within the domain of integrated optiCS, where the complicated mathematical functions required to describe the lens profiles are most easily realised. Connections are made between the study of these lenses and the exciting new field of optical computing. A special class of non-uniform lenses which are conceptually perfect optical instruments forms the main area of interest in the present study. Historically, the development of these lenses has followed two distinct lines, related to two possible methods of physically obtaining the required variation in path of light rays passing through the lens. In one method the optical path is made to vary directly, whilst the other method involves controlling the fi'lysical path, and thus the optical path, through the principle of equivalence. The dual development has been continued in the field of integrated optiCS, where lenses based on direct control of the optical path are termed variable-index lenses and those based on physical path control are termed geodesic lenses. The perfect variable-index lens studied in this work was the well-known Luneburg lens. Perfect geodesic lens designs have also been published. The design formulae for both types of lens are presented in chapter two. A simpler lens, of spherical geometry, is also presented which is easily analyzed and characterised and which serves as an archetypal model against which the performance of the more sophisticated lenses can be assessed. Chapter three investigates the problems involved in modelling fabrication conditions in a thermal-evaporation-invacuum environment so that lens profiles can actually be constructed. Chapter four goes into methods of tracing rays through these lenses in some detail. Ray-tracing has long been the classical tool of optical designers, providing a useful guide to optical performance. Ray methods, which effectively provide image error evaluations, are not entirely-appropriate for those lenses which are conceptually perfect within the geometrical optics approximation. Diffraction effects prevent the lenses from attaining true perfection. In such cases the wave-field produced by the lenses in the image space is the important quantity. In chapter five, the beam-propagation method (BPM) is used to study diffraction arrl associated effects in inhomogeneous lenses. '!he method allows the propagation of complicated waveshapes in lnhomogeneous media, normally a difficult task. Furthermore, anlsotropic effects and the interaction between acoustic waves aoo optical waves can be studied with the method. Negative focal shifts are reported which are not predicted by geometrical optics or the usual approximate diffraction theories. The fabrication of lenses is considered in chapter six. Planar waveguide measurements car r ied out on the var ious materials used in the study are presented. A major problem in the fabrication of geodesic lenses, that of obtaining a uniform wavegulde layer over the complete lens area, is dealt with in some detail in chapter seven. In chapter eight, extensive tests on the experimental performance of several lenses are reported. Near diffraction-limited performance is reported for geodesic lenses. More limited performance figures are obtained for Luneburg lenses though the possibility of high performance is lndicated if profile resolution can be improved. The themes of the thesls are pulled together for discussion in chapter nine and conclusions are drawn as to the relative merits of the various lenses. Possible means of improving fabrication procedures, thus driving lenses closer to ultimate resolution limits, are presented. The greatest problem faced is that of scatter ing in the waveguide, which appears to be accentuated as the waveguide traverses the lens surface. If the scattering problem can be successfully dealt with it is concluded that integrated optical lenses could be important and viable components in addresslng the problem of fast, high-throughput data processing.