On embedding trees into uniformly convex Banach spaces

In thin film optical systems including thin film optical waveguides, of such materials as Nb2O5, it is desirable to fabricate thin film lenses. One of the types of lenses which can be made is the step-in-thickness type. This type of thin-film lens can be fabricated by plasma etching through a photoresist mask in such materials as Nb2O5 and Ta2O5. Plasma etching yields an etch wall with smooth steep sides which is important for good quality thin-film lenses; however, the etch rate is too variable for reproducible etch depth based upon etch time, and the bottom of the etch is very rough, causing excessive scattering loss. It has been found that a sandwich-like structure of Nb2O5, TiO2 and Nb2O5 provides an improved arrangement in that a good control of the etch depth and a smooth flat bottom in the etch areas have been achieved by introducing the layer of TiO2 as an etch stop.