Theory of The Single-Material Fiber

A dielectric optical waveguide made entirely of one type of material is callcd a " s i n g l e - m a t e r i a l fiber." 1 F i g u r e 1 s h o w s s u c h a s t r u c t u r e schematically. It may be regarded as a rectangular dielectric waveguide supported by two infinitely extended slabs made of the same material. Such a structure has been shown to be capable of supporting modes that are concentrated near the enlarged section of the waveguide and that do not lose power by energy seepage into the slabs. 1,2 Single-material fibers are usually made of pure fused silica. Since no other material is needed to form a waveguide, the low-loss properties of pure fused silica can be fully utilized. 3 The single-material fiber has been described by means of an approximate theory by Marcatili. 1 The theory presented here serves the purposes of proving that truly guided modes do indeed exist in singlematerial fibers and of providing more precise solutions for comparison with the approximate theory. An analysis of the guided modes of the single-material fiber is presented in this paper. The mode field is expressed as a superposition of the guided modes as well as the radiation modes of the two types of slabs. The enlarged region, henceforth called the core, can be regarded as a slab joined by narrower support slabs on either side. Since the radiation modes of the slabs have a continuous spectrum of eigenvalues 4 5 (propagation constants), their contribution to the total field 1619