Theory of the Single-Material, Helicoidal Fiber

The best-known single-mode optical fiber is the clad fiber. If the difference in refractive index between core and cladding is small, single-mode propagation can be achieved for core diameters t h a t are large compared with the wavelength. It is, however, desirable to use just one material, such as quartz, t h a t exhibits low impurity and scattering losses. In a previous work, 1 we indicated that single-mode propagation could be achieved in a single-material configuration t h a t we called a "helicoidal fiber." Figure 1 represents a more recent version of this type of fiber. To explain the mechanism of operation, let us consider first a cylindrical dielectric rod with radius a = p. The refractive index of the rod is perhaps n = 1.45 (quartz), and the surrounding medium is air. Waves are guided along the rod boundary as shown in Fig. 2a. These so-called "whispering-gallery modes" can be represented by rays repeatedly reflected from the boundary because of total reflection. In the interior of the rod, the modes are described by Bessel functions J,,(kr) X exp (ivfy), where v is a large integer and kr is a large number of the order of v. Because kr and v are both large and comparable to one 1643