The first clad optical fibers developed for imaging were what we now call step-index multimode fibers. Developers tested a variety of cladding materials with low refractive indexes, including margarine, beeswax, and plastics. However, the key practical development was a way to apply a cladding of glass with lower refractive index than the core.
As we will see glass comes in many different formulations with varied refractive indexes. The simplest way to make glass-clad fibers is to slip a rod of high-index glass into a tube with lower refractive index, heat the tube so the softened glass collapses onto the rod, let them fuse together, then heat the whole preform, and pull a fiber from the molten end.
The cladding of imaging fibers generally is a thin layer surrounding a thicker core. The reason for this design is that imaging fibers are assembled in bundles, with light focused on one end of the bundle to emerge at the other. Light falling on the fiber cores is transmitted from one end to the other, but light falling on the cladding is lost. The thinner the cladding, the more light falls on the fiber cores and the higher the transmission efficiency.
Reducing the size of individual fibers increases the resolution of images transmitted through a bundle, but very fine fibers are hard to handle and vulnerable to breakage.
Typically, the smallest loose fibers used in imaging bundles are about 20um (0.02 mm, or 0.0008 in.). Even at this size, they remain large relative to the wavelength of visible light (0.4 to 0.7 um in air), and you can get away with considering light guiding as determined by total internal reflection of light rays at the core-cladding boundary. (The highest-resolution fiber bundles are made by melting fibers together and stretching the whole solid block.)