Generally，we need different refractive index to realize a refractive index contrast to confine the light

tasarım sırasında çekirdek ve kaplamanın aynı veya farklı malzemeden yapılması önemli değil ,önemli olan verimin en iyi şekilde alınması. Ama genellikle verimin en iyi şekilde alınması için aynı malzemeden yapılması tercih edilir.

No, the core and cladding of an optical fiber must have different refractive indices. The cladding material have a lower refractive index than the core. it’s important to choose materials for the core and cladding that have different refractive indices.

Macah and Jamal correctly identify the need to have a higher refractive index core surrounded by a lower index cladding to create a structure that confines the light in a fiber. In the case of single mode fiber (SMF), the core and cladding are constructed to only allow a single mode to propagate. All other modes leak out quickly. SMF's are used throughout the telecom system for longer transmission distances. Since the single allowed mode propagates without 'touching' the outside of the fiber, the loss can be very low. At 1.3 and more so at 1.55um, the modal and material losses are so low that light can propagate for many km and still carry messages without significant information loss. There are many kinds of SMF structures with different number of concentric layers, some with distinct changes in refractive index and some with gradual (graded) index changes, but all of them have higher index cores. This answer is only the tip of the iceberg on this interesting question.

The refractive index of the core is higher than that of the cladding, so light in the core that strikes the boundary with the cladding at an angle shallower than critical angle will be reflected back into the core by total internal reflection

Right, Alliance Tony-Mayeko. Good point -- the confinement of light is based on total internal reflection (TIR). To understand this, a one-dimensional, three-layer structure is the easiest learning exercise. All you need is a sandwich of three layers with indices n1, n2, n1 where n2 > n1. The layers with n1 are infinite in thickness and layer with n2 has thickness d. Now, figure out the angle of TIR for a wave with wavelength lambda and relate that to the modal index that characterizes the propagation speed in the layered structure. By pointing out this connection, Alliance Tony-Mayeko has linked two understandable physical phenomena (TIR and modal confinement) that probably answer Miami Mohammed's question best of all.