 no is air, the equation for the NA of the glass fiber simplifies to (5.9) This equation states that for all angles of incident where the inequality 0 O1 Oacc is satisfied the incident ray will propagate within the fiber. The parameter NA expresses the propensity of the fiber to accept and propagate light within the solid cone defined by an angle, 20acc. The equation for the NA can be also expressed in terms of the difference between the refractive indices of core and cladding-that is, (5.10) With these simplifications the NA can now be written as NA = n1(21)¹/2 (5.11) To appreciate the numbers involved, consider a fiber made of silica glass whose core refractive index is 1.5 and that of the cladding is 1.46. The Ocrit and the NA of the fiber are calculated to be Oacc=sin-1NA=sin-10.346=20.24 = = Material Characteristics of Fibers-Losses Cladding Refractive Index Refractive Index Cladding Fig. 5.5 (a) Multimode and (b) single-mode propagation for step index fiber. If one uses the equation for the approximation of NA, equation 5.11, the result is =0.346 If the ray does not lie in the meridional plane, the analysis for obtaining the NA is slightly more complex. The discussion up to now has been based on the launching and propagation of a single ray. Because all the rays with a reflection angle less that the critical angle can propagate, it is expected that a number of rays will propagate provided they can be launched into the fiber. The class of fiber that can support the simultaneous propagation of a number of rays is known as multimode fiber. The term "mode" is used in a more sophisticated analysis of light propagation using Maxwell's equations, and it corresponds to one solution of the equations. Therefore, the concept of a ray and a mode are equivalent, and in the rest of this chapter the term "mode" will be used. A fiber that allows the propagation of one mode only is called a single-mode fiber. A fiber can be multimode or single mode, and the behavior depends on the relative dimensions of the core and the wav