 © 2002 Elsevier Inc. All rights reserved CHAPTER 6.1 Optical fiber, cable and connectors constants are, and their spatial transverse profile. To do this we have to solve Eq. (6.1.3) for a typical fiber geometry n1(r) (Fig. 6.1-1). Because of the inherent cylindrical geometry of an optical fiber, Eq. (6.1.3) is transformed into cylin- , = 0 -50 um drical coordinates and the modes of spatial dependence -120 um -120 um are described with the coordinates r, , and z. Because the solution is dependent on the specific refractive index profile, it has to be specified. In Fig. 6.1-2 the most common refractive index profiles are shown. For step- 10 um 10 um index profile in Fig. 6.1-2c, a complete analytical set of solutions can be given [3]. These solutions can be grouped into three different types of modes: TE, TM, and hybrid modes, of which the hybrid modes are further separated into EH and HE modes. It turns out that for typical fibers used in tele- and data communication the refractive index difference between core and cladding, N1-N2, is SO small ( ~0.002-0.008) that most of the TE, TM, and hybrid modes are degenerate and it is sufficient to use a single notation for all these modes-the LP notation. An LP mode is referred to as LPlm, where the l and m subscripts are related to the number of radial and azimuthal zeros of a particular mode. The fundamental mode, and the only one propagating in a single-mode fiber, is the LP01 mode. This mode is shown in Fig. 6.1-3. To quickly figure out if a particular LP mode will propagate, it is very useful to define two dimensionless parameters, Vand b. (6.1.4) where a is the core radius, a is the wavelength of light, and A 11 (n1-n2)/n1. The V number is sometimes called the normalized frequency. The normalized propagation constant b is defined as Fig. 6.1-2 Refractive index profiles of (a) step-index multimode fibers, (b) graded-index multimode fibers, (c) match-cladding single-mode fibers, (d, e) depressed-cladding, single-mode fibers, (6.1.5) (f-h) dispersion-shifted fibers, an