ent of many important engineering applications. [Free space wave vector], In the case of optical fibers used for tele- and data communication it is sufficient to use a scalar wave ap- proximation to describe light propagation in single-mode n(x, y) [Refractive index]. fibers and a ray approximation for light propagation in multimode fibers. The variable kn corresponds to the phase constant for For the ray approximation to be valid the diameter a plane wave propagating in a medium with refrac- of the light beam has to be much larger than the tive index n. There is an equivalent wave equation to wavelength. In the wave picture we will assume a har- Eq. (6.1.3) for the H component. We have to solve only monically time-varying wave propagating in the Z di- the wave equation for the longitudinal components E2 rection with phase constant B. The electric field can be and H. The reason for this is that Ex and Ey can both be expressed as calculated from Ez and H using Maxwell's equations. E = E0(x,y)cos(wt - (zz). (6.1.1) 6.1.1.2 Single-mode fiber This is more conveniently expressed in the phasor for- In an infinitely large isotropic and homogeneous medium malism as a light wave can propagate as a plane wave and the phase constant for the plane wave can take on any value, limited (6.1.2) only by the available frequencies of the light itself. When light is confined to a specific region in space, boundary where the real part of the right-hand side is assumed. conditions imposed on the light will restrict the phase A wave's propagation in a medium is governed by the constant B to a limited set of values. Each possible wave equation. For the particular wave in Eq. (6.1.2) the phase constant B represents a mode. In other words, wave equation for the electric Z component is when light is confined it can propagate only in a limited number of ways. For an engineer it is important to find out how many (6.1.3) modes can propagate in the fiber, what their phase Communications Engineering Desk Reference; ISBN: 9780123746481 Copyright