Optical Communications, 2nd Edition

1.3 TRANSMITTED OPTICAL FIELDS

The field from an optical source is transmitted as a propagating optical field. It is necessary to properly describe this emanating field to determine power flow. Because the transmitted field is an electromagnetic wave, it is described at any spatial point by solutions to Maxwell's equations. Let ξ represent a point of a selected coordinate system in which the field source is located at the origin, as shown in Figure 1.13. At any time t, the radiation field is described at ξ by a unit vector i in the direction of field flow and its electrical field function

Figure 1.13. Three-dimensional coordinate space.

where Real{ · } means “real part of” and f(t, ξ) is referred to as the complex field. At each point ξ, the field has an intensity given by

where Z_w is the wave impedance (i.e., the impedance of the medium; in free space, Z_w = 377 ohms). The instantaneous power of the complex field over a planar area A at time t is given by the surface integral of the intensity over the area,

where the integration is over all ξ in A, and θ is the angle between the normal ...