ABSTRACT
For this initial discussion, let us choose our propagation direction as the z-axis. Since this is a plane wave, it will have no variation in either the x-or y-direction and will, therefore, be a function of distance, z, and time, t, only. Because we are dealing with linear eects, we can represent this wave in complex form for its electric eld as
E i t z= −( )⎡⎣ ⎤⎦E exp ,ω κ (13.1)
with a similar expression for the magnetic eld, H. In a simple isotropic medium E, H and the direction of propagation are mutually perpendicular and form a right-handed set. e amplitude E is complex and so contains any relative phase, as does the magnetic eld amplitude, H. is expression contains an implied sign convention, because the phase term could equally well be written (κz − ωt). e velocity of the wave is given by ω/κ and in vacuo is a constant, c. Interaction with materials alters the velocity of the wave to v, and the greater the interaction, the slower is v. is change in velocity is expressed by the parameter refractive index, n, that is given by c/v. In linear processes, the frequency is invariant and so the wave vector or wave number, κ, will vary according to the material. κ is normally given by 2π/λ, where λ is the actual wavelength. However, we use wavelength to characterize the wave and a variable wavelength would cause problems for us. We therefore dene wavelength λ as the value it would have in
vacuo and write κ as 2πn/λ. A convenient way of handling absorption with waves in the complex form is to replace n by (n − ik), where k is known as the extinction coecient. is introduces an exponential decay into the wave as it propagates.
