3 Light with Multiple Frequency Components
So far we have considered the electromagnetic field to be monochromatic. This has allowed us to compute
light-field amplitudes in a quasi-static optical setup. In this section, we introduce the frequency of the light
as a new degree of freedom. In fact, we consider a field consisting of a finite and discrete number of
frequency components. We write this as
with complex amplitude factors , as the angular frequency of the light field and . In
many cases the analysis compares different fields at one specific location only, in which case we can set
In the following sections the concept of light modulation is introduced. As this inherently involves light
fields with multiple frequency components, it makes use of this type of field description. Again we start with
the two-mirror cavity to illustrate how the concept of modulation can be used to model the effect of mirror
Figure 15: Example traces for phase and amplitude modulation: the upper plot a) shows a
phase-modulated sine wave and the lower plot b) depicts an amplitude-modulated sine wave. Phase
modulation is characterised by the fact that it mostly affects the zero crossings of the sine wave.
Amplitude modulation affects mostly the maximum amplitude of the wave. The equations show the
modulation terms in red with the modulation index and the modulation frequency.