ABSTRACT
In most parts of this handbook, we deal with linear optical effects. Linear optics means that the optical
power at the outputs of an optical device always scales linearly with input power. The device may
spectrally or spatially filter the input beam; it may split the input beam into a multitude of output beams;
regardless of what the device does, the output power always relates linearly to the input power. Looking
through textbooks on classical optics from the pre-laser era, the impression may arise that the linearity
of optical phenomena is a given thing as there is no mention of any nonlinear effects. This is in strong
contrast, e.g. to acoustics, where nonlinearities are so widespread that the art lies more in their avoidance
than in the observation of nonlinearities. One may think of a cheap set of speakers just as one simple
example. Increasing the volume, these speakers will start to sound increasingly annoying with more and
more audible distortion. This distortion is not related to the frequency-dependence of the speaker’s
transmission characteristics, because this would be independent of volume. The distortion effect is
related to unwanted harmonics of the input. These harmonics arise due to nonlinearities between the
emitted acoustic wave and the input current to the speaker’s solenoid. Beyond a certain drive amplitude,
the speaker’s membrane position does not linearly follow the current any more. These harmonics
are not necessarily bad. All musical instruments also rely on acoustic nonlinearities, giving rise to a
characteristic spectrum of overtones of the excited fundamental vibration of a chord. This characteristic
spectrum allows us to distinguish different musical instruments. The omnipresence of nonlinearities in
acoustics is in strong contrast to optics, where similar effects could not be observed until the advent of
the laser.
