1.3 Cavity modes
Axial modes
The cavity provides positive feedback which is necessary to amplify
light travelling in a given direction – that is, along the cavity axis.
Cavity axis
d
Mirrors can be planar or curved
To avoid destructive interference of photons of different phases, we
need an exact integer number, n, of half wavelengths spanning the
mirror separation, d. That is,
n = 2d / λ
λ = 2d / n
ν = nc / 2d
Waves that fulfil these conditions are the axial modes of the cavity.
Cavity modes
Example: (cf. 9.1 in Hollas)
A laser cavity is 10.339 96 cm long and operates at a wavelength of 533.647 8 nm.
(a) How many half wavelengths are there along the length of the cavity?
(b) What is the next longer wavelength that will be a mode of the cavity?
(c) What is the difference in frequency between these two consecutive modes?
(d) What is the time taken for a photon to make a round trip in the cavity?
Cavity modes
It can readily be shown that the separation of allowed frequencies
is:
Δν = c / 2d
The cavity transmission (and laser modes) thus looks like:
How do the cavity modes affect the laser emission?
Cavity modes
The Gain profile must be combined with the cavity modes to
determine the laser output.
As a result, lasers often produce a multimode spectrum
Single mode operation can be achieved, but the laser power is
generally lower.
Cavity modes
Transverse modes
There are also cavity modes perpendicular to the cavity axis. These
modes are the transverse modes of the cavity and are usually
labelled TEMij (transverse electromagnetic) modes.
These modes describe the spatial distribution of the cavity
modes. The subscripts i and j describe the number of nodes along
each axis:
TEM00 is most commonly encountered – it describes a Gaussian
beam profile.