2.2 The two-mirror resonator
The linear optical resonator, also called a cavity is formed by two partially-transparent mirrors, arranged
in parallel as shown in Figure 5. This simple setup makes a very good example with which to illustrate how
a mathematical model of an interferometer can be derived, using the equations introduced in
Figure 5: Simplified schematic of a two mirror cavity. The two mirrors are defined by the amplitude
coefficients for reflection and transmission. Further, the resulting cavity is characterised by its length
. Light field amplitudes are shown and identified by a variable name, where necessary to permit
their mutual coupling to be computed.
The cavity is defined by a propagation length (in vacuum), the amplitude reflectivities ,
and the amplitude transmittances , . The amplitude at each point in the cavity can be
computed simply as the superposition of fields. The entire set of equations can be written as
The circulating field impinging on the first mirror (surface) can now be computed as
This then yields
We can directly compute the reflected field to be
while the transmitted field becomes
The properties of two mirror cavities will be discussed in more detail in Section 5.1.