The behaviour of the (ideal) cavity is determined by the length of the cavity , the wavelength of the
laser
and the reflectivity and transmittance of the mirrors. Assuming an input power of
, we
obtain
Figure 25 shows a plot of the circulating light power
over the laser frequency. The
maximum power is reached when the cosine function in the denominator becomes equal to
one, i.e., at
with
an integer. This is called the cavity resonance. The lowest
power values are reached at anti-resonance when
. We can also rewrite
Another characteristic parameter of a cavity is its linewidth, usually given as full width at half maximum
(FWHM) or its pole frequency, . In order to compute the linewidth we have to ask at which frequency
the circulating power becomes half the maximum:
The behaviour of a two mirror cavity depends on the length of the cavity (with respect to the frequency of the laser) and on the reflectivities of the mirrors. Regarding the mirror parameters one distinguishes three cases5:
The differences between these three cases can seem subtle mathematically but have a strong impact on
the application of cavities in laser systems. One of the main differences is the phase evolution of the light
fields, which is shown in Figure 26. The circulating power shows that the resonance effect is better used in
over-coupled cavities; this is illustrated in Figure 27
, which shows the transmitted and circulating power for
the three different cases. Only in the impedance-matched case can the cavity transmit (on resonance) all
the incident power. Given the same total transmission
, the overcoupled case allows for the largest
circulating power and thus a stronger ‘resonance effect’ of the cavity, for example, when the
cavity is used as a mode filter. Hence, most commonly used cavities are impedance matched or
overcoupled.
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