
Fabry-Perot Interferometer Chapter 3: Fabry-Pérot Interferometry
Rev C, December 3, 2018 Page 3
Chapter 3 Fabry-Pérot Interferometry
The SA200 is a high finesse Spectrum Analyzer used to examine the fine structures of the spectral
characteristics of CW lasers. The spectrum analyzer consists of a confocal cavity that contains two high
reflectivity mirrors; by varying the mirror separation with a piezoelectric transducer the cavity acts as a very
narrow band-pass filter. Knowing the free spectral range of the SA200 allows the time-base of an
oscilloscope to be calibrated to facilitate quantitative measurements of a laser line shape. The confocal
cavity design, for which the mirror spacing, d, and radius, r, are identical, allows for an easy alignment
procedure. Mirrors shown below are AR coated on the outer surfaces and HR coated on the inner surfaces.
Illustration of the confocal cavity design, where the mirror spacing is chosen equal
to the radius of curvature of the mirrors.
3.1. Free Spectral Range
To scan the spectra of the laser beam entering the Scanning Fabry-Pérot interferometer, a small
displacement is applied to one of the cavity mirrors mounted on the piezoelectric transducers. This is done
by fine tuning the ramp voltage applied to the piezoelectric elements using the controller SA201. When the
mirror spacing becomes equal to an integral number of half the wavelength of the laser, constructive
interferences occur. That spectral response of the signal can be visualized with a scope. A series of
periodical peaks appear on the screen of the scope. The distance between consecutive peaks is called the
free spectral range (FSR) of the instrument.
From a user's perspective, the free spectral range of a confocal cavity is given by
FSR = c/4d,
where c is the speed of light and d is the cavity length, instead of c/2d as would be the case for a plano-
plano cavity; the factor of 2 in the denominator can be understood by inspecting the ray trace shown on the
next page in Figure 2. Note that a ray entering the cavity at a height ‘H’ parallel to the optical axis of the
cavity makes a triangular figure eight pattern as it traverses the cavity. From this pattern it is clear that the
ray makes four reflections from the cavity mirrors instead of the two that would result in a plano-plano cavity.
Hence the total round-trip path through the cavity is given as 4d instead of 2d.
This figure shows a simplified ray-trace for a ray entering the cavity at height ‘H’.
The curvature of the mirrors ‘r’ and the separation being set precisely to ‘r’ ensures that the
input ray is imaged back onto itself after traveling a distance of approximately 4r.
d