Confocal Fabry-Perot Interferometer

A confocal interferometer, sometimes called incorrectly a spherical FPI, consists of two spherical mirrors M, Mj with equal curvatures (radius r) which oppose each other at a distance d = r (Fig.4.48a) [4.32-36]. These interferometers have gained great importance in laser physics firstly, as high-resolution spectrum analyzers for detecting the mode structure and the linewidth of lasers [4.34-36] and secondly, in the nearly confocal form, as laser resonators (Sect. 5.2). 

Because of spherical aberration rays with different distances pj from the axis will not all go through F but will intersect the axis at different positions F depending on and 9. Also each ray will not exactly reach the 

The optical path difference As between two successive rays passing through P can be calculated from geometrical optics. For pj r and 1 one obtains for the near confocal case d r [4.35] 

An incident light beam with diameter D = 2pj therefore produces, in the central plane of a confocal FPI, an interference pattern of concentric rings. Analogous of the treatment in Sect.4.2.5, the intensity I(p,A) is obtained by adding all amplitudes with their correct phases S = 5o+(27t/A)As. According to (4.51) we get 

The free spectral range 5i/, i.e., the frequency separation between successive interference maxima, is for the near-confocal FPI with p d 

Because of spherical aberration, rays with different distances p from the axis will not all go through F but will intersect the axis at different positions F depending on p and 0. Also, each ray will not exactly reach the entrance point Pi after four passages through the confocal FPI since it is slightly shifted at successive passages. However, it can be shown [4.36,4.39] that for sufficiently small angles 9, all rays intersect at a distance p p, 9) from the axis in the vicinity of the two points P and P located in the central plane of the confocal FPI (Fig. 4.48b). 

The radius pm of the mth-order interference ring is obtained from (4.73), 

An incident light beam with diameter D = 2pi therefore produces, in the central plane of a confocal FPI, an interference pattern of concentric rings. Analogous of 

Trajectories of rays in a confocal F,P,I. with off-axis incidence, (a) Incident beam parallel to the F,P,I, axis, (b) Inclined incident beam. 

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So far polarization spectroscopy has been applied to a number of small molecules17,18. Figure 4 illustrates a small section of a Doppler-free polarization spectrum of CSj, which shows rotational lines of the Cljly XlEg transition around the bandhead of the v = 9 v" = 14. Note that many rotational lines fall within the Doppler-width of about 600 MHz. The frequency marks, which are 60 MHz apart, are generated with a 120 cm confocal Fabry-Perot interferometer. 

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