A compact (L≈5 cm) spherical Fabry-Pérot interferometer with adjustable mirror spacing is used to produce interference fringes with frequency separation (c/2L)/N,N≲20. These fringes are used as frequency markers in a Doppler-free saturation spectroscopy experiment. The conditions for observation of the fringes are discussed in terms of the eigenmodes of the cavity with high transverse indices.

1.
J. M. Vaughan, The Fabry-Perot Interferometer. History, Theory, Practice and Applications (Hilger, Bristol, 1989);
G. Hernandez, Fabry-Perot Interferometers (Cambridge University Press, Cambridge, 1988).
2.
A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).
3.
W. Demtröder, Laser Spectroscopy (Springer, Berlin, 1998).
4.
D.
Budker
,
D. J.
Orlando
, and
V.
Yashchuk
Am. J. Phys.
67
,
584
(
1999
).
5.
We use the paraxial approximation and assume that L is effectively the same for all modes. In order to ensure sufficiently close equality of the spacing between transverse modes, we require that (see, e.g., Ref. 3) ρ4/R3<λ/100, where ρ is a typical size characterizing the width and offset from the axis of the input laser beam. This means that ρ is limited to ∼1 mm for the interferometers used in this work. Larger beam sizes and offsets lead to broader and asymmetric transmission peaks.
6.
We emphasize that observation of multiple modes outside the confocal condition has been described by many authors [see, e.g.,
R. A.
Boyd
,
J. L.
Bliss
, and
K. G.
Libbrecht
,
Am. J. Phys.
64
,
1109
(
1996
)], but they are usually considered a useless “jumble.“ We point out, however, that when the resonance condition is satisfied, the observed pattern may be quite regular (Figs. 5 and 6) and useful for applications.
The problem has also been analyzed in the ray-tracing approach in
D.
Herriott
,
H.
Kogelnik
, and
R.
Kompner
,
Appl. Opt.
3
,
523
(
1964
)
[see also
J. R.
Johnson
,
Appl. Opt.
7
,
1061
(
1968
)]. In that work, the relation of the extra cavity resonances to the appearance of closed ray paths and applications to laser resonators and absorption cells are discussed.
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