I. INTRODUCTION High finesse optical cavities play an important role in modern physics, especially in preci- sion experiments: one famous example concerns the gravitational wave searches [1–5] where relative sensitivities range from γ rel ∼ 10 − 21 $_{/}$√$_{Hz to}$ γ rel ∼ 2 × 10 − 23 $_{/}$√$_{Hz, but many}$ other experiments include high finesse cavities, such as optomechanics measurements [6] achieving γ rel ∼ 2 × 10 − 17 $_{/}$√$_{Hz or tests of the isotropy of light propagation [7] where}$ γ rel ∼ 1 × 10 − 17 $_{/}$√$_{Hz.}$ Since the first electro- and magneto-optical effects have been discovered, about 150 years ago, the sensitivity of the experiments has improved by more than 10 orders of magnitude. In particular, the insertion of an optical cavity – resonant or multipass – between the polarizer and the analyzer, first suggested by E. Zavattini as early as 1979 [8], brought the sensitivity down by several orders of magnitude thanks to the accumulation of the birefringence effect on a longer optical path. This approach has been widely used for the past 20 years, leading in particular to several measurements of Kerr [9–12] and Cotton-Mouton [13–16] effects in gases. Table I presents an overview of the most recent experimental results. We use two quan- tities to compare the achieved sensitivities: the sensitivity γ n , i.e. the noise equivalent birefringence at the relevant detection frequency, and the value δn of the smallest birefrin- gence actually measured, as inferred from the published data. The former is very useful to compare the sensitivity of each experiment to the shot-noise limit, but since the mea- surement times range from a few tens of ms [18] to several tens of ks [19, 20], it cannot be used to directly compare the actual sensitivities of different experimental set-ups. The relevant parameter for this purpose is the smallest measured birefringence: it ranges from $^{1}$× 10 − 13 $^{to 1}$× 10 − 17 for the experiments using the Pound-Drever-Hall frequency stabiliza- tion scheme, which is to be compared with the shot-noise limited birefringence 2 × 10 − 15 $^{measured without any cavity at Tokyo University [20]. The present smallest value 4}$× 10 − 19 was measured with an original locking scheme using optical feedback [12]; note that it is less than one order of magnitude above the shot-noise limit. All these results were obtained after several years of development. In 2000, an alternative approach was proposed by J.L. Hall and coworkers [21], who sug- gested converting birefringence effects into frequency effects. This can be done by measuring 2