Year Group Effect Technique γ n (1 $_{/}$√$_{Hz)}$ δn 2000 Tel-Aviv [10] Kerr Resonant cavity ellipsometer $^{3}$× 10 − 15 $^{1}$× 10 − 13 2005 BMV [11] Kerr Resonant cavity ellipsometer $^{2}$× 10 − 15 $^{1}$× 10 − 15 2009 PVLAS [15, 19] Cotton-Mouton Resonant cavity ellipsometer $^{5}$× 10 − 17 $^{1}$× 10 − 17 2009 Q & A [16] Cotton-Mouton Resonant cavity ellipsometer $^{1}$× 10 − 15 $^{1}$× 10 − 15 2009 BMV [17, 18] Cotton-Mouton Resonant cavity ellipsometer $^{2}$× 10 − 18 $^{2}$× 10 − 15 2009 LASIM/LSP [12] Kerr Resonant cavity ellipsometer $^{8}$× 10 − 19 $^{4}$× 10 − 19 2003 Tokyo [20] Cotton-Mouton Single pass ellipsometer $^{3}$× 10 − 13 $^{2}$× 10 − 15 2000 JILA [21] Sensitivity test Frequency measurement $^{2}$× 10 − 15 $^{1}$× 10 − 17 2009 This work Sensitivity test Frequency measurement $^{1}$× 10 − 16 $^{2}$× 10 − 18 TABLE I: Review of recent experimental results concerning small birefringence measurements in gases. The reported γ n is the noise equivalent birefringence at the detection frequency, while δn corresponds to the smallest measured birefringence value inferred from the published data. the resonance frequency of a Fabry-Perot cavity. Indeed, this approach takes advantage of the recent progress in frequency metrology and should result in an unsurpassed sensitivity along with an impressive dynamic range. The tests performed by J.L. Hall and coworkers lead to an equivalent sensitivity δn = δν/ν ≃ 1 × 10 − 17 (see Table I), which appeared to be limited by various experimental effects, including vibrations, perfectible optical isolation and birefringence noise of the cavity mirrors. In fact, J.L. Hall’s proposal is similar to the method used in large active ring lasers aimed at precisely measuring the Earth rotation rate [22, 23] thanks to the Sagnac effect. These rings have areas of tens to hundreds of square meters, and exhibit a relative frequency sensitivity on the order of 10 − 18 − 10 − 20 $_{/}$√$_{Hz.}$ In this paper, we present promising sensitivity tests performed on an apparatus which is based on the same idea but aims at measuring small directional anisotropies of the propaga- tion medium. Indeed, we have built a ring cavity, so that one can distinguish two propagation directions. A laser light beam is frequency-stabilized to the clockwise cavity resonance, and injected into the cavity both clockwise and counterclockwise. The counterclockwise error signal yields the value of the directional anisotropy. Our first goal is to measure the magneto-electric directional anisotropy of light which 3