Figure 1

Experimental setup. A Nd:YAG laser is frequency locked to the Fabry-Pérot cavity consisting of mirrors $M$${}_1$ and $M$${}_2$. The laser beam is linearly polarized by polarizer $P$ and analyzed with polarizer $A$. This analyzer allows one to extract the extraordinary beam sent on photodiode Ph${}_e$ as well as the ordinary beam sent on photodiode Ph${}_t$. The beam reflected by the cavity analyzed on the photodiode Ph${}_r$ is used for the cavity locking. A transverse magnetic field $B$ can be applied inside the cavity in order to study the magnetic birefringence of the medium. The following denotations are used: EOM, electro-optic modulator; AOM, acousto-optic modulator; and PDH, Pound-Drever-Hall.Reuse & Permissions

Figure 2

Normalized profile of the square of the magnetic field along the longitudinal $z$axis (solid line) inside one X-coil. This is compared to the equivalent uniform magnetic field (dashed line) over the effective magnetic length $L_B$ (see the text).Reuse & Permissions

Figure 3

Time evolution of the intensity of the ordinary beam (gray solid line). The laser is switched off at $t=t_0$. Experimental data are fitted by an exponential decay (black dashed line), giving a photon lifetime of $\tau =1.16$ ms, a finesse of $F=481000$, and a linewidth of $\Delta \nu =c/2n{L}_{c}F=137$ Hz.Reuse & Permissions

Figure 4

Time evolution of the intensity of the extraordinary beam (gray solid line). The laser is switched off at $t=t_0$. Experimental data are perfectly fitted by Eq. (13) (black dashed line).Reuse & Permissions

Figure 5

Airy function of our Fabry-Pérot cavity (with a linewidth of $\Delta \nu =$ 137 Hz, a transmission of $T_c=20\%$, and where $m$ is an integer). The frequency of the ordinary beam is assumed to be locked at the top of the transmission function (solid line) and the frequency ${\nu }_e$ of the extraordinary beam is shifted from ${\nu }_t$ by a quantity $\delta \nu$ (dashed line).Reuse & Permissions

Figure 6

Attenuation factor $a$ as a function of the phase retardation $\delta$ between both polarizations.Reuse & Permissions

Figure 7

Experimental setup for the cavity length measurement. Two laser beams that are frequency shifted relative to each other by the AOM2 are injected into the cavity. The frequency of the laser is frequency modulated with a voltage ramp applied on a piezoelement (PZT) mounted on the crystal resonator of the laser. Photodiode Ph${}_t$ allows us to observe the typical Fabry-Pérot peaks from which the ${\Delta }^{\text{FSR}}$ measurement is performed.Reuse & Permissions

Figure 8

Transmission peaks of the Fabry-Pérot cavity as a function of the laser frequency. Two beams are sent to the interferometer: The second beam (dashed line) is frequency shifted by $2f_{\mathrm{AOM}}2$ relative to the first beam (solid line). The adjustment of $f_{\mathrm{AOM}2}$ in order to superimpose both series of peaks allows us to precisely measure the free spectral range ${\Delta }^{\text{FSR}}$ of the cavity.Reuse & Permissions

Figure 9

Correlation factor $\kappa$ between the square of the magnetic field and the ellipticity as a function of the angle ${\theta }_P$ of the incident polarization.Reuse & Permissions

Figure 10

Profile of the temperature inside the vacuum pipe along the longitudinal $z$axis. The X-coil is also schematized at the center. The temperature variation does not exceed 1 K inside the tube that runs through it.Reuse & Permissions

Figure 11

Cotton-Mouton effect measurements on 32.1$\times {10}^{-3}$ atm of molecular nitrogen: top, normalized intensity of the ordinary beam as a function of time; middle, intensity of the extraordinary beam divided by the mean of $I_t$ as a function of time; and bottom, square of the magnetic field as a function of time.Reuse & Permissions

Figure 12

Cotton-Mouton effect measurement on 32.1$\times {10}^{-3}$ atm of molecular nitrogen. The gray line denotes the total ellipticity as a function of time and the dashed line denotes the square of the magnetic field filtered by a first-order low-pass filter corresponding to the cavity filtering.Reuse & Permissions

Figure 13

Magnetic birefringence of molecular nitrogen as a function of pressure. The solid line corresponds to the linear fit of the experimental data.Reuse & Permissions

Figure 14

Typical ellipticity (gray) measured during a magnetic pulse (black) performed in vacuum. Acoustic perturbations generate ellipticity oscillations starting at 4 ms.Reuse & Permissions