Experimental investigation of the magnetochiral index in liquids

We showed through experiments that the magnetochiral index is polarization invariant and reported its wavelength dependence. These properties were investigated with limonene and using a specially-designed ${\mathrm{Ar}}^{+}$-ring active interferometer. A Fresnel drag-type optical bias inside the discharge tube, combined with two calibrations and the circumvention of systematic errors, allowed us to reach a detection level in the range of ${10}^{-12}$ when measuring the change in the magnetochiral index of intracavity liquid samples. Our results are in agreement with the different predictions made for magnetochiral refraction.

Figure 1

(a) Schematic of the interferometer. Counter-propagating waves of frequencies ${\nu }_{\mathit{ccw}}$ and ${\nu }_{\mathit{cw}}$ oscillate inside a ring cavity (not to scale) made of four mirrors $M_i$ $(i=1,4)$. They probe nonreciprocal optical index differences $\Delta n_{\mathit{NR}}=n_{\mathit{ccw}}-n_{\mathit{cw}}$. A beam splitter BS and two mirrors $M_5$ and $M_6$ combine the output beams onto a detector $D$ to measure the beat note frequency $\Delta \nu$. $M_6$ can move at speed $u$ to infer the sign of $\Delta \nu$. An ${\mathrm{Ar}}^{+}$-ion discharge tube provides the gain. $C$, cathode; $A$, anode. (b) Detection of the magnetochiral birefringence: two cells $C_1$ and $C_2$, submitted to two rotating opposite magnetic fields $H$ and $-H$ are inserted inside the cavity.

Figure 2

(a) The beat note signal of the ring laser at $39\mathrm{kHz}$. ${\mathrm{U}}_D$, output voltage from $D$. (b) The baseline obtained by demodulating the beat note $\Delta {\nu }_0$. It presents root-mean-square variations $\Delta {\nu }_{\mathit{rms}}=8\mathrm{Hz}$ over $10\mathrm{s}$.

Figure 3

Variations of the optical bias $\Delta {\nu }_0$ versus the discharge current $I$. Dots, measurements; dashed curve, pressure difference $P_C-P_A$ between the anode and the cathode (from Ref. 20), with arbitrary scales.

Figure 4

(a) Observation of the Sagnac effect. Dots, experimental beat note frequency with respect to the angular frequency $\Omega$ of the ring interferometer; solid line, linear fit. (b) Observation of the Fresnel drag effect. Dots, experimental nonreciprocal index difference $\Delta n_{\mathit{FE}}$ as a function of the speed $v$ of the intracavity glass plate; dashed line, linear fit.

Figure 5

(a) Longitudinal magnetic field $H$ versus time when the magnets rotate. (b) Beat note frequency versus time when cell $C_1$ is strained. Curve I: $C_1$ and $C_2$ are filled with racemic limonene; Curve II, $C_1$ is filled with $R(+)$ limonene and $C_2$ with $S(-)$ limonene. Curve III, $C_1$ is filled with $S(-)$ limonene and $C_2$ with $R(+)$ limonene. (c) Baseline, beatnote frequency when both cells are filled with racemic limonene and strain is not applied.

Figure 6

Typical evolution of the beat note frequency. (a) $R(+)$ [respectively $S(-)$] limonene is filled in $C_1$ (respectively, $C_2$). (b) Samples interchanged in the cells with respect to (a). Dashed curves: sinusoidal fits. The baseline is shown in Fig. 5c.

Figure 7

Magnetochiral index of limonene $\Delta n_{\mathit{MC}}$ as a function of the magnetic field $H$. Dashed line, linear fit.

Figure 8

(a) Experimental setup to vary the incident polarization on the cells. $L_1$, $L_2$, half-wave plates, with neutral axis at an angle $\gamma$ with respect to the $x$ axis. (b) Corresponding beat note evolution for three values of $\gamma$. The time evolutions in the left column correspond to $R(+)$ limonene in $C_1$ and $S(-)$ limonene in $C_2$. The liquids were interchanged to record the time evolutions in the right column.

Figure 9

Experimental evidence of magnetochiral dispersion: the magnetochiral index of $R(+)$ limonene, $\Delta n_{\mathit{MC}}$, is reported as a function of the magnetic field $H$. Gray line, $\lambda =488\mathrm{nm}$; black line, $\lambda =514\mathrm{nm}$.