Performance of a Sagnac interferometer to observe vacuum optical nonlinearity

In quantum electrodynamics, vacuum becomes a nonlinear optical medium: its optical index should be modified in the presence of intense external electromagnetic fields. The DeLLight project (Deflection of Light by Light) aims to observe this effect using intense focused femtosecond laser pulses delivered by LASERIX. The principle is to measure with a Sagnac interferometer the deflection of a low-intensity focused pulse (probe) crossing the vacuum index gradient induced by a high-intensity pulse (pump). A Sagnac interferometer working with femtosecond laser pulses has been developed for the DeLLight project. Compared to previous prototypes, the interferometer now includes the focusing of the probe beam in the interaction area. In this article, we measure and characterize the critical experimental parameters limiting the sensitivity of the interferometer, namely, the extinction factor, the spatial resolution, and the waist at focus of the probe pulse. We discuss future improvements.

Figure 1

Optical scheme of the DeLLight Sagnac interferometer. The pump beam is in red. The probe and reference pulses counterpropagating inside the interferometer are in dark blue. The destructive interference is in light blue. The back-reflections on the rear side of the beamsplitter, used for the beam-pointing suppression, are given in the dashed line. See text for details.

Figure 2

Correction factor $r_{\mathrm{tilt}}$ as a function of the duration $\mathrm{\Delta }t$ (fwhm) of the pump and probe pulses, for two different values of the tilt angle between the probe and the pump beam. The expected signal is around $20\%$ smaller with a pulse duration of 200 fs, compared with 30 fs.

Figure 3

(a), (b) CCD images recorded in the dark output of the DeLLight interferometer at maximal extinction, with a spectral filter and without spatial filter (the white dotted area corresponds to the Region of Interest (RoI) of the expected interference signal): (a) raw intensity profile; (b) same image with saturated back-reflections in order to visualize the residual intensity pattern of the interference signal; (c) distribution of the extinction factor in the RoI shown in the left panel.

Figure 4

Same as Fig. 3 but with both a spatial filter and a spectral filter in the dark output of the interferometer.

Figure 5

Same as Fig. 3 with a spatial filter and no spectral filter in the dark output of the interferometer.

Figure 6

Extinction factor $\mathcal{F}$ as a function of the intensity $I_{\mathrm{in}}$ of the incident pulse entering the interferometer. The extinction factor has been normalized to 1 for the lowest intensity value. Measurements have been performed with a beamsplitter of thickness $e=6.35$ mm, a incident beam size $w=1$ mm, and a pulse duration $\mathrm{\Delta }t\simeq 70$ fs. Data (red dots) are in good agreement with the expected value (blue curve) calculated using Eq. (16) with $n_2=2\times {10}^{-16}$ ${\mathrm{cm}}^2$/W and $\mathrm{\Delta }t=75$ fs.

Figure 7

CCD images of the intensity profiles of the interference signal and the back-reflections in the dark output of the interferometer. (a) Intensity profiles at maximal extinction (interference signal in the white dotted area), with ${\mathcal{F}}_{\max }\simeq 3\times {10}^{-6}$. (b) Intensity profiles with a degraded extinction ${\mathcal{F}}_{\beta }\simeq 5\times {10}^{-4}$.

Figure 8

Spatial resolution ${\sigma }_y$, as a function of the intensity of the pulses $I_{\max }$, given in adu content of the pixel at maximum of the intensity profile, measured with the Basler CCD camera model acA4024-29um. The red points correspond to the measured values from data. The cyan points correspond to the expected shot noise values calculated by Monte Carlo simulations. The fitted cyan line corresponds to the expected variation of the shot noise as a function of the square root of the number of detected photo-electrons.

Figure 9

Measurement of the spatial resolution obtained with 4000 successive laser shots at 10 Hz. (a) Distribution of the barycenters in intensity of the interference signal as a function of the ON-OFF measurement $i$ (with $w_{\mathrm{RoI}}=w/2$). Upper plot: Raw barycenter position for the OFF data ${\overline{y}}_{\mathrm{sig}}^{\mathrm{OFF}}\left(i\right)$ without any pointing correction. Middle plot: ON-OFF subtraction of the raw barycenter positions ${\overline{y}}_{\mathrm{sig}}^{\mathrm{ON}}\left(i\right)-{\overline{y}}_{\mathrm{sig}}^{\mathrm{OFF}}\left(i\right)$. Lower plot: corrected signal $\mathrm{\Delta }y\left(i\right)$, after beam-pointing correction. The achieved spatial resolution is ${\sigma }_y(w_{\mathrm{RoI}}=w/2)=32.5\pm 0.7$ nm and the average signal is $\mathrm{\Delta }y=\langle \mathrm{\Delta }y\left(i\right)\rangle =890\pm 730$ pm, which is compatible with the expected zero value. (b) Corresponding frequency spectra.

Figure 10

Spatial resolution ${\sigma }_y$ as a function of the RoI-size $w_{\mathrm{RoI}}$ (in FWHM unit) with the low-amplification configuration. (Red) Data. (Blue) Monte Carlo simulation with an angular mechanical vibration ${\sigma }_{\theta }=50$ nrad. (Green) Shot noise of the CCD camera (5.86 $\mu \mathrm{m}$) measured on a dedicated test bench.

Figure 11

Same as Fig. 10 but in the high-amplification configuration and an angular mechanical vibration ${\sigma }_{\theta }=70$ nrad for the Monte Carlo simulation.

Figure 12

Expected deflection signal $\mathrm{\Delta }y\left(\mathrm{Up}\text{−}\mathrm{Down}\right)$ (in red) measured in the dark output of the DeLLight interferometer and optimum extinction factor ${\mathcal{F}}_0$ (in blue) as a function of the pulse duration (fwhm), with $E_{\mathrm{pump}}=2.5$ J, $W_0=w_0=5\mu \mathrm{m}$, $f=250$ mm ($w=12.5$ mm), ${\sigma }_y=15$ nm, and ${\theta }_{\mathrm{tilt}}={10}^{\circ }$.