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tokens: range to obtain the constant horizontal polarisation pattern we are looking for. If these structures have an optical depth that is too low or too high, the central belt shows multiple scatterings as seen in both Figs. 12 and 13 . In extreme cases with very high optical depth in the outer torus, we have no photons in this region, a case close to the simulations of model 2 (see Fig. 7 ). These two conditions seem to be important to produce the features we are expecting. A last remark is that the photons detected from the ionisation cone are no longer just scattered once at high optical depth in the cone ( Fig. 12 ). However, the centrosymmetric pattern seems to be approximatively conserved for double scattering in the cone. 4.4 Reproducing the NGC 1068 observations Based on previous simulations, we tried to reproduce the SPHERE observations of NGC 1068. As we observed constant polarisation orientation in the core of NGC 1068 in both the H and Ks bands, we need in our simulation an optical depth τ ≥ 20 at 2.2 μ m to be able to generate such polarisation features. We changed our previous model 5 to adapt it to these larger wavelengths. Here, the torus has an optical depth τ Ks = 19, which gives τ H = 35 and τ V =169. We note that this is in therange of the current estimation of the density of dust in the torus (see Sect. 5.6 ). For this simulation we used a mixture of silicates and graphites to rely on a realistic dust composition for an AGN, inspired by Wolf Henning (1999) . We adapted their mass ratio to a number ratio according to Guillet (2008) leading to 57% silicates, 28.67% parallel graphites, and 14.33% orthogonal graphites. With these parameters, the maps in Fig. 14 are now able to reproduce some of the observed features. Namely, the nearly constant horizontal polarisation in the central part is similar to that observed on NGC 1068 at 1.6 and 2.2 μ m. We are, however, not yet able to reproduce the ridge that appears at the very centre of the SPHERE observations. Fig. 14 Maps of the observed averaged number of scattering with an inclination angle of 90 ° at 1.6 ( top ) and 2.2 μ m ( bottom ). Polarisation vectors are shown, their lengths being proportional to the polarisation degree and their position angles representing the polarisation angle. 5 Discussion 5.1 Photons significance One major concern is the simulation strategy of conserving the packets until they exit the simulation box, whatever their number of interactions.We must verify to what extent the detected photons are relevant. The energy of each packet is decreased according to the albedo at each interaction, as is the number of photons in the packet. Therefore, it is common at the end to record photon packets with energies 10 4 times lower than the initial energy. If a high energy packet reaches a pixel previously populated only with low energy ones, it will totally dominate the pixel so that Q and U values and the polarisation parameters will be essentially linked to this