Context :

Aims : In this paper , we aim to constrain the properties of dust structures in the central first parsecs of Active Galactic Nuclei ( AGN ) .
Our goal is to study the required optical depth and composition of different dusty and ionised structures .

Methods : We developed a radiative transfer code , MontAGN , optimised for polarimetric observations in the infrared .
With both this code and STOKES , designed to be relevant from the hard X-ray band to near-infrared wavelengths , we investigate the polarisation emerging from a characteristic model of the AGN environment .
For that purpose , we compare predictions of our models with previous infrared observations of NGC 1068 , and try to reproduce several key polarisation patterns revealed by polarisation mapping .

Results : We constrain the required dust structures as well as their densities .
More precisely , we find out that the electron density inside the ionisation cone is about 2.0 \times 10 ^ { 9 } m ^ { -3 } .
With structures constituted of spherical grains of constant density , we also highlight that the torus should be thicker than 20 in term of K band optical depth to block direct light from the centre .
It should also have a stratification in density , with a lesser dense outer rim with an optical depth at 2.2 \mu m typically between 0.8 and 4 for observing the double scattering effect previously proposed .

Conclusions : We bring constraints on the dust structures in the inner parsecs of an AGN model supposed to describe NGC 1068 .
When compared to observations , this leads to optical depth of at least 20 in Ks band for the torus of NGC 1068 , corresponding to \tau _ { V } \approx 170 , which is within the range of current estimation based on observations .
In the future , we will improve our study by including non uniform dust structures and aligned elongated grains to constrain other possible interpretations of the observations .