The data recording device comprises a two-dimensional array of microdots of nanometric dimensions arranged facing a storage medium. The storage medium comprises a sensitive area preferably comprising a flexible membrane and extended at its periphery by a flexible fixing membrane. The sensitive area of the storage medium is thus flexibly fixed to an external frame, allowing movement of the sensitive area in its plane and perpendicularly to its plane. The microdots are preferably formed on a convex front face of a substrate, enabling contact between each of the microdots and the sensitive area to be ensured in all cases. The radius of curvature of the convex surface is preferably comprised between 0.5 m and 5 m.