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Micro- and nanostructuring with laser-induced periodic surface structures (LIPSS) has been demonstrated to be feasible in a wide variety of materials including metals, semiconductors and dielectrics. Suitable processing regimes for flat, curved and complex surfaces have been identified for many materials, allowing the generation of diverse applications in fields such as optics, tribology and medicine, to name a few. A common side effect when producing such structures in air environment is the formation of a thin surface oxide layer in the laser irradiated areas. Previous studies have shown that oxidation plays an important role in the tribological performance for which the structures where created, and very recently it has been shown that the laser-induced oxide graded layers may contribute to the formation of a new type of embedded low-spatial frequency LIPSS (LSFL) with annomalous orientation parallel to the laser polarization, in addition to the appearance of the well-known high-spatial frequency LIPSS (HSFL) at the surface. In this contribution, we explore this effect experimentally for chromium nitride (CrN) irradiated with femtosecond laser pulses and compare the findings to finite-difference time-domain (FDTD) simulations of the intensity distributions at different depth positions.