Diamond is a radiation hard material, which makes it suitable for its use in high energy physics experiments as a particle detector. To further reduce the effects of radiation damage, diamond detectors can be fabricated by inscribing graphitic electrodes perpendicular to the surface-the so-called 3D detectors. This can be done via processing with a femtosecond laser. Herein, a systematic study of the cross section of the graphitic wires inscribed into diamond is shown as a function of laser pulse energy, stage translational speed and, for the first time, polarization for a single crystal and polycrystalline chemical vapour deposition (CVD) diamond samples. No dependence of the electrode width with speed polarization and sample for the same pulse energies within uncertainties are observed. The graphitic content of the electrodes is studied in terms of Raman spectrometry: no clear dependence on the fabrication parameters studied is observed.