An apparatus for cutting human or animal tissue, such as a cornea, or a lens, said apparatus including: - a laser source for emitting a treatment laser beam in the form of pulses, - a shaping system - such as a spatial light modulator - positioned downstream of the laser source, for transforming the treatment laser beam into a single phase-modulated treatment laser beam, the shaping system being able to modulate the phase of the wavefront of the treatment laser beam according to a modulation set value calculated to distribute the energy of the single modulated treatment laser beam into at least two impact points forming a pattern in a focusing plane, - an optical coupler between the laser source and the shaping system, - a polarization corrector for modifying the polarization of the treatment laser beam upstream of the optical coupler, the polarization corrector being mounted between the laser source and the shaping system, characterized in that: • the optical coupler includes a photonic crystal fiber, and in that • the polarization corrector is configured to modify the polarization of the treatment laser beam upstream of the optical coupler so that the polarization of the treatment laser beam downstream of the optical coupler corresponds to a desired reference polarization, said polarization corrector comprising: ▪ means for measuring a polarization variation between an input end of the optical coupler and an output end of the optical coupler, and ▪ means for modifying the polarization of the treatment laser beam upstream of the optical coupler so as to compensate for the measured polarization variation. - a laser source for emitting a treatment laser beam in the form of pulses, - a shaping system - such as a spatial light modulator - positioned downstream of the laser source, for transforming the treatment laser beam into a single phase-modulated treatment laser beam, the shaping system being able to modulate the phase of the wavefront of the treatment laser beam according to a modulation set value calculated to distribute the energy of the single modulated treatment laser beam into at least two impact points forming a pattern in a focusing plane, - an optical coupler between the laser source and the shaping system, - a polarization corrector for modifying the polarization of the treatment laser beam upstream of the optical coupler, the polarization corrector being mounted between the laser source and the shaping system, • the optical coupler includes a photonic crystal fiber, and in that • the polarization corrector is configured to modify the polarization of the treatment laser beam upstream of the optical coupler so that the polarization of the treatment laser beam downstream of the optical coupler corresponds to a desired reference polarization, said polarization corrector comprising: ▪ means for measuring a polarization variation between an input end of the optical coupler and an output end of the optical coupler, and ▪ means for modifying the polarization of the treatment laser beam upstream of the optical coupler so as to compensate for the measured polarization variation. ▪ means for measuring a polarization variation between an input end of the optical coupler and an output end of the optical coupler, and ▪ means for modifying the polarization of the treatment laser beam upstream of the optical coupler so as to compensate for the measured polarization variation.