Integral field spectroscopy coupled with an extreme adaptive optics system and coronagraphy allows a marked improvement of the standard spectroscopic simultaneous differential imaging calibration technique. Hence, with an integral field spectrograph (IFS) direct imaging of extrasolar giant planets becomes potentially feasible over a wide range of ages, masses, and separations from the hosting stars. This aim represents the prime goal of the planet finder instrument for the VLT (SPHERE). Inside SPHERE, the IFS channel exploits various spectral features of the candidate planets in the near infrared, in order to reduce the speckles noise at the level of the stellar background noise, over a field of view comprised between the coronagraphic inner working angle and the outer working angle provided by the SPHERE extreme adaptive optic system (SAXO). The IFS allows then to realize an extensive spectroscopic simultaneous differential imaging calibration technique, and at least in few cases, to get the spectrum of the candidate extrasolar giant planets. Here we present the IFS baseline design, which is based upon a new optical concept we developed for its integral field unit (BIGRE). When applied to the technical specifications of SPHERE IFS, a BIGRE integral field unit is able to take into account all the effects appearing when integral field spectroscopy is used in diffraction limited conditions and for high-contrast imaging purposes. Finally a BIGRE-oriented IFS optical design is shown here to reach the requested high optical quality by standard lenses-based optical devices.