In this thesis, I explore an innovative way of designing high resolution spectrograph using Adaptive Optics. Most of the RV spectrographs are installed on 4 meter class telescopes and are working in seeing-limited conditions, however, a strong limitation for the adaptation of this instrumentation onto large telescope exists. Telescopes and radial-velocity spectrographs size issue as well as the technology proposed to overcome this problem (Adaptive Optics) are addressed in this thesis. With adaptive optics the telescope optical étendue can be reduced without loosing photons, thus allow us to build very compact spectrographs, cheaper and easier to stabilized. Moreover, a direct application of this concept is presented through this thesis with the NIRPS instrument.