A new kind of nonresonant optical recirculator, dedicated to the production of γ rays by means of Compton backscattering, is described. This novel instrument, inspired by optical multipass systems, has its design focused on high flux and very small spectral bandwidth of the γ -ray beam. It has been developed to fulfill the project specifications of the European Extreme Light Infrastructure “Nuclear Pillar,” i.e., the Gamma Beam System. Our system allows a single high power laser pulse to recirculate 32 times synchronized on the radio frequency driving accelerating cavities for the electron beam. Namely, the polarization of the laser beam and crossing angle between laser and electrons are preserved all along the 32 passes. Moreover, optical aberrations are kept at a negligible level. The general tools developed for designing, optimizing, and aligning the system are described. A detailed simulation demonstrates the high efficiency of the device.