In order to get efficient transport of pump power through an active medium, we have used an optical cavity for pumping a solid-state thin-disc laser. Through this method, it is possible to recycle a pump system and combine a homogenizer and a pump system. In this system, a quasi-cavity is employed such that it is equipped, on both sides, with mirrors that have a transparent hole at their centres. In this work, the necessary conditions for recycling a pump system have been derived analytically. Moreover, the dependence of the absorption efficiency on the geometrical dimensions of the optical cavity, the divergence of the injected pump beam and the length of the quasi-cavity have been investigated, respectively.