This paper shows the possibility of the use of a solid-state alexandrite laser as a radiation source for the method of spin-exchange optical pumping of noble gases (xenon, krypton). The use of dispersive optical elements in the laser cavity will allows the adjusting of the radiation wavelength exactly in the rubidium spectral absorption lines 794.7 nm and 780 nm. To obtain a hyperpolarized state of noble gases, it is necessary to excite rubidium atoms for further spin-exchange process with the noble gas nuclei. This fact will allow the increasing of the magnetic resonance imaging contrast in the field of diagnosis of respiratory organs diseases.