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It has been shown that for nonlinear atomic ionization, transfer of thedegree of circular polarization from incident to fluorescence light is maximumat the Cooper minimum (see Phys. Rev. A \textbf{100}, 011401(R) (2019)). Untilthe present, however, it is still a challenge to produce and detectcircularly-polarized light at xuv and x-ray photon energies. We here show, thattransfer of linear polarization is strongly enhanced at the Cooper minimum intwo-photon ionization and can be readily detected using current free-electronlaser facilities by measurements of the degree of linear polarization of thecharacteristic $L\alpha_1$ and $L\alpha_2$ lines. Two-photon ionization of$2p_{3/2}$ electron of tungsten atom is proposed to demonstrate the presentedphenomena and realization of such experiment is discussed in detail.

Enhanced polarization transfer to the characteristic $L\alpha$ x-ray lines near the nonlinear Cooper minimum of two-photon ionization