We introduce an original optical cavity design intended to efficiently output-couple extreme ultraviolet (XUV) light produced via cavity-enhanced high harmonic generation (CE-HHG). It supports the amplification of oppositely circularly polarized modes, crossing with a small angle in the high finesse cavity, where circularly polarized HHG scheme (NCP-HHG) will be implemented. We present an analytical model, numerical simulations, and experimental results obtained with a low-power continuous (CW) laser, demonstrating the strong potential of the cavity as an efficient XUV output coupling method. In particular, it is well suited for producing the 7th harmonic (H7) from an Ytterbium frequency comb at 8.4 eV, which is of particular interest for precision nuclear spectroscopy of Thorium.

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