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Muon pairs can be produced in the annihilation of ultra-high energy (UHE, $E\gtrsim 10^{18} \,\mathrm{eV}$) photons with low energy cosmic backgroundradiation in the intergalactic space, giving birth to neutrinos. Although thebranching ratio of muon pair production is low, products of other channels,which are mainly electron/positron pairs, will probably transfer most of theirenergies into the new generated UHE photon in the subsequent interaction withthe cosmic background radiation via Compton scattering in deep Klein-Nishinaregime. The regeneration of these new UHE photons then provides a second chanceto produce the muon pairs, enhancing the neutrino flux. We investigate theneutrino production in the propagation of UHE photons in the intergalacticspace at different redshifts, considering various competing processes such aspair production, double pair production for UHE photons, and triplet productionand synchrotron radiation for UHE electrons. Regarding the least energeticoutgoing particles as energy loss, we obtain the effective penetration lengthof the leading particle, as well as energy loss rate including the neutrinoemission rate in the cascade process. Finally, we find that an extra componentof UHE neutrinos will arise from the propagation of UHE cosmic rays due to thegenerated UHE photons and electron/positrons. However, the flux of thiscomponent is quite small, with a flux of at most $10\%$ of that of theconventional cosmogenic neutrino at a few EeV, in the absence of a strongintergalactic magnetic field and a strong cosmic radio background. The precisecontribution of extra component depends on several factors, e.g., cosmic radiobackground, intergalactic magnetic field, the spectrum of proton, which will bediscussed in this work.

Neutrino Production in Electromagnetic Cascades: An extra component of cosmogenic neutrino at ultrahigh energies