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We reanalyze the data on the in-plane far infrared conductivity of underdopedorthoII YBa$_{2}$Cu$_{3}$O$_{6.50}$ (YBCO$_{6.50}$) in terms of a model inwhich a pseudogap opens on part of the Fermi surface with the remaining ungapedpiece proportional to the temperature. The motivation for our model comes fromrecent angle-resolved photoemission spectroscopy data in underdopedBi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212), which have revealed the existenceof arcs on the Fermi surface. We find the optical data to be consistent witharc formation. In addition we find some evidence that the electronic stateslost below the pseudogap energy $\Delta_{pg}$ are recovered in the energyregion immediately above it at least for temperatures near $T_c$.

Fermi surface arcs and the infrared conductivity of underdoped YBa$_{2}$Cu$_{3}$O$_{6.50}$