Modal cutoff and the V parameter in photonic crystal fibers

We address the long-standing unresolved problem concerning the $V$ parameter in a photonic crystal fiber. In formulating the parameter appropriate for a core defect in a periodic structure, we argue that the multimode cutoff occurs at a wavelength ${\lambda }^{*}$ that satisfies $V_{\mathrm{PCF}}\left({\lambda }^{*}\right)=\pi$. By comparing this approach with numerics and recent cutoff calculations we confirm this result.