“…Especially, the wavelength converter that can convert a signal to one of the wavelength in Λ is referred to as FWC. For example, FWC can be expressed as WC( [1], Λ), WC(Λ, [1]) or WC[Λ, Λ]). We also define [i, j] as a subset of ( j − i) wavelengths {λ i , λ i+1 , ..., λ j−1 }, and In current AWG-based nonblocking WXC designs, two different request models have been mainly considered [9], [10], namely the (λ, F, λ , F ) and (λ, F, F ) request models.…”