Atheoreticaldesignispresentedfora1×Mwavelength-selectiveswitch（WSS）thatroutesanyoneofNincomingwavelengthsignalstoanyoneofMoutputports.Thisplanaron-chipdevicecomprisesofa1×Ndemultiplexer,agroupofNswitching'trees'actuatedbyelectro-opticalorthermo-opticalmeans,andanM-foldsetofN×1multiplexers.Treesutilize1×2switches.TheWSSinsertionlossisproportionalto(log2（M+N+1）)Alongwithcrosstalkfromtrees,crosstalkispresentateachcross-illuminatedwaveguideintersectionwithintheWSS,andthereareatmostN-1suchcrossingsperpath.TheselossandcrosstalkpropertieswilllikelyplaceapracticallimitofN=M=16upontheWSSsize.Byconstrainingthe1×2switchingenergyto1fJ∕bit,wefindthatresonant,narrowband1×2switchesarerequired.The1×2devicesproposedherearenanobeamMach–Zehndersandasymmetriccontra-directionalcouplerswithgratingassistance.
