Inthiswork,westudythephotonicbandofcumulativeFibonaccilattices,ofwhichthestructureiscomposedofallgeneratedunitsinaFibonaccisequence.TheresultsarecomparedwithdistributedBraggreflector(DBR)structureswiththesamenumbersoflayers.Photonicbandgapsarefoundattwocharacteristicfrequencies,symmetricallyseparatedfromthecentralbandgapintheDBRcounterpart.FieldamplitudeandphasedistributionintheFibonaccilatticeindicatesaninterferentialoriginofthebandgaps.Fouriertransformontherefractiveindexprofileiscarriedout,andtheresultconfirmsadeterminatelong-rangeperiodicitythatagreeswellwiththephotonicbandstructure.
