The　2D　Maxwell　eigenproblems　are　studied　from　a　new　point　of　view.　An　electromagnetic　problem　is　cast　from　the　Lagrangian　system　with　single　variable　into　the　Hamiltonian　system　with　dual　variables.　The　electric　and　magnetic　components　transverse　to　the　wave　propagation　direction　are　treated　as　dual　variables　to　each　other.　Higher　order　curl-conforming　and　divergence-conforming　vector　basis　functions　are　used　to　construct　dual　vector　spectral　elements.　Numerical　examples　demonstrate　some　unique　advantages　of　the　proposed　method.