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Spinor–electron waveguided optics based on the Dirac equation

A preliminary quantum analysis, based on the Dirac equation, of the propagation of spinor–electron waves in electron waveguides is presented. The wave equations for spin-up (SU) and spin-down (SD) electron waves in electron guides are derived and their analogy with TE and TM light modes in dielectric guides is stressed. The spinor–electron waveguided propagation in a electron wave slab waveguide is solved exactly using the Dirac equation, that is, the exact amplitudes and dispersion equations of the spinor–electron waveguided modes are calculated. The main consequences related to the spinor modal structure are discussed: phase retardations (spin polarization), modal cutoff conditions and the non-relativistic limit.