“…1,2 The electron waveguided optics is necessary since in low-dimensional structures, such as 1D and 2D Al C Ga 1−C As nanostructures (where C is a concentration) implementing quantum wells, quantum wires and so on, a pronounced wave nature of the electrons is obtained and therefore both interference and spinor effects must be taken into account; accordingly, the electron optics of these devices would must be formulated by a rigorous quantum spinor wave theory, that is, by solving the Dirac equation. Theoretical and applied studies about electron waveguides based on the Schršdinger equation have been reported in the last years, [1][2][3][4][5] however, to our knowledge, the fully relativistic spinor nature of the guided electron-waves has not been taken into account; that is, a spinor-electron waveguided optics fully based on the Dirac equation has not been developed for 1D and 2D electron wave devices. It must be noted that some works, in the recent past, have developed an electron optics based on approximate solutions of the Dirac equation but very far from these kind of devices, that is, they have been oriented, for instance, to the study of imaging processes with bulk electron lenses; 6,7 only recently a preliminary study 8 has put the basis to find Dirac modes and moreover a particular slab electron guide was solved: a symmetric 2D electron guide, in such a way that original results related to spinor dispersion equations, spinor mode cuttof conditions, and so on, were obtained; these results can not be derived by using or Schrödinger equation either Pauli-Schrödinger equation (that is, the Schrödinger equation corrected with the relativistic term of Pauli); in short, the primary aim of this work is to generalize the above results by solving the spinor-electron waves propagation in asymmetric 2D and 1D electron waveguides and in particular in a channel electron waveguide, which is, to a certain extent, analogous to the vector light waves propagation in dielectric channel waveguides (the building blocks in integrated photonics and optoelectronics) which confine the light in a bidimensional region with a width of the order of the light wavelength.…”