Finite difference method determination of the nano-hetero-interface wave-function engineering of inter-subband LASER functionality

A novel LASER action nano-hetero-structure of the inter-subband, mid-infrared functionality type is designed on the basis of optically pumped dual resonant tunnelling of conductivity electrons within an appropriately energetically determined scheme of five subbands hosted by two communicating asymmetric, approximately rectangular quantum wells (QWs). The upper LASER action level employed is the second excited subband of the nanostructure's back, wider QW and is provided with electrons via resonant tunnelling from the first excited subband of the nanostructure's front QW populated through remotely ignited optical pumping out of the local fundamental subband. The first excited back QW subband functions as the lower LASER action level, directly delivering the received electrons to the local fundamental subband - via fast vertical longitudinal optical phonon scattering - wherefrom they are being recycled back to the nanostructure's front QW fundamental subband by virtue of a second-reverse sense-resonant tunnelling-mediated normal charge transport mechanism. The handling of the de Broglie wave-function problem evolves into a numerical calculation of a Sturm-Liouville eigensystem solved by means of a finite difference method employing an appropriate tridiagonal coefficient matrix.