SUSY transformation of guided modes in semiconductor waveguides

Properly designed waveguides are of great importance for efficient operation of mid-infrared and tera-hertz quantum cascade semiconductor laser. Such waveguides comprise layers with suitably chosen doping, which determines refractive index, which enables bound modes to exist. It is of great interest to tailor the structure so to get minimal losses and maximal modal overlap with the active (gain) layer. In this paper we use the analogy between the Schrödinger and Helmholtz equations, and employ supersymmetric quantum mechanics, extended into the complex domain, in order to vary refractive index profile in search for better waveguide design.