Dispersion of a planarized double metal waveguide of a quantum cascade laser in the Sub-THz frequency range

We present an analytically precise equation for calculating dispersion of modes propagating in a planarized double metal waveguide of a quantum cascade laser (QCL). The resulting solution is based on a modification of Marcatili’s method, which involves specifying ideal conductor-type boundary conditions at metal contact points with the active region. The absence of a cutoff frequency for the fundamental mode E^y₀₀ is demonstrated, and dispersion of this mode is studied in the frequency range below 1 THz, including the microwave range. To estimate the possible value of the real refractive index of the QCL heterostructure, various electron density distribution profiles along the cascade are considered.