Analysis of Eigenmodes of Laser Based on Finite Quantum Nanowire Grating

We consider a source-free problem of the H-polarized field in the presence of a finite grating made of quantum nanowires. In the analysis, we use mathematically grounded Lasing Eigenvalue Problem formalism, according to which at the threshold the natural-mode frequency is considered real-valued. We look for it as a part of two-component eigenvalue, together with the corresponding threshold value of material gain in the quantum wires. To build characteristic equation, we use the field expansions in local coordinates of each wire and addition theorems for cylindrical functions. The obtained determinantal equation has a guaranteed convergence. We find grating modes of such laser with the lowest threshold values, and study the dependences of modal thresholds and wavelengths on the various parameters of the grating.