Electromagnetic Engineering of a Single-Mode Nanolaser on a Metal Plasmonic Strip Placed into a Circular Quantum Wire

We investigate the emission of waves by a thin silver nanostrip placed into the center of a circular quantum wire (QWR), in the visible-light range. Our analysis uses the mathematically grounded approach called lasing eigenvalue problem (LEP). Keeping in mind that at the threshold the lasing-mode frequency is real valued (does not attenuate in time), the LEP is formulated as a boundary-value problem for the Maxwell equations with exact boundary conditions and the Sommerfeld radiation condition. The eigenvalues are pairs of real numbers, where the first is the emission wavelength and the second is the associated threshold value of material gain in the QWR. Due to the twofold symmetry of the cross-sectional geometry, we split the studied problem into four different independent classes of symmetry and derive four symmetry-adapted Green's functions of the QWR without strip. On imposing the generalized boundary conditions and taking into account these Green's functions, we obtain four independent integral equations (IEs) at strip's median line. We discretize these IEs with the Nystrom-type schemes and further look for the eigenvalues of each class separately with the aid of iterative search algorithm. Our analysis shows that such a plasmonic-strip-based nanolaser can emit visible light on the localized surface plasmon modes and also on the shell modes or QWR polariton modes perturbed by the strip. Single-mode operation is apparently possible provided that the QWR diameter is small, and hence, the first shell mode is blue-shifted.