Modal Near Fields of Tunable Plasmonic Laser Shaped as Circular Quantum Wire Decorated with Graphene Strip

We consider the threshold conditions and field patterns for the modes of a circular quantum wire, made of the gain material, decorated with a conformal graphene strip. The electromagnetic boundary value problem is partially inverted analytically and transformed to a Fredholm second-kind matrix equation. This yields a determinantal equation, which we treat using the Lasing Eigenvalue Problem (LEP) approach, i.e. look for its roots as ordered pairs of the mode-specific real-valued emission frequencies and associated values of the threshold material gain. Preliminary results obtained for a microsize configuration show that the plasmon modes of the strip have lower thresholds than those of the dielectric wire modes and can be tuned in wide range.