Tunable enhancement of the cylindrical Luneburg lens focusing ability with the aid of a conformal graphene strip

We consider the plane wave focusing characteristics of the layered cylindrical Luneburg lens equipped with a conformal strip of graphene, in the H-polarization case. The angular width and location of the strip is arbitrary, and its surface impedance is characterized with the aid of the quantum-physics Kubo formalism. We use a mathematically accurate full-wave analytical regularization technique, which is based on the explicit inversion of the problem static part and yields a Fredholm second-kind matrix equation. This guarantees the convergence of the resulting meshless numerical algorithm. We compute the focusing ability of a microsize lens as a function of the frequency in the wide range up to 60 THz. This analysis shows that a graphene strip, placed into the focal area of the Luneburg lens, enhances its focusing ability at the resonance frequency of the strip plasmon mode proportionally to the quality factor. This frequency is defined by the strip width and is tunable with the aid of graphene’s chemical potential.