A Surface Plasmon–Polariton in a Symmetric Dielectric Waveguide with Active Graphene Plates

A theoretical study of the plasmon modes’ characteristics is carried out in a structure consisting of two active graphene layers separated by a dielectric barrier layer. A general dispersion relation is obtained, the numerical analysis of which reveals the possibility of controlling the parameters of amplified surface modes in the region of graphene negative conductivity. In particular, their dispersion is controlled by changing the chemical potential of the graphene layers. For antisymmetric plasmons, their dependence on the barrier layer parameters was revealed. An increase in the chemical potential makes it possible to expand the region of existence of the amplified plasmons, which is accompanied not only by an increase in the amplification coefficient but also by a shift to the region of higher frequencies of the amplified modes. For the first time, modal bistability was also demonstrated in a limited frequency range for antisymmetric plasmons, due to the appearance of additional modes, in which the phase velocity decreases sharply near the cutoff, and the group velocities of the modes entering the bistability turn out to be opposite in sign. The frequency dependences of the real and imaginary parts of the plasmon propagation constant are analyzed, the distributions of wave fields in the structure are plotted, and the frequency dependence of the depth of the plasmon–polariton is given

Поверхностные плазмон-поляритоны в двуслойной графеновой структуре с диэлектрическим барьерным слоем при различных режимах управления

The dispersion dependences of a symmetric dielectric waveguide with graphene plates were compared in two regimes of graphene potential control from two sides of the structure. A general dispersion relation was obtained, the numerical analysis of which reveals the possibility of controlling the parameters of amplified surface modes. A numerical analysis of the dispersion relation solutions in the case of symmetry and asymmetry of the control potential on graphene layers has been carried out. A solution has been found that grows in amplitude with time in the region of negative conductivity of graphene in the presence of an inverse population of the levelsСравниваются дисперсионные зависимости симметричного диэлектрического волновода с графеновыми обкладками в двух режимах управления потенциалом графена с двух сторон структуры. Получено общее дисперсионное соотношение, численный анализ которого выявил возможность управления параметрами усиливаемых поверхностных мод. Проведен численный анализ решений дисперсионного соотношения в случае симметрии и асимметрии управляющего потенциала на графеновых слоях. В области отрицательной проводимости графена при наличии инверсной населенности уровней обнаружено решение, растущее по амплитуде во времен