Epsilon-near-zero
(ENZ) mode, supported by a thin layer at the
frequency where the real part of the dielectric constant vanishes,
can significantly enhance the light–matter interaction at the
deep subwavelength scale. However, ENZ modes exhibit the flat spectral
dispersion which results in small group velocities and extremely short
propagation lengths. Here, we propose a strong coupling system consisting
of a polar dielectric GaAs nanolayer and a graphene sheet. In this
system, ENZ mode and graphene plasmon (GP) mode can be simultaneously
excited and they strongly couple with each other. The dispersions
of the coupled ENZ–GP modes are characterized by an anti-crossing
effect with a Rabi splitting energy on the order of 1/3 of the mode
frequency. The figures of merit for the coupled modes, defined as
the propagation length times the field confinement factor, are much
larger than those of the uncoupled single mode. The hybridized ENZ–GP
modes exhibit the combined features of long propagation length and
strong optical field confinement, which can be used in the field of
nanophotonic integration and communication.