  The efficient amplification and lasing of electromagnetic radiation at
terahertz (THz) frequencies is a non-trivial task achieved mainly by quantum
cascade laser configurations with limited tunability and narrowband
functionality. There is a strong need of compact and efficient THz
electromagnetic sources with reconfigurable operation in a broad frequency
range. Photoexcited graphene can act as the gain medium to produce coherent
radiation at low THz frequencies but its response is very weak due to its
ultrathin thickness. In this work, we demonstrate an alternative design to
achieve efficient tunable and compact THz amplifiers and lasers with broadband
operation based on active THz hyperbolic metamaterials (HMM) designed by
multiple stacked photoexcited graphene layers separated by thin dielectric
sheets. The hyperbolic THz response of the proposed ultrathin active HMM is
analytically and numerically studied and characterized. When the graphene-based
HMM structure is periodically patterned, a broadband slow-wave propagation
regime is identified, thanks to the hyperbolic dispersion. In this scenario,
reconfigurable amplification of THz waves in a broad frequency range is
obtained, which can be made tunable by varying the quasi-Fermi level of
graphene. We demonstrate that the THz response of the presented tunable THz
amplifiers or lasers is controlled by the incident optical pumping
(photodoping) and the loaded dielectric materials in the HMM waveguide array,
an interesting property that can have great potential for THz amplification,
emission, and sensing applications.
