Approaching to a Nanolaser via Hyperbolic Metasurface Supporting Whispering Gallery Modes

We employed coordination transformation and designed a hyperbolic metasurface composed of metallic stripes and air trenches that revealed hyperbolic dispersion curves in the cylindrical coordination. Due to the mismatch of k_q between hyperbolic metasurface and surface plasma polaritons, such metasurfaces could function as a good resonance cavity for surface waves. To validate this idea, we employed finite element method to simulate the designed metasurface composed of a quantum well on top of a GaAs substrate, functioning as an active material, a 100-nm-thick MgF₂ spacer (permittivity of 1.8) and a 100-nm-thick silver (permittivity of -42.495+i×Í0.52152). The calculated mode showed the nature of a whispering gallery mode of TM_9,2 with a quality factor of 66.33, a modal volume of 4×10^-22, the normalized mode volume of 5×10^-3(λ/ 2n)³, and the Purcell factor of 4726. Then, to test the lasing ability of the calculated whispering gallery mode, we used finite difference time domain simulation to demonstrate indeed such a cavity could be lasing at a frequency of 326 THz when optically pumped. Finally, such metasurface could be realized by focus ion beam and we believe that this proposed hyperbolic metasurface could facilitate the development of integrated photonics.