Whispering-gallery-mode (WGM) hexagonal optical micro-/nanocavities can be utilized as high-quality (Q) resonators for realizing compact-size low-threshold lasers. In this paper, the progress in WGM hexagonal micro-/nanocavity lasers is reviewed comprehensively. High-Q WGMs in hexagonal cavities are divided into two kinds of resonances propagating along hexagonal and triangular periodic orbits, with distinct mode characteristics according to theoretical analyses and numerical simulations; however, WGMs in a wavelength-scale nanocavity cannot be well described by the ray model. Hexagonal micro-/nanocavity lasers can be constructed by both bottom-up and top-down processes, leading to a diversity of these lasers. The ZnO- or nitride-based semiconductor material generally has a wurtzite crystal structure and typically presents a natural hexagonal cross section. Bottom-up growth guarantees smooth surface faceting and hence reduces the scattering loss effectively. Laser emissions have been successfully demonstrated in hexagonal micro-/nanocavities synthesized with various materials and structures. Furthermore, slight deformation can be easily introduced and precisely controlled in top-down fabrication, which allows lasing-mode manipulation. WGM lasing with excellent single-transverse-mode property was realized in waveguide-coupled ideal and deformed hexagonal microcavity lasers.

Stable dual-mode semiconductor lasers can be applied for the photonic generation of microwave and terahertz waves. In this paper, the mode characteristics of a variable curvature microresonator are investigated by a two-dimensional finite element method for realizing stable dual-mode lasing. The microresonator features a smooth boundary and the same symmetry as a square resonator. A small variable-curvature microresonator with a radius of 4 μm can support the fundamental four-bounce mode and the circular-like mode simultaneously, with quality factors up to the order of 104 and 105, respectively. The dual modes in the phase space of the Poincaré surface of sections distribute far from each other and can maintain enough stability for dual-mode lasing. Furthermore, the refractive index and waveguide can modulate the dual-mode wavelength difference and quality factors efficiently thanks to the spatially separated fields of these two modes.