Modal characteristics of terahertz surface-emitting distributed-feedback lasers with a second-order concentric-circular metal grating

A theoretical model is developed to study the modal characteristics of a second-order concentric-circular metal grating surface-emitting distributed-feedback (DFB) laser operating at terahertz regime. A series of high-order diffracted fields, which can be expressed as a Floquet-Bloch expansion of Hankel functions, is assumed to be generated from the concentric-circular metal grating. The resonant frequencies and transverse profiles of all the diffracted fields can be deduced from the related eigenequations established through the boundary conditions of the interfaces of the metal-dielectric-metal waveguide. The results show that the interference of the diffracted cylindrical waves can form two types of resonant modes, namely, quasisymmetric and quasiantisymmetric modes. Surface radiation is excited mainly by the influence of quasisymmetric modes, which exhibit constructive interference with the grating geometry. Furthermore, the resultant intensities of the diffracted waves decay exponentially from the center of the circular grating, indicating that the proposed grating geometry has the potential to realize surface terahertz radiation with excellent beam quality. The influence of grating duty cycle on the resonant conditions and transverse distributions of the diffracted fields are also investigated.