Design and analysis of terahertz surface-emitting distributed-feedback lasers with circular metal grating

Circular surface-emitting quantum-cascade lasers (QCLs) are good candidate to provide high-power low-divergent single-mode terahertz (THz) waves. These devices employ the metallic cladding layer and 2^nd-order circular metal grating to provide surface-coupling mechanism and ultra-high light confinement to improve the lasing efficiency. Under such a big index contrast in metal grating, high-order diffracted waves cannot be overlooked, leading to dramatic change of the transverse modal distribution with the variation of grating duty cycle. Therefore, the conventional coupled-wave technique used for small-index contrast grating becomes inapplicable for this investigation. To solve this problem, we express the field distribution as a Floquet-Bloch expansion of Hankel functions to take into account the high-order diffraction waves. First, the coupled-wave equations of transverse-magnetic mode are derived under the infinite-length approximation. The detailed transverse-mode characteristics of symmetric and anti-symmetric modes supported in the circular waveguide as well as the effects of device parameters are analyzed. Based on the results of infinite-length assumption, the coupled-mode equations of finite-length device are then derived, which allows us to investigate the threshold and modal characteristics of the considered THz surface-emitting circular QCLs. It is observed that the proposed structure has the potential to realize vertical THz radiation with beam quality of subwavelength dimension.