Guiding Pure Vector Mode in Hollow Core Fiber Based on a Momentum Selection Theory

The attraction of hollow core fibers (HCF) lies in the long-distance mode retention ability and the transmission speed close to physical limit. Long-term efforts have been made to get a balance between large core and pure mode. However, the unique light guide mechanism of HCFs makes it a difficult question to decrease the number of the allowed modes. New theory of mode control in such fibers is desired. In this paper, we propose a new space for observing optical states based on the principle of representation transformation, so-called the wave vector space (k-space). The mode observation in the k-space provides a different perspective where the mechanical properties of the light are more obvious. We observe typical fiber modes in the k-space and clarify differences of their momentum characteristics, based on which a mode selection principle is proposed. As a theoretical proof of the principle, a novel 19-cell hollow-core photonic bandgap fiber (HC-PBGF) structure that only supports single pure vector mode is exhibited. The designed optical fiber supports only TE01 mode over a bandwidth of 80 nm with the lowest loss of 0.8 dB/km. This example proves the practicality of the proposed momentum selection theory and will inspire breakthroughs in other optical studies.