Effective numerical aperture of antiresonant hollow core fibers

We present an analytical framework for characterizing the light coupling behavior of antiresonant hollow core fibers (AR-HCFs) through the introduction of an effective numerical aperture. This concept is particularly relevant for few-mode AR-HCFs, which are increasingly employed in applications such as low-loss delivery of multi-kilowatt-level laser beams and ultra-low latency communication in high-frequency trading and data center environments. Our model defines effective numerical aperture based on the divergence angles of higher-order modes supported by fiber. To validate this approach, we selectively excited individual hollow-core modes in an AR-HCF and measured their divergence using far-field intensity profiles. The measured values showed excellent agreement with theoretical predictions, confirming the validity of the model. This study provides a practical and intuitive tool for evaluating the free-space coupling characteristics of specific spatial modes in AR-HCFs, addressing a critical gap in the understanding of multimode fiber behavior.