Research on effective optical path length ratio of hollow waveguide for optical gas sensors

Hollow waveguide (HWG) as an absorption cell for gas spectral sensing has the advantages of low transmission loss, fast response speed, and high path length to volume ratio. However, the transmission of laser beams in HWGs relies on the multiple reflections by the inner wall, and it makes the path length of laser beams emitted from HWGs unequal, thereby limiting the high-precision measurement of gas concentration. Two mathematical models were established based on geometric optics to characterize the effective path length ratio (EPLR) distribution of the laser beam emitted from a straight HWG and a bent HWG, respectively. The effects of HWG parameters and incident conditions on EPLR distribution was investigated, and quantitative analysis was carried out. Experimental verification was performed by basing heterodyne interferometry. A formula to calculate the equivalent path length ratio of a laser beam propagating in an HWG was given, which simplifies the complicated calculation caused by the path length not unique and demonstrates 1-6% reduction in measurement error. The proposed method has guiding significance for high-precision measurement of absorption spectroscopy, and can extend to both substrate-integrated HWG (iHWG) and liquid waveguide capillary cell (LWCC) based optical sensors.