ABCD matrix model of quadric interface-lensed fiber and its application in coupling efficiency calculation

In order to simplify the theoretical coupling efficiency calculation of a laser diode (LD) to a single-mode fiber (SMF) with a quadric lens formed on the fiber tip, based on the Gaussian beam approximation, using the ABCD matrix method the relationship between the coupling efficiency and the structure parameters of quadric surface-lensed fiber is studied and analyzed in detail, and the coupling efficiency can reach as high as 99.87% with optimizing parameters of lensed fiber in theoretical simulation. Meanwhile, under paraxial approximation, the ABCD matrix for refraction of different quadric surface micro-lens can be formulated as a unified expression. This result can give some guidance suggestions for fabricating the quadric interface-lensed fiber.