Coupling of a laser diode to single mode circular core graded index fiber via hyperbolic microlens on the fiber tip and identification of the suitable refractive index profile with consideration for possible misalignments

Abstract

With an aim to explore the suitable refractive index profile for maximum coupling, we present a theoretical investigation of coupling optics involving a laser diode and single mode circular core graded index fiber via a hyperbolic microlens on the fiber tip in absence and presence of any possible transverse and angular misalignments. By employing Gaussian field distributions for both the source and the fiber and also ABCD matrix for hyperbolic microlens under paraxial approximation, we formulate analytical expressions for the concerned coupling efficiencies. The investigations are performed for two different light-emitting wavelengths of 1.3 and 1.5 μm for such fibers with different profile exponents in refractive index profile. Further, it is observed that out of the studied refractive index profiles, the triangular index profile having the dispersion-shifted merit comes out to be the most suitable profile to couple laser diode to single mode circular core graded index fiber for two wavelengths of practical interest. The analysis should find use in ongoing investigations for optimum launch optics for the design of hyperbolic microlens either directly on the graded index circular core single mode fiber tip or such fiber attached to single mode fiber to achieve a long working distance.