Efficient coupling of a laser diode to a parabolic microlens tipped circular core photonic crystal fiber using ABCD matrix formalism with consideration for possible misalignments

Abstract

We present, for the first time, a theoretical investigation of coupling optics involving a laser diode and a series of photonic crystal fibers with different air filling ratio and hole pitch via a parabolic microlens of three different focal parameters on the fiber tip in absence and presence of possible transverse and angular misalignments. By employing Gaussian field distributions for both the source and the fiber and also already derived ABCD matrix for parabolic microlens under paraxial approximation, we formulate analytical expressions for the concerned coupling efficiencies for two different light-emitting wavelengths of 1.3 and 1.5 µm, respectively. Further, it is observed that, for a fit focal parameter of 8.0 µm of parabolic microlens, photonic crystal fiber with air filling ratio of 0.35 and hole pitch of 5.0 µm comes out to be the most suitable one to couple laser diode for both wavelengths of practical interest. Moreover, the coupling efficiency can reach to 97.13% for excitement by a laser diode emitting specially light of wavelength λ = 1.3 µm. The analysis should find use in ongoing investigations for optimum launch optics for the design of parabolic microlens on the single mode photonic crystal fiber tip to achieve long working distance.