Remarkable robustness of self-imaging distance for a misaligned paraxial Gaussian input and variation in the nonparaxial regime

Abstract

The variation of focusing distance in a parabolic graded-index slab with the width of a one-dimensional Gaussian input fed at its waist, both axially and misaligned, into the waveguide is studied in paraxial and beyond-paraxial regimes. We obtain analytical expressions, scalable in terms of material parameters, for input coupling coefficients for such a Gaussian input. The focusing distance shows remarkable stability for an axially fed input for beam width exceeding the fundamental mode width of the waveguide. There is a smooth variation for the other regime of beam width. In the paraxial domain, we identify a unique beam width of ∼0.76 times the fundamental mode width for which the self-imaging distance is nearly independent of misalignment. The stability, a well-known sharp shift of the focusing point for an axially fed beam of width around that of the fundamental mode, and remarkable stability of self-imaging distance with misalignment at the unique beam width should be useful for efficiency enhancement of device interconnects, sensing, and lensing applications.