Ray analysis of tapered graded-index planar waveguides and fibers

Abstract

Propagation properties of linearly tapered parabolic-index optical waveguides are investigated. Tapers with planar (two-dimensional) and fiber (three-dimensional) geometries are considered. A ray optics approach is used in the analysis, assuming that the characteristic dimensions of tapered waveguides are small compared to the wavelength of light.

Closed form analytical solutions are obtained for ray trajectories in tapers with small slope and small index difference between the core and cladding. To assess the accuracy of analytical solutions, exact ray trajectories in planar waveguides are determined using numerical techniques and compared to those obtained from the analytical method. The agreement between the analytical and numerical solutions is excellent.

It is observed that ray trajectories exhibit the behavior of modulated sinusoidal functions with decreasing amplitude and period as light travels toward the smaller end of the taper. This illustrates the power concentrating capability of the taper.

Applications of these graded-index tapers when used to couple power from light sources to planar and fiber waveguides and when they are used to connect two waveguides of different core sizes are addressed. Coupling efficiencies for light source coupling and radiation loss of tapers when used to connect two dissimilar waveguides are calculated. Numerical results for example cases are provided. A novel application of the taper as collimated beam concentrator is also proposed.