Abstract

The method of path integration is applied to the analysis of a model of a graded-index waveguide taper whose refractive index varies with position z along the guide and coordinates x and y transverse to the direction of propagation, as 1 − ½c(z)x2 − ½b2y2. Detailed calculations are presented for the case in which c(z) ∝ 1/z2, which describes the linear taper. Comments are made about tapers corresponding to other forms of c(z). We obtain an exact closed-form solution for the propagator and coupling efficiency of a linearly tapering graded-index waveguide.

© 1991 Optical Society of America

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