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
Original Manuscript: October 8, 1990
Revised Manuscript: March 7, 1991
Manuscript Accepted: March 14, 1991
Published: August 1, 1991
Constantinos C. Constantinou and Raymund C. Jones, "Path-integral analysis of tapered, graded-index waveguides," J. Opt. Soc. Am. A 8, 1240-1244 (1991)