A modified WKB method for the improved phase shift at a turning point

Author

Xiang, Feng ; Yip, Gar Lam

Author_Institution

Dept. of Electr. Eng., McGill Univ., Montreal, Que., Canada

Volume

12

Issue

3

fYear

1994

fDate

3/1/1994 12:00:00 AM

Firstpage

443

Lastpage

452

Abstract

With the presence of an index or/and index slope discontinuity in a planar waveguide, the phase shift at the turning point which is near or at the discontinuity is no longer a constant (π/2) as in the conventional WKB method. In this paper, we present analytical expressions of this phase shift. Not only the index discontinuity, but also the index slope discontinuity have been taken into account in deriving these expressions. Numerical results show a significant improvement over the conventional WKB method after a modified phase shift has been used. According to our results, the phase shift is π/6 instead of π/2 or zero at the cutoff for a waveguide with a truncated index profile. As a by-product, we found a more accurate phase shift expression for the total internal reflection at an index discontinuity where the index slopes on both sides of the discontinuity have been considered

Keywords

WKB calculations; integrated optics; optical waveguide theory; optical waveguides; refractive index; accurate phase shift expression; improved phase shift; index discontinuity; index slope discontinuity; modified WKB method; modified phase shift; planar waveguide; total internal reflection; truncated index profile; turning point; Frequency; Helium; Optical reflection; Optical surface waves; Optical waveguides; Planar waveguides; Propagation constant; Surface waves; Turning; Waveguide discontinuities;

fLanguage

English

Journal_Title

Lightwave Technology, Journal of

Publisher

ieee

ISSN

0733-8724

Type

jour

DOI

10.1109/50.285327

Filename

285327