Phase shift at a turning point in a planar optical waveguide

We present a novel matrix approach to proving that the phase shift at a tur ning point in a planar optical waveguide is exactly equal to pi rather than to pi /2 or to some other value, We also show the existence of phase contr ibutions from reflected subwaves, which to our knowledge have never been ta ken into account previously. (C) 2001 Optical Society of America.