Disappearance of modes in planar Bragg waveguides

We show how the forbidden bands of a Bragg reflector may shrink to points and how some classes of the guided modes of a planar Bragg waveguide may disappear altogether by shrinking with the forbidden bands. We derive the general conditions to determine the missing modes and explain these conditions with examples. It is possible, for example, to design a Bragg waveguide that rejects all antisymmetric modes and supports only symmetric modes for the TE polarization. We also highlight the effect of Brewster incidence on the interpretation of the missing modes for the TM polarization. © 2007 Optical Society of America.