Properties of the quarter-wave Bragg reflection waveguide: theory

The Bragg reflection waveguide (BRW), or one-dimensional photonic crystal waveguide, has recently been proposed for a wide spectrum of applications ranging from particle acceleration to nonlinear frequency conversion. Here, we conduct a thorough analytical investigation of the quarter-wave BRW, in which the layers of the resonant cladding have a thickness corresponding to one quarter of the transverse wavelength of a desired guided mode. An analytical solution to the mode dispersion equation is derived, and it is shown that the quarter-wave BRW is polarization degenerate, although the TE and TM mode profiles differ significantly as the external Brewster's angle condition in the cladding is approached. Analytical expressions for waveguide properties such as the modal normalization constants, propagation loss, and overlap factors between the mode and each waveguide layer are derived, as are dispersion and tuning curves. (c) 2006 Optical Society of America.