The quarter-wave Bragg reflection waveguide: Analytical solutions and properties

摘要

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. In this work, we conduct a thorough analytical investigation of the quarter-wave BRW, in which the transverse wavevector has a phase thickness of π/2 in each layer of the resonant cladding. For this case, 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 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. Finally, a perturbation theory is developed to calculate dispersion and tuning curves for the waveguide.