The Bragg reflection waveguide (BRW), or one-dimensional photonic bandgap waveguide, has recently received much
interest for applications such as nonlinear frequency conversion, mechanically tunable air-core filters, and electron
accelerators. One variation of this waveguide is the quarter-wave BRW (QtW-BRW), in which all cladding layers have
a phase thickness of π/2. This places the mode in the center of the cladding stopband, ensuring the strongest possible
confinement for a given pair of cladding materials. In addition, operating at the quarter-wave point permits the effective
index of the guided modes to be given by a simple closed-form expression.
For many applications of BRWs, the dispersion of effective index with frequency is of primary concern. In this
work, we use a perturbation approach to derive analytical expressions for the dispersion of a QtW-BRW, and compare
the results to numerical simulations to demonstrate accuracy. Several interesting properties of these waveguides are
developed. The birefringence of the guides changes sign at the quarter-wave point. For fundamental modes of even
symmetry, the first-order dispersion is always normal if the material dispersion is normal. It is shown that for certain
QtW-BRW designs, group index and group velocity dispersion (GVD) can be orders of magnitude higher than is the
case for their constituent materials, or on the other hand, very small or zero values of GVD can be attained. We will
conclude with a discussion of the applications of such waveguides.