Control of reflectivity and stop bands in a Bragg stack with a four-layer period

We provide a general expression for the band dispersion in a Bragg stack with a four-layer period, and show how the expression is considerably simplified in the case of a perturbed two-layer Bragg stack, where every second layer has refractive index n1 and n2, respectively. We present a range of analytical expressions to describe key features of the band dispersion, including the dependence of the band gap and of the evanescent decay length on variations in layer thickness for TE and TM polarized light incident perpendicular and at an angle to the Bragg stack.