Dispersion properties of planar Bragg waveguides

We reformulate the leaky mode condition of planar Bragg waveguides as two simple, separate conditions on the propagation constant; a phase match condition and a loss formula. These relations enable efficient numerical calculations of the mode properties. Furthermore, we use the phase match condition as a starting point to discuss the dispersion of waveguides with advanced cladding structures. In particular, we point out that chirped claddings, where the effective reflection point is dependent on frequency, do not give dispersion characteristics significantly different from metallic waveguides or waveguides with periodic claddings.