We propose a set of numerical and analytical tools to address electromagnetic wave propagation in dielectric mirrors and waveguides designed on the principles of omnidirectional reflectivity. Design concepts of the broad frequency range of omnireflectivity will be presented, as well as the deleterious role of imperfections in scattering to the surface and radiation states will be investigated. Omnidirectional reflector technology will have a meaningful commercial effect in multiple markets, including efficient radiation delivery at any desirable wavelengths, in particular, visible and mid IR ranges. Anticipated applications include high power delivery of visible to mid IR radiation for laser surgery, as well as for industrial cutting and welding laser tools. IR spectroscopy for medical diagnostics. IR image transmission and optical communications.