In this section we discuss in more detail the guiding properties of photonic bandgap waveguides, where light is confined in a low refractive index core. We first describe guidance of TE and TM waves in a waveguide featuring an infinite periodic reflector operating at a frequency in the center of a bandgap. In this case, radiation loss from the waveguide core is completely suppressed. We then use perturbation theory to characterize modal propagation loss due to absorption losses of the constitutive materials. Finally, we characterize radiation losses when the confining reflector contains a finite number of layers.

Figure 4.1 presents a schematic of a waveguide with a low refractive index core surrounded by a periodic multilayer reflector. The analysis of guided states in such a waveguide is similar to the analysis of defect states presented at the end of Section 3. As demonstrated in that section, a core of low refractive index nc surrounded by a quarter-wave reflector can support guided modes with propagation constants above the light line of the core refractive index kx ⊂ [0, ωnc]. Note that a core state with kx = 0 defines electromagnetic oscillations perpendicular to a multilayer plane, therefore such a state is a Fabry–Perot resonance rather than a guided mode. In the opposite extreme, a core state with kx ̴ ωnc defines a mode propagating at grazing angles with respect to the walls of a waveguide core, which is typical of the lowest-loss leaky mode of a large-core photonic bandgap waveguide.