The PBG guiding mechanism can be explained either by the anti-resonant reflecting optical waveguides (ARROW) model [
16] or by the coupled mode theory [
17]. These methods have also been applied to estimate the spectral position of the bandgaps [
18–
20]. Guiding light in a low-index core can be described in terms of anti-resonant scattering of the light at surrounding dielectric optical cavities. At resonance those cavities are transparent and light will escape from the core, while for wavelengths between resonances light is reflected back and in this way confined to the core. ARROW model was first considered with planar geometries [
21], where the high-index cladding constituted a Fabry-Perot like resonator. Similar arguments were later on used for a cladding structure consisting of dielectric cylinders [
16,
22–
24]. With the high refractive index inclusions, the filled holes form isolated cladding waveguides. The allowed states of the cladding waveguide form bands of super modes, which split up in effective index and bandgaps are formed between the bands. First band contains coupled states of LP
01 modes, second band contains coupled states of LP
11 modes, etc. When the high refractive index inclusions are anisotropic, in this case LCs, the individual bands of super modes further split up due to the different electric field distributions of transverse electric (TE), transverse magnetic (TM) and hybrid modes. New and narrow bandgaps can be formed [
25]. The notch appearing in the transmission spectrum is caused by a cladding mode crossing a bandgap, forming a so-called “avoided-crossing” with the core mode of the bandgap [
26].