3D localization in a channel waveguide in a photonic crystal with 2D periodicity

A high refractive index plate with a periodic system of holes (a planar photonic crystal, PPC) is considered. The thickness of the plate as well as the distance between holes is comparable with the light wavelength. Three-dimensional band structure calculations show that a PPC supporting only a few guided modes (by keeping the thickness of the PPC small enough) can have a photonic band gap (PBG). A missing row of holes in a PPC with a PBG acts as a channel waveguide and can support modes of two types: refractive modes and diffractive ones. In-plane confinement of the latter is due to the PBG. The dispersion curves of diffractive modes have points where the group velocity is equal to zero, enabling localization of light in the direction of the waveguide. Thus, 3D localization of light takes place, localization in the direction perpendicular to the plane of the slab being due to the complete internal reflection and localization in the plane of the slab being due to the diffraction on the photonic crystal lattice.

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