Photonic Bands and Radiation Losses in Photonic Crystal Waveguides

A method for the theoretical description of two-dimensional (2D) photonic crystals embedded in planar waveguides is presented, which is based on an expansion of the magnetic field in the basis of guided modes of an effective waveguide. The method yields the dispersion of photonic modes below and above the light line, and in the latter case it gives also the radiative losses of quasi-guided modes due to diffraction out of the plane. Photonic bands and gap maps of strong- and weak-index contrast systems display confinement effects and other notable differences compared to the ideal 2D case. The radiative losses in periodic 2D systems are found to increase with the refractive index contrast between core and cladding, and with the radius of the holes in the triangular lattice.