Modeling of quasi-guiding light within the lower refractive index core layer(s)

It is well known that light can be guided within layer(s) having refractive index higher than that of the surroundings by means of the total internal reflection principles. However, using a proper structure, light can also be quasi-confined into layer(s) with refractive indices lower than the surroundings. In this case the light is quasi-guided. In this work, we will show that using proper mathematical tools we can model the latter case of confining light. We used the Galerkin finite element method with Sommerfeld-like boundary conditions to conduct numerical investigations on this class of structures. We investigate numerically the properties of the anti-resonant reflecting optical waveguides (ARROW), leaky step- and graded-index waveguides, planar Bragg and hollow waveguides. Through the modal solutions (i.e. the complex-valued mode indices and modal field profiles), we present an intuitive interpretation of the unique properties of such structures, e.g. the anti-crossing between core and cladding resonance modes in ARROW, the growing-up of field in the high-index substrate/cladding of leaky waveguides, and the relation between Bragg and hollow waveguides.