Analytical Dispersion Theory for Optical Waves in Regular Microwaveguides

A method for analysis of dispersion characteristics of guided optical modes propagating in the optical waveguides with small cross-sections is proposed. The method is based on introduction of a correction factor for a longitudinal wavenumber of propagating modes. The correction factor arises when a cross-section of the basic rectangular waveguide is subjected to perturbation. The electromagnetic field distributions along with the mode longitudinal wavenumber are found by means of variable separation method. The longitudinal wavenumber correction factor is analytically calculated in terms of coupled mode theory. The combined use of the complete set of equations of electrodynamics together with the concept of effective sources gives rise to the correction factor in the form of an intermodal coupling coefficient. It is pointed out that the coupling coefficient consists of two components, namely bulk and surface, owing to accurate account of the electrodynamics boundary conditions. Using the method proposed, the dispersion characteristics of the fundamental modes propagating in the practically employed optical waveguides having a trapezoidal cross-section are calculated. An impact of the waveguide cross-section shape to cladding dielectric constant ratio on the mode dispersion characteristics is analyzed. The necessity to take into consideration an imperfection of the waveguide cross-section in a wide range of operating wavelengths is demonstrated