Scalar Product in the Space of Waveguide Modes of an Open Planar Waveguide

To implement the method of adiabatic waveguide modes for modeling the propagation of polarized monochromatic electromagnetic radiation in irregular integrated optics structures it is necessary to expand the desired solution in basic adiabatic waveguide modes. This expansion requires the use of the scalar product in the space of waveguide vector fields of integrated optics waveguide. This work solves the first stage of this problem - the construction of the scalar product in the space of vector solutions of the eigenmode problem (classical and generalized) waveguide modes of an open planar waveguide. In constructing the mentioned sesquilinear form, we used the Lorentz reciprocity principle of waveguide modes and tensor form of the Ostrogradsky-Gauss theorem.