Calculation of the coupling coefficient of two optical waveguide ends separated by layered medium

The coupling coefficient between two optical waveguide ends which are separated by a layered medium is calculated. The coupling is determined between given modes of the waveguides. The optical beam propagating in the three-dimensional structure is represented as an angular spectrum of electromagnetic plane waves. The coupled field is calculated by fulfilling the boundary conditions for the plane wave components at the planes separating the layers. The maximum coupling is calculated by optimizing the characteristic data of the layer between the two waveguides. A two-dimensional example is presented where the attenuation is minimized by optimizing the refractive index and thickness of the separating layer. The attenuation versus the thickness of the separating layer is also calculated