Abstract-The mathematical model elaborated in this paper is based on the concept of intrinsic modes in order to analyze and synthesize optical wave propagation along a non-uniform optical structure which is used in integrated optics communication as tapered optical coupler. The new mathematical model is simply developed by introducing modifications to the intrinsic integral, and its numerical evaluation illustrates the electromagnetic field distribution inside a taper thin film and also outside the waveguide constituted by the substrate and the cladding of lower refractive index. The proposed method permits efficiently tracking the behaviour of the optical waves both inside and outside the optical waveguide, and quantifying the radiation and optical coupling occurring from the taper thin film of higher refractive index to adjacent mediums until a total energy transfer; this happens at thicknesses lower than waveguide cutoff thickness of each mode. The new model can be applied to all types of tapered optical coupler, made from different optical materials and having different wedge angles.

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We introduce a mathematical model based on a concept of intrinsic mode in order to analyse and synthesise optical wave propagation and radiation occurring in a non-uniform optical waveguide used in integrated optics as optical coupler. The model is based on numerical evaluation of electromagnetic wave by applying an intrinsic field integral to evaluate the field behaviour inside the optical waveguide. To analyse the field distribution inside the non-uniform waveguide and predict the beam propagation of optical energy involved in the propagation process, it is necessary to track the motion of any observation point along the tapered waveguide itself. Physically, the rays of the spectrum undergo reflections on the waveguide boundaries until the cutoff occurs and the phenomena of radiation begin. The numerical results show good agreement with those obtained by classical methods of evaluation used by other works.