GUIDED MODES OF A PLANAR GRADIENT WAVEGUIDE

The mathematical model oflightpropagationin aplanargradient optical waveguide consists of the Maxwell’s equations supplemented by the matter equations and boundary conditions. In the coordinates adapted to the waveguide geometry,theMaxwell’s equationsareseparatedintotwoindependentsetsforthe TE and TM polarizations. Each of the systems can be transformed to a second orderordinarydifferential equation. TheboundaryconditionsforMaxwell’sequations are reduced to two pairs of boundary conditions for the obtained equations. Thus, theproblem ofdescribinga complete set of modesin a regularplanar waveguide is formulated in terms of an eigenvalue problem. For each polarization there are three types of waveguide modes: guided modes, substrate radiation modes, and cover radiation modes. In this work we implement the numerical-analytical calculation of all types of waveguide modes.