Ray theory of electromagnetic surface-wave modes in integrated optical systems

A systematic ray theory of electromagnetic surface-wave modes in integrated optical systems is presented. It is shown that in a slowly varying, horizontally layered optical waveguide the vertical components of the electromagnetic field satisfy two separate second-order differential equations that correspond to TE and TM modes, respectively. In the horizontal direction, we develop a ray theory; in the vertical direction the application of the transverse resonance conditions leads to an eigenvalue problem. In the vertical direction the resulting solutions then behave as ordinary surface-wave modes, while in the horizontal direction they possess all properties of two-dimensional electromagnetic rays. The properties of the surface-wave ray modes are discussed, in particular their propagation coefficients, for which a stationary expression (in the variational sense) is derived. Applications are briefly indicated.