Approximate green´s function representations for the analysis of SAW and leaky wave devices

The Green´s function or boundary element method (BEM) is the preferred technique for rigorous SAW device analysis. However, because of its computational cost, its principal application is the analysis of mode propagation in periodic structures to determine parameters that can then be used in simplified coupling of modes (COM) or P-matrix models. In this paper, rigorous representations are derived that express the Green´s function in terms of a continuous superposition of modes. The derivations include detailed analysis of the Green´s function properties as a function of both frequency and wavenumber, and representations are obtained for both the slowness and spatial domains. Approximate forms are then generated by replacing the continuous mode superposition by a discrete one. The Green´s function can be approximated to any required degree of accuracy, and the resulting approximations are applicable to any type of wave on any type of substrate. The long-range spatial components in the approximate forms are represented by exponential terms. The separable properties of these terms allow this class of approximation to be applied to general SAW and leaky wave device analysis in such a way that the computational effort increases only linearly with device size.