Bridging pole and coupled wave formalisms for grating waveguide resonance analysis and design synthesis.

The algebraic polar expression of resonant reflection from a grating waveguide excited by a free space wave is formulated in terms of the physically meaningful phenomenological parameters of the coupled wave formalism. The reflection coefficient is simply represented as a circle in the complex plane which sheds light on the behaviour of the modulus and phase of anomalous reflection. Analytical expressions are derived for the phenomenological parameters that can now be calculated from optogeometrical quantities which are simple to measure. The relevance and usefulness of bridging the two formalisms is shown in the example of the design of an evanescent wave biosensor.