Abstract
This paper presents an electromagnetic consistent model for the scattering behaviour of reconfigurable intelligent surfaces (RISs) illuminated by multiple incident waves in complex indoor environments. The proposed model addresses the fundamental gap between idealised analytical formulations and realistic multipath excitation conditions typically encountered in indoor propagation. By combining principles of physical optics and diffraction grating theory, closed-form expressions for the reflection coefficients of all Floquet-Bloch modes are derived as explicit functions of arbitrary incident angles, phases, and amplitudes. The formulation captures multimode reradiation, parasitic scattering, and diffuse components in a computationally efficient manner, enabling seamless integration into large-scale ray-based simulators. Validation through full-wave simulations demonstrates the accuracy and generality of the model across a wide range of excitation and configuration parameters. The proposed approach provides a practical yet physics-based framework for analysing, designing, and optimising RIS-assisted wireless systems in realistic indoor multipath environments.