Waves in long-range connected waveguide: Single and multiple interaction regions

Plane wave propagation within a conventional waveguide integrated with external spring-like links is investigated. The long-range forces exerted by these additional connections secure the interaction between any two arbitrary distant particles. The long-range operators are assumed to be located inside a window, which itself may include one or several sub-windows. The effects induced by the long-range forces are perceived by examining the corresponding dispersion relation. The modification of the dynamics promotes unconventional phenomena including negative group velocity and wave stopping. Besides, it is shown how the larger the number of included sub-windows, the softer the links and how the two cases of a system equipped with a single sub-window and a system with multiple sub-windows and softer links produce similar effects.