Restricted homogeneous system of tunnel-coupled waveguides and Bragg diffraction of light in it

A system of tunnel-coupled straight waveguides is studied. The dependence of the number of modes in this system on the number N of waveguides, the distance between waveguides, and the number of modes in an individual waveguide is considered. It is shown that modes of the order m=N and N+1 in the system of coupled waveguides are Bragg modes, i.e., the angle between their propagation direction and the system axis is close to the Bragg angle. The effective refractive indices n^* of these modes are different, i.e., the dependence n^*(m) changes abruptly. It is found that radiation modes play an important role in the formation of Bragg modes if an individual waveguide of the system is single-mode and the distance between the waveguides is sufficiently large. It is shown that the angular excitation regions of guided and radiation modes of the system near Bragg angles are overlapped.