Light localization effects in a quasi-homogeneous rhombic waveguide array

Use is made of the coupled-mode method to theoretically study the effects of laser radiation propagation in a quasi-one-dimensional rhombic waveguide array consisting of three parallel waveguide arrays, with the interaction of each waveguide with its nearest neighbors and between the waveguides of the arrays taken into account. Analytical expressions are derived that allow one to accurately predict the occurrence of the light localization effect in relation to the values of the coupling constants. It is shown that the spectrum of linear waves in the system has one flat band. A particular solution of the system of coupled-wave equations is obtained, which describes strongly localized radiation propagating without transverse diffraction along the entire array. The parameter values are found for which the Anderson localization effect is observed in the rhombic array.