It is known that, for the isolated dielectric cylinder waveguide, there exists the cutoff frequency ω * below which there are no guided (radiationless) modes. It is shown in the paper that the infinite plane periodic array of such waveguides possesses guided modes in the frequency domain which is below the frequency ω * . So far as the finite array is concerned, the modes in this frequency domain are weakly radiating ones, but their quality factor Q increases as Q(N ) ∼ N 3 , N being the number of the waveguides in the array. This dependence is obtained both numerically, using the multiple scattering formalism, and is justified within the framework a simple analytical model.

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We consider here the multi‐flavour electron–hole plasma formed with the charges of opposite signs separated spatially in a bilayer. The temperature of the system is assumed to be smaller than the degenerate temperature of both the electrons and holes. It is found that, if the charge density is sufficiently small, the system has a negative compressibility, and the homogeneous in‐layer charge distribution is thermodynamically unstable. As a result, the system breaks down into 2 co‐existing phases, the denser one being an electron–hole liquid. New sound excitation branch, inherent in the multi‐flavour 2‐dimensional plasma, proves to be unstable exactly for the same density region in which the system is thermodynamically unstable. As the inter‐layer distance increases, the plasmon spectrum of the electron–hole liquid becomes softer for finite momenta. Once the dispersion curve for the plasmon spectrum crosses the momentum axis, the plasmon spectrum becomes unstable. As a result, the system experiences a quantum phase transition leading to the formation of a charge density wave.

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