Exceptional points in trimers of dielectric cylinders

Eigenmodes in equilateral and isosceles triangular trimers of infinite cylinders have been studied using the theory of multiwave scattering. Equations have been derived for the eigenfrequencies of the exceptional points where eigenfrequencies and eigenvectors are degenerate. The symmetry of the isosceles triangular trimer determines the separation of modes antisymmetric in the base direction. In the case of the equilateral triangular trimer, modes are separated into symmetric and double degenerate rotational modes. It has been found that damping symmetric modes in the trimer have a higher $Q$-factor compared to a dimer, which is of significant importance for applications of effects based on exceptional points. The behavior of complex eigenfrequencies in the isosceles triangular trimer has also been studied depending on the ratio of the lengths of its base and leg. At the point corresponding to the equilateral triangular trimer, the $Q$-factors of symmetric and antisymmetric modes have the local maximum and minimum, respectively.