Multimode -symmetry thresholds and third-order exceptional points in coupled dielectric waveguides with loss and gain

Abstract

Abstract A pair of coupled dielectric waveguides with balanced loss and gain is the basic system for observing the phenomena of parity-time ( ) symmetry and exceptional points (EPs). We use the multimode analytical approach to study the peculiarities of interaction between the modes excited in such an archetypal structure. With this approach, the conditions for symmetry breaking are obtained in the special case of the hybrid HE and EH modes resulting in the ordinary second-order EPs (or -symmetry thresholds). The coupling of modes with the different azimuthal indices (the TM 01 and HE 21 modes in our study) generates the uncommon types of EPs. First, there are the so-called multimode -symmetry thresholds due to interaction of hybrid and transverse modes. Second, the third-order EPs appear as a result of three-modes degeneracy of real eigenvalues. It is noteworthy that an increase in the EPs order is achieved without both breaking the symmetry and introducing additional elements into the waveguide structure. The results obtained with the multimode analytical approach are in perfect agreement with the independent full-wave simulations.