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Loss compensation via inserting gain is of fundamental importance indifferent branches of photonics, nanoplasmonics, and metamaterial science. Thiseffect has found an impressive implementation in the parity-time symmetric(PT-symmetric) structures possessing balanced distribution of loss and gain. Inthis work, we generalize this phenomenon to the asymmetric systemsdemonstrating loss compensation in the coupled multi-mode loss-gain dielectricwaveguides of different radii. We show that similar to the PT-symmetric coupledsingle-mode waveguides of identical radii, the asymmetric systems support theexceptional points called here the loss compensation (LC) thresholds where thefrequency spectrum undergoes a transition from complex to real values.Moreover, the LC-symmetry thresholds can be obtained for dissimilar modesexcited in the waveguides providing an additional degree of freedom to controlthe system response. In particular, changing loss and gain of asymmetriccoupled waveguides, we observe loss compensation for TM and TE modes as well asfor the hybrid HE and EH modes.

Multimode parity-time and loss-compensation symmetries in coupled waveguides with loss and gain