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