  The eigenoscillations in a two-dimensional dimer made of gain and lossy
nanoparticles were investigated within exact analytical approach. It was shown
that there are eigenoscillations for which all Joule losses are exactly
compensated by the gain. Among such solutions, there are solutions with a new
type of symmetry, which we refer to as Loss Compensation Symmetry (LCS) as well
as well-known PT (parity-time) symmetric solutions. The modes with LCS unlike
PT symmetric ones allow one to achieve full loss compensation with
significantly less gain that in the case of PT symmetry. This effect paves way
to the new loss compensation methods in optics.
