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In non-hermitian systems, the particular position at which two eigenstatescoalesce under a variation of a parameter in the complex plane is called anexceptional point. A non-perturbative theory is proposed which describes theevolution of modes in 2D open dielectric systems when permittivity distributionis modified. We successfully test this theory in a 2D disordered system topredict the position in the parameter space of the exceptional point betweentwo Anderson-localized states. We observe that the accuracy of the predictiondepends on the number of localized states accounted for. Such an exceptionalpoint is experimentally accessible in practically relevant disordered photonicsystems

Coalescence of Anderson-localized modes at an exceptional point in 2D random media