Geometrical phase imprinted on eigenfunctions near an exceptional point

We illustrate how to get the geometric phase from eigenfunctions in the vicinity of an exceptional point in a dielectric microcavity whose non-Hermitian character comes from the outgoing-wave boundary condition. It is shown that the geometrical phase +/-pi can be obtained either from total variation of the inner product of eigenfunctions or from a continuous change of phase plot, not of intensity plot, during a double cyclic parameter variation encircling the exceptional point. One can use either of the two ways by properly choosing the arbitrary phase of the calculated eigenfunctions.