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Crystals of the layered chalcogenide semiconductor gallium selenide (GaSe) were studied with fluorescence lifetime imaging microscopy in the frequency domain, the excitation source being a cw frequency-doubled Nd:YAG laser modulated between 25 and 50 MHz. The non-zero photoluminescence (PL) lifetime leads to a change of the relative modulation amplitude (m) and a phase lag (phi) of the luminescence with respect to the excitation. The data were analyzed with the polar-plot (or phasor) approach by plotting m sin phi versus m cos phi. Data points of different spots on the sample show strong inhomogeneities and form looping structures in the polar plot. Moreover, they extend distinctly outside the characteristic semi-circle. The latter point is due to the nearly quadratic variation of the PL signal with excitation intensity, whereas the looping structures indicate the presence of energy transfer processes between (at least) two different emitting states. The analysis of the data shows that the same exciton state(s) are involved in both absorption and PL emission of GaSe. (C) 2014 AIP Publishing LLC.