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Summary form only given. A lot of researches have been made under the new class of surface emitting DBR lasers with circular grating up to date. The reason for such interest is the potential possibilities to obtain high-power and low-divergence beam of circular symmetry. Recently, a new idea of grating-coupled surface-emitting lasers (GCSEL) with integrated focusing outcoupler has been proposed. This structure consists of three regions; active, first order grating as a resonator and second order grating as a outcoupler. The purpose of this work is to investigate the effect of the presence of the focusing outcoupler on the mode spectrum at the threshold. In our model the outcoupler is described by the complex reflectivity at the end of first order grating responsible for feedback.