We have studied the fine structure polarization splitting of exciton emission lines related to isoelectronic centers in an nitrogen-doped GaAs. The nitrogen doping has been performed in atomically controlled way using the ͑3 ϫ 3͒ nitrogen stable surface of GaAs͑001͒, which forms a series of distinct, strong, narrow bandwidth luminescence lines. The localized bound excitons have been found to consist of four signals, which can be selected by linear polarization. Magnetic-field-induced change in the splitting shows a quadratic dependence of the bright exciton splitting owing to the in-plane Zeeman interaction. Our calculations of the optical selection characteristics considering both the J-J coupling and local-field effects demonstrate the polarization splitting depending on the symmetry of the isoelectronic center.Nitrogen ͑N͒ has a strong electronegativity and creates isoelectronic centers in III-V semiconductors such as GaAs and GaP. The electronic states created by the N-related centers cause substantial localization of excitons. Incorporation of a small amount of N atoms leads to dramatic changes in the local electronic structure of the host semiconductor. 1,2 In the impurity limit, the localized electronic states relating to N pairs and N clusters have been observed to show resolution-limited luminescence lines. 3,4 The extremely narrow bandwidth luminescence has been attracting strong interest for light sources such as single photons and eventready polarization entangled photon pairs utilized in quantum information processing. From the same point of view, the atomlike properties of single self-assembled semiconductor quantum dots ͑QDs͒ have been widely studied. 5-10 However, the emission energy is difficult to control and, furthermore, the exchange interactions in the in-plane asymmetries of the QD cause a significant fine structure splitting of the intermediate exciton states, which eventually gives rise to the so-called "which path" information. 9 In contrast to the self-assembled QDs, utilization of the impurity states in semiconductor materials can achieve a narrow bandwidth bound exciton emission with defined photon energy. Recently, each individual bound exciton has been demonstrated to be able to generate single photons. 11-13 Since the fine structure splitting of the impurity center is influenced by the electron-hole exchange interactions and the symmetry, understanding of the detailed structure of the polarization splitting and the interactions in the center is indispensable to control the fine structure.Here, we have studied the fine structure polarization splitting of exciton emission lines related to N pairs in GaAs. The in-plane Zeeman interaction causes a field evolution of the split states. To understand detailed exchange interactions in the centers, we performed calculations of the optical selection characteristics considering both the J-J coupling and local-field effects.N atomic-layer doped GaAs has been grown on an undoped GaAs͑001͒ substrate by molecular-beam epitaxy. Before doping N, a 3...