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Space-mapping (SM) technique is applied for design optimization of antireflection (AR) coatings for photonic devices such as the semiconductor optical amplifiers (SOA). The approximate and efficient transfer matrix method (TMM) serves as the coarse model for design optimization, whereas the time-intensive and accurate finite-difference time-domain (FDTD) method is used as the fine model for model calibration. A mapping is established between the parameter spaces of the coarse and the fine models so that the fine model design becomes the inverse mapping of the optimized coarse model design. Remarkable performance of the SM technique in terms of efficiency and accuracy in the design optimization is demonstrated by way of examples. It is shown that, in the context of multilayer coating design, the desired broadband ultralow reflectivities can be obtained within three fine model (FDTD) calculations.