This work demonstrates a systematic and efficient way of searching two-dimensional periodic nanostructures with wavelength-selective radiative properties appealing to thermophotovoltaic emitters. The orthogonal array from the Taguchi method benefits the optimization of structure depth, periods, and filling ratios among 1024 combinations. The spectral emittance from optimized structures is above 0.9 at wavelengths between 1.0 and 2.0 mu m, but the emittance is below 0.2 at wavelengths between 2.0 and 4.0 mu m. Furthermore, such spectral emittance characteristics can be kept for wide ranges of emission direction and either polarization. Representative emittance spectra from an example of convex rectangular structures are plotted and compared to those of concave structures in previous works. The comparison shows that radiative properties of convex structures are dominated by cavity resonances while those of concave structures are the interplay of multiple mechanisms. All numerical results are obtained from validated programs based on the rigorous coupled-wave analysis. (C) 2010 Elsevier Ltd. All rights reserved.