Optical properties of guided-mode resonant gratings with linearly varying period

Guided-mode resonant gratings with spatially varying parameters are widely used as linear variable optical filters, and their behavior is often described using the so-called local periodic approximation, in which the structure is locally replaced by a strictly periodic grating with the period coinciding with the "local" period at the considered point. In this work, we investigate the optical properties of guided-mode resonant gratings with the period linearly varying along the periodicity direction. Using full-wave numerical simulations, we show that when the period change rate is relatively high (about 0.5-1 mu m/mm for the considered structures), the local periodic approximation becomes inapplicable, and the linewidth and the line shape of the resonances depend significantly on the period change rate. We qualitatively explain the appearance of an asymmetric non-Fano line shape with secondary maxima by analyzing the local photonic band structure of the studied varying-period gratings. For a more accurate description of such gratings, we develop a spatiotemporal coupled-mode theory, the predictions of which are in good agreement with the rigorous numerical simulation results. The validity of the derived theoretical model is additionally confirmed by a proof-of-concept experiment with a varying-period guided-mode resonant grating. The obtained results may find application in the design of compact linear variable filters based on resonant gratings with spatially varying parameters.