We discuss the design of gratings that extract THz waves from the surface of quantum cascade lasers, in which the THz wave is generated by difference-frequency generation with Cerenkov phase-matching. The grating is a type of highcontrast- grating (HCG), which has been shown to be a good element of meta-surfaces. Although bare HCGs monolithically fabricated on the semiconductor do not work well, we found that the efficiency is increased to 34% in 1st order grating, 43% in 2nd order grating, and 75% in sub-1st order grating, by capping the ridge of the grating and the bottom of the groove by a metal layer.
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