Single-order diffraction grating designed by trapezoidal transmission function

Diffraction grating is a widely used dispersion element in spectral analysis from the infrared to the x-ray region. Traditionally, it has a square-wave transmission function, suffering from high-order diffraction contamination. Single-order diffraction can be achieved by sinusoidal amplitude transmission grating, but the fabrication is difficult. Here, we propose a novel idea to design a grating based on trapezoidal transmission function, which makes traditional grating a special case. Grating designed by this idea can not only suppress higher order diffraction by several orders of magnitude as sinusoidal amplitude grating does but also greatly reduce the fabrication difficulty to the level of processing for traditional grating. It offers a new opportunity for fabrication of grating with single-order diffraction and measurement of spectrum without contamination of high-order harmonic components. This idea can easily extend to varied-line-space grating, concave grating with single-order diffraction, or zone plates with single foci and will bring great changes in the field of grating applications.