Diffraction efficiency management by complex binary gratings

The diffraction efficiencies of a complex binary diffractiongrating with a rectangular profile are controlled throughthe steps’ phases, amplitudes, and duty cycle, based onanalytical expressions. It is demonstrated that the zerothdiffraction order can be canceled for any arbitrary value ofthe duty cycle, provided that a π-phase difference is imposed,along with a specific ratio of the steps’ amplitudes. Thisfeature is not feasible for separated amplitude-only andphase-only rectangular binary gratings in the context ofone-dimensional gratings. In this framework, a key analyticrelationship between the duty cycle and the steps’ amplitude ratio is derived, allowing the design of such gratingswith this desired feature across a wide range of conditions,not limited to a duty cycle of 0.5. Concerning the higherdiffraction orders, it is proved that their intensities cancel ormaximize for fixed duty cycle no matter the amplitude andphase values of the steps. The intensity of the m-th diffraction order possesses m maxima and m − 1 zeros on the fullrange of the duty cycle. All these features were corroboratedexperimentally. The broad insight of such a grating allowsthe design of gratings with diffraction efficiencies tailoredfor specific applications.