Teaching diffraction gratings by means of a phasor analysis

Abstract

Diffraction gratings play a very important educational role in describing wave properties of light. In this work we present a simple phasor technique to fully describe binary amplitude diffraction gratings with different slit widths relative to the grating period, as well as binary phase gratings with different phase shift. This analysis, which is directly derived from the Huygens principle, introduces a slit phasor to account for the diffracted orders relative intensity, and a grating phasor that accounts for the grating’s resolving power. The proposed phasor technique is mathematically equivalent to the Fourier transform calculation of the diffraction orders amplitude, and it can be useful to explain binary diffraction gratings in a simple manner in introductory physics courses. Experimental results probing this theoretical analysis are included with the use of a liquid crystal display.