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.

Generation of phase-only holograms by laser ablation of nanoparticulate ITO layers

“…equally wide areas with a phase shift of 0 and π. It can be shown that such a structure also displays a first order intensity of 40.5% while no light goes to the zero order [21]. A binary hologram can be regarded as a structure being constituted of a sum of binary gratings with different periods.…”

Determination of the effective refractive index of nanoparticulate ITO layers

“…The deflection angles can be calculated from the diffraction grating law and will depend on the wavelength of the incident light and the grating period, while the relative intensity of the diffracted orders will be affected by the grating fill factor and the phase shift introduced by the imposed ITO structure. Extending the phasor analysis presented in [18,19], the intensity of the m th diffraction order can be calculated as …”