Introduction: diffraction gratings

When a polychromatic beam of light is shined upon a translucent planar material etched with a periodic pattern known as a diffraction grating, the different colors of the beam of light propagate in different directions. Such a diffraction grating can be used as a monochromator of light or as a spectrometer, as schematically illustrated in Fig. 8.1.

The physics of a diffraction grating can be understood by a simple interference argument: we suppose that light of wavelength λ is normally incident upon a thin opaque screen containing a large number of periodically arranged narrow apertures (slits) separated by a distance Δ. Because the light is normally incident upon the grating, the phase of the field is the same within each aperture. Each aperture produces a spherical wave, and we consider the overlap of the fields from two such elements in a direction θ from the normal to the surface; this is illustrated in Fig. 8.2.

As can be seen from the picture, the wave emanating from aperture 2 has to travel a distance Δsin θ farther than the wave emanating from aperture 1. This translates to a phase difference between the two waves of kΔsin θ, where k = 2π/λ is the wavenumber of the light.