Pendellösung

The Pendellösung effect or phenomenon is seen in diffraction in which there is a beating in the intensity of electromagnetic waves travelling within a crystal lattice. It was predicted by P. P. Ewald in 1916^[1] and first observed in electron diffraction of magnesium oxide in 1942 by Robert D. Heidenreich^[2] and in X-ray diffraction by Norio Kato and Andrew Richard Lang in 1959.^[3]

At the exit surface of a photonic crystal (PhC), the intensity of the diffracted wave can be periodically modulated, showing a maximum in the "positive" (forward diffracted) or in the "negative" (diffracted) direction, depending on the crystal slab thickness.

The Pendellösung effect in photonic crystals can be understood as a beating phenomenon due to the phase modulation between coexisting plane wave components, propagating in the same direction.^[4][5]

This thickness dependence is a direct result of the so-called Pendellösung phenomenon, consisting of the periodic exchange inside the crystal of the energy between direct and diffracted beams.^[6]

The Pendellösung interference effect was predicted by dynamical diffraction and also by its fellow theories developed for visible light.