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.^[2]

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.^[3]^[4]

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.^[5]

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

References

^ Ewald, P. P. (1916). "Zur Begründung der Kristalloptik". Annalen der Physik (in German). 354 (2): 117–143. Bibcode:1916AnP...354..117E. doi:10.1002/andp.19163540202.
^ Heidenreich, Robert D. (1942-09-01). "Electron Reflections in MgO Crystals with the Electron Microscope". Physical Review. 62 (5–6): 291–292. Bibcode:1942PhRv...62..291H. doi:10.1103/PhysRev.62.291. ISSN 0031-899X.
^ Savo, S.; Gennaro, E. Di; Miletto, C.; Andreone, A.; Dardano, P.; Moretti, L.; Mocella, V. (2008-06-09). "Pendellösung effect in photonic crystals". Optics Express. 16 (12): 9097–9105. arXiv:0804.1701. Bibcode:2008OExpr..16.9097S. doi:10.1364/OE.16.009097. ISSN 1094-4087. PMID 18545621. S2CID 12456215.
^ Baruchel, J.; Guigay, J.P.; Mazuré-Espejo, C.; Schlenker, M.; Schweizer, J. (1983-05-01). "Observation of pendellösung effect in polarized neutron scattering from a magnetic crystal". Physica B+C. 120 (1–3): 80. Bibcode:1983PhyBC.120...80B. doi:10.1016/0378-4363(83)90343-1. ISSN 0378-4363.
^ Punegov, Vasily I. (2021). "X-ray Laue diffraction by sectioned multilayers. I. Pendellösung effect and rocking curves". Journal of Synchrotron Radiation. 28 (5): 1466–1475. doi:10.1107/S1600577521006408. ISSN 1600-5775. PMID 34475294. S2CID 237398971.

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[1] Ewald, P. P. (1916). "Zur Begründung der Kristalloptik". Annalen der Physik (in German). 354 (2): 117–143. Bibcode:1916AnP...354..117E. doi:10.1002/andp.19163540202.

[2] Heidenreich, Robert D. (1942-09-01). "Electron Reflections in MgO Crystals with the Electron Microscope". Physical Review. 62 (5–6): 291–292. Bibcode:1942PhRv...62..291H. doi:10.1103/PhysRev.62.291. ISSN 0031-899X.

[3] Savo, S.; Gennaro, E. Di; Miletto, C.; Andreone, A.; Dardano, P.; Moretti, L.; Mocella, V. (2008-06-09). "Pendellösung effect in photonic crystals". Optics Express. 16 (12): 9097–9105. arXiv:0804.1701. Bibcode:2008OExpr..16.9097S. doi:10.1364/OE.16.009097. ISSN 1094-4087. PMID 18545621. S2CID 12456215.

[4] Baruchel, J.; Guigay, J.P.; Mazuré-Espejo, C.; Schlenker, M.; Schweizer, J. (1983-05-01). "Observation of pendellösung effect in polarized neutron scattering from a magnetic crystal". Physica B+C. 120 (1–3): 80. Bibcode:1983PhyBC.120...80B. doi:10.1016/0378-4363(83)90343-1. ISSN 0378-4363.

[5] Punegov, Vasily I. (2021). "X-ray Laue diffraction by sectioned multilayers. I. Pendellösung effect and rocking curves". Journal of Synchrotron Radiation. 28 (5): 1466–1475. doi:10.1107/S1600577521006408. ISSN 1600-5775. PMID 34475294. S2CID 237398971.