Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals
Open accessAbstract
We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor omega/deltaomega (omega: frequency of an x ray, deltaomega: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.
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The centre-of-energy velocity of the wave packet contains an anomalous contribution proportional to the Berry curvature of the band, and this contribution is responsible for various Hall effects.
“Based on the semi-classic equations of motion for wave packet propagation in the presence of Berry curvature1,19,20,33,34, the centre-of-energy velocity of the wave packet contains an ‘anomalous’ contribution proportional to the Berry curvature of the band, and this contribution is responsible for various Hall effects1,19,33.”
From Photonic Hall effect and helical Zitterbewegung in a synthetic Weyl system (2019) · cites this paper as [33]
On p. 2, the paper describes an anomalous velocity term for light that gives rise to an optical Hall effect; p. 1 links momentum-space Berry curvature to transverse wave-packet displacement. It does not establish that this contribution is responsible for various Hall effects. For its own deformed-crystal result, p. 3 says the momentum-space Berry curvature does not affect the result at the approximation used. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe spin-orbit interaction of light and spin-to-orbit conversion of angular momentum, which can be associated with the spin Hall effect, occurs upon scattering of polarized plane waves on various non-planar objects, such as lenses or small scatterers, or in inhomogeneous anisotropic media.
“Finally, the spin-orbit interaction of light and spin-to-orbit conversion of the angular momentum (which can be associated with the spin Hall effect) occurs upon the scattering of polarized plane waves on various non-planar objects, such as lenses or small scatterers, or in inhomogeneous anisotropic media [67,145 -152].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [145]
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Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
Bliokh, K. Y. (2009) · Journal of Optics A: Pure and Applied Optics · doi:10.1088/1464-4258/11/9/094009 · Cited by 217 · see citing works
Photonic Hall effect and helical Zitterbewegung in a synthetic Weyl system
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- Authors
- Sawada, K., Murakami, S., & Nagaosa, N.
- Affiliations
- The University of Tokyo (JP)
- Japan Science and Technology Agency (JP)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-04-21
- Volume
- 96
- Issue
- 15
- Pages
- 154802-154802
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2087715540
- Cited by
- 29
- References
- 23
- Citations by year
- 2026: 1 · 2025: 2 · 2021: 1 · 2020: 1 · 2019: 1 · 2017: 4 · 2016: 3 · 2014: 1 · 2013: 3 · 2012: 2
- FWCI
- 1.21
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Tokyo Tech Research Repository (Tokyo Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Crystallography and Radiation Phenomena
- Physical Sciences › Materials Science › Materials Chemistry › X-ray Diffraction in Crystallography
- Physical Sciences › Physics and Astronomy › Radiation › Advanced X-ray Imaging Techniques
- Keywords
- dynamical diffraction, crystal deformation, Berry phase, equations of motion, Bragg diffraction, Bragg gap, geometrical optics, X-ray diffraction
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