25 October 1996 Symmetry considerations in the formation and rotation of hexagonal scattering patterns in photorefractive KNbO3
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Self-organization of scattering into reconfigurable hexagonal arrays has been observed in KNbO3 by a number of researchers. Further, depending on the experimental configuration and the direction of the pump beam, these hexagonal arrays are observed to rotate about the main pump beam. In this paper we report on the results of the application of symmetry considerations to the analysis of these observations. The hexagonal array formation is postulated to develop through an interaction between secondary beams generated from the ring of beams formed from the original pump beam through a winner-take-all process. Starting with a model of the experimental configuration in which the feedback is provided by reflection from a surface which is perpendicular to the c-axis of the orthorhombic KNbO3 crystal, we find that rotation of this hexagonal pattern is allowed by the crystal symmetry and depends on the direction of the main pump beam with respect to the crystallographic a- b- and c-axes. The direction of rotation is reversed when the beam direction is reflected in either of the two crystallographic reflection planes but will remain the same when the beam is rotated 180 degrees about the twofold crystal c-axis. The rotation of the hexagonal array should vanish when the beam lies in either of the two reflection planes, or is aligned with the c-axis. In this paper we will present the results of these symmetry considerations, and compare the results to observations.
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John O. Dimmock, John O. Dimmock, } "Symmetry considerations in the formation and rotation of hexagonal scattering patterns in photorefractive KNbO3", Proc. SPIE 2849, Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications II, (25 October 1996); doi: 10.1117/12.255493; https://doi.org/10.1117/12.255493

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