Measurements of Pancharatnam-Berry phase in mode transformations on hybrid-order Poincaré sphere.

We report direct measurements of the Pancharatnam-Berry (PB) phase in mode transformations on a hybrid-order Poincaré sphere. This geometric phase arises when the vector vortex states undergo a cyclic transformation over a closed circuit on a hybrid-order Poincaré sphere. The measured PB phase is proportional to the solid angle of the closed circuit, as well as to the variation of the total angular momenta between north and south poles. More importantly, a zero PB phase has been demonstrated, despite the vector vortex states taken through a closed circuit on the hybrid-order Poincaré sphere. This interesting phenomenon can be explained as being due to the zero Berry curvature.

[1]  D. Nolan,et al.  Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light. , 2011, Physical review letters.

[2]  Shuangchun Wen,et al.  Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere , 2017 .

[3]  Gabriel F Calvo.  Wigner representation and geometric transformations of optical orbital angular momentum spatial modes. , 2005, Optics letters.

[4]  D. Nolan,et al.  Higher order Pancharatnam-Berry phase and the angular momentum of light. , 2012, Physical review letters.

[5]  D. Fan,et al.  Hybrid-order Poincare sphere , 2014, 1411.2476.

[6]  Shuangchun Wen,et al.  Geometric phase Doppler effect: when structured light meets rotating structured materials. , 2017, Optics express.

[7]  D. Hakobyan,et al.  Optical torque reversal and spin-orbit rotational Doppler shift experiments. , 2015, Optics express.

[8]  M J Padgett,et al.  Poincaré-sphere equivalent for light beams containing orbital angular momentum. , 1999, Optics letters.

[9]  Etienne Brasselet,et al.  Left-handed optical radiation torque , 2014, Nature Photonics.

[10]  L. Marrucci,et al.  Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. , 2006, Physical review letters.

[11]  S. Pancharatnam,et al.  Generalized theory of interference, and its applications , 1956 .

[12]  M. Berry.  The Adiabatic Phase and Pancharatnam's Phase for Polarized Light , 1987 .

[13]  M. Berry.  Quantal phase factors accompanying adiabatic changes , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[14]  L J Wang,et al.  Measurement of the Pancharatnam phase for a light beam. , 1988, Optics letters.

[15]  Rajendra Bhandari,et al.  Polarization of light and topological phases , 1997 .

[16]  Z. Bomzon,et al.  Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings. , 2002, Optics letters.

[17]  Q. Zhan.  Cylindrical vector beams: from mathematical concepts to applications , 2009 .

[18]  Xiaohui Ling,et al.  Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere , 2016 .

[19]  Gerd Leuchs,et al.  Classical and quantum properties of cylindrically polarized states of light. , 2010, Optics express.

[20]  R E Williams,et al.  Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum. , 2003, Physical review letters.

[21]  Analysis of the Pancharatnam-Berry phase of vector vortex states using the Hamiltonian based on the Maxwell-Schrödinger equation , 2016, 1602.02474.

[22]  Samuel,et al.  Observation of topological phase by use of a laser interferometer. , 1988, Physical review letters.