Exact ground states and domain walls in one dimensional chiral magnets

We determine exactly the phase structure of a chiral magnet in one spatial dimension with the Dzyaloshinskii-Moriya (DM) interaction and a potential that is a function of the third component of the magnetization vector, n3, with a Zeeman (linear with the coefficient B) term and an anisotropy (quadratic with the coefficient A) term, constrained so that 2A ≤ |B|. For large values of potential parameters A and B, the system is in one of the ferromagnetic phases, whereas it is in the spiral phase for small values. In the spiral phase we find a continuum of spiral solutions, which are one-dimensionally modulated solutions with various periods. The ground state is determined as the spiral solution with the lowest average energy density. As the phase boundary approaches, the period of the lowest energy spiral solution diverges, and the spiral solutions become domain wall solutions with zero energy at the boundary. The energy of the domain wall solutions is positive in the homogeneous phase region, but is negative in the spiral phase region, signaling the instability of the homogeneous (ferromagnetic) state. The order of the phase transition between spiral and homogeneous phases and between polarized (n3 = ±1) and canted (n3 ≠ ±1) ferromagnetic phases is found to be second order.

A modified multiplexed vortex helico-conical petal-like zone plate

A modified multiplexed vortex helico-conical petal-like zone plate (MMVHPZP) is proposed to generate a polygon-like beam or light-arm beam with an adjustable opening. The MMVHPZP consists of the modified helico-conical petal-like zone plate (MHPZP) with the topological charge l and exponent n, and the multiplexed vortex spiral phase plate (MVSPP) with the inner topological charge l1 and outer topological charge l2. Moreover, when l1 is equal or unequal to l2, the MMVHPZP has the adjustable polygon-like beam or light-arm beam, respectively. In addition, when n is small or large, the number of arms is equal to the absolute difference between l1 and l2 or the sum of one and the absolute difference between l1 and l2, respectively. Furthermore, for the different l1 or l2, the opening is constant. With the increase of the n or l, the opening is larger. When l1 is greater or less than l2, the rotation direction of arms is the anticlockwise or clockwise direction, respectively.

Systematically Investigating the Structural Variety of Crystalline and Kaleidoscopic Vortex Lattices by Using Laser Beam Arrays

We theoretically demonstrate that a family of vortex-lattice structures can be flexibly generated using a multi-beam interference approach. Numerical calculation presents a variety of crystalline and kaleidoscopic patterns. Based on the numerical analysis, we experimentally realized these structure beams by combining an amplitude mask with multiple apertures and a spiral phase plate. The excellent agreement between the experimental and theoretical results not only validates the presented method, but also manifests the structure of vortex lattices.