Search results for "symmetry"
showing 10 items of 3576 documents
Dipole soliton-vortices
2007
On universal symmetry grounds, we analyze the existence of a new type of discrete-symmetry vortex solitons that can be considered as coherent states of dipole solitons carrying a nonzero topological charge. Remarkably, they can be also interpreted as excited angular Bloch states. The stability of new soliton states is elucidated numerically.
Wavelength-flattened directional couplers for mirror-symmetric interferometers
2005
In the context of guided optics, we derive, analytically and geometrically, a rigorous general criterion to design wavelength insensitive interferometers with mirror symmetry, which are needed for wavelength multiplexing/demultiplexing. The criterion is applied to a practical case, resulting in an interferometer that works on a band wider than 70 nm.
Nodal solitons and the nonlinear breaking of discrete symmetry
2005
We present a new type of soliton solutions in nonlinear photonic systems with discrete point-symmetry. These solitons have their origin in a novel mechanism of breaking of discrete symmetry by the presence of nonlinearities. These so-called nodal solitons are characterized by nodal lines determined by the discrete symmetry of the system. Our physical realization of such a system is a 2D nonlinear photonic crystal fiber owning C6v symmetry.
Three-dimensional level-curve scanning based on intersection of laser lines
2005
A dimensional measurement system that also tracks object movements is presented here. The method directly yields the level curves of an object. It is an extension of collimation methods, coupled with the use of structured lighting with features formed from several luminous planes intersecting in a single line. This line defines a set of points of the space at a fixed distance Z 0 from the measuring head. The locus of the points of the object where the lighting is reduced to a single line is the level curve sought. The introduction of an asymmetry into the lighting structure permits one to determine the direction as well as an approximate value of the value of the distance to the level curve…
Theory for the control of dark rays by means of discrete symmetry diffractive elements
2013
We present an analytical theory that describes the disintegration of a highly charged phase singularity by the presence of a thin discrete symmetry diffractive element, i.e., an optical diffractive element possessing rotational symmetry of finite order. The process is described in terms of dark rays, defined as the trajectories where there is no light, i.e., those for which the complex optical field vanishes. We provide explicit analytical expressions for the equations that describe the dark ray trajectories. We show that dark rays follow straight line trajectories asymptotically, like ordinary rays, but with properties which differ in essential features with respect to their bright counter…
Specular reflection of spin-polarized electrons from the W(001) spin-filter crystal in a large range of scattering energies and angles
2015
Extending previous work on the imaging spin-filter technique based on electron diffraction from W(001) in the specular (00)-LEED (low-energy electron diffraction) spot, we studied the scattering-energy and angle-of-incidence landscape of spin sensitivity $S$ and reflectivity ${I/I}_{0}$. The setup includes a spin-polarized GaAs electron source and a rotatable delay-line detector for spatially resolving detection. We measured the intensity and spin asymmetry of the specularly reflected beam for energies between 14 and 37 eV and angles of incidence between ${30}^{\ensuremath{\circ}}$ and ${60}^{\ensuremath{\circ}}$. Resulting energy-angular landscapes show rather good agreement with theory [r…
Lau rings: In-register incoherent superposition of radial self-images
1989
Abstract We describe an optical method for obtaining in-register, incoherent superposition of self-images, with radial symmetry. That is, the Lau effect is implemented, either at infinity or at finite distances, in the form of bright and dark rings of high visibility. This is applied for visualizing radially phase structures, with good-signal-to-noise ratio.
The local group K(4) in the algebraic approach to vibrational spectra of tetrahedral molecules: Application to silane
1992
Abstract In a previous paper, Michelot and Moret-Bailly (J. Phys., 48, 51 (1987)) proposed an algebraic treatment of vibrational stretching modes in polyatomic molecules. They used the properties of the group chain U(p + 1) ⊃ U(p) ⊃ S(p) ⊃ G for the study of p identical oscillators. The molecule, with p equivalent bonds described as a system of p oscillators, has a symmetry group G. We develop in this paper an application to p = 4 equivalent oscillators. We show that, for a tetrahedral molecule, the group chain U(5) ⊃ U(4) ⊃ S(4) ≈ Td can be completed, in a local point of view, with a particular group K(4): U(5) ⊃ U(4) ⊃ K(4) ⊃ S(4) ≈ T d This group provides us with available labels which c…
Rotational States of the Helium Trimer in the Symmetry-Adapted Hyperradial-Adiabatic Approach
2003
We have searched for bound rotationally excited states of the helium trimer using the symmetry-adapted hyperradial adiabatic approach. Since the calculated J p = 2+ and J p = 1− potential curves are both completely repulsive, we infer that there are no bound rotational states of 4He3. A recent adiabatic calculation [1] based on the direct solution of the Coriolis-coupled Schrodinger equation agrees with this conclusion.
Dynamics of mean-field spin models from basic results in abstract differential equations
1992
The infinite-volume limit of the dynamics of (generalized) mean-field spin models is obtained through a direct analysis of the equations of motion, in a large class of representations of the spin algebra. The resulting dynamics fits into a general framework for systems with long-range interaction: variables at infinity appear in the time evolution of local variables and spontaneous symmetry breaking with an energy gap follows from this mechanism. The independence of the construction of the approximation scheme in finite volume is proven. © 1992 Plenum Publishing Corporation.