Related papers: Hidden symmetry and nonlinear paraxial atom optics
Superpositions of paraxial laser beam modes to generate atom-optical lenses based on the optical dipole force are investigated theoretically. Thin, wide, parabolic, cylindrical and circular atom lenses with numerical apertures much greater…
We study both experimentally and theoretically the losses induced by parametric excitation in far-off-resonance optical lattices. The atoms confined in a 1D sinusoidal lattice present an excitation spectrum and dynamics substantially…
We show that all laser beams gradually lose their initial phase information in nonlinear propagation. Therefore, if two beams travel a sufficiently long distance before interacting, it is not possible to predict whether they would intersect…
A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept…
Coupling light to ensembles of strongly interacting particles has emerged as a promising route toward achieving few photon nonlinearities. One specific way to implement this kind of nonlinearity is to interface light with highly excited…
The theory of Bloembergen and Pershan for the light waves at the boundary of nonlinear media is extended to a nonlinear two-dimensional atomic crystal, i.e. a single planar atomic lattice, placed in between linear bulk media. The crystal is…
Nonlinear optical phenomena play important roles in the vast emerging fields of micro- and nano-technology. This paper describes the general characteristics of nonlinear optical materials and systems, with a focus on parametric…
We construct the closed form solution of an elastic beam with axial load using Lie symmetry method. A beam with spatially varying physical properties such as mass and second moment of inertia is considered. The governing fourth order…
Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are…
A bosonized nonlinear (polynomial) supersymmetry is revealed as a hidden symmetry of the finite-gap Lame equation. This gives a natural explanation for peculiar properties of the periodic quantum system underlying diverse models and…
We put forward a technique to unveil to which symmetry group a nonlinear crystal belongs, making use of nonlinear optics with structured light. We consider as example the process of spontaneous parametric down-conversion. The crystal, which…
Making use of a generalized quantum theory of paraxial light propagation where the radiation-axis and the temporal coordinates play exchanged roles, we discuss the potential of bulk nonlinear optical media in cavityless configurations for…
Realization and manipulation of parity-time (PT) symmetry in multidimensional systems are highly desirable for exploring nontrivial physics and uncovering exotic phenomena in non-Hermitian systems. Here, we report the first experimental…
We review and extend the analogies between Gaussian pulse propagation and Gaussian beam diffraction. In addition to the well-known parallels between pulse dispersion in optical fiber and CW beam diffraction in free space, we review temporal…
The temporal evolution of an atomic wave packet interacting with object and reference electromagnetic waves is investigated beyond the weak perturbation of the initial state. It is shown that the diffraction of an ultracold atomic beam by…
The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question readily accessible to atomic systems is related…
A scheme for polarization control using two laser beams in a non-linear optical medium is studied using both co- and counter-propagating beam geometries. In particular, we show that under certain conditions it is possible for two laser…
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new…
We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. In a first part, a mathematical…
We investigate light propagation through materials with periodically modulated gain/loss profile in both transverse and longitudinal directions, i.e. in material with two-dimensional modulation in space. We predict effects of…