The ultimate goal of dark ray optics" is to control and manipulate the trajectories of phase singularities -i.e., day rays- in an analogous way as we deal with ordinary rays. The development of these analogies requires an adequate mathematical description. We will describe the fundamental concepts of this mathematical approach by emphasizing the essential role played by the symmetry properties of the optical elements used to manipulate highly charged or multi-singular Gaussian beams. We will unveil the nontrivial connections between discrete symmetry, OAM and the topological properties of these beams embedding nontrivial dark ray structures.
Full control of the dark ray structure of an optical beam requires an adequate mathematical framework to describe its properties. In this presentation we will provide a new set of mathematical tools whose ultimate goal is to complete a full mathematical representation of dark ray optics. Using this mathematical representation we will discuss the different possibilities to achieve full control of the dark rays trajectories using standard optical elements in an analogous way to the manipulation of ordinary bright rays in geometrical optics.
We present the numerical modeling of the interaction between a spatial soliton and a surface plasmon polariton under
leak and strong coupling in the following two cases: at metal/dielectric/Kerr structures and metal/Kerr structures in 1D.
Here, we solved the vectorial and nonlinear wave equation using a novel iterative method based in self-autoconsistency,
and we found two kinds of nonlinear stationary solutions called odd and even modes. On the other hand, the propagation
of the stationary solutions is performed for the metal/Kerr system, and quantitatively it shows that odd modes are more
stable than even modes when the spatial soliton and surface plasmon are strongly coupled. Also, we analyzed the
influence of the dielectric layer between the metal and Kerr media, and we discuss their implication and feasibility for
applications in photonic nanodevices. Additionally, the advantages and disadvantages of the numeric method used to
obtain the stationary solutions are discussed. The results obtained in this work are reproducible and contributes with new
information for the development of power-tunable photonic nanocircuits based in nonlinear plasmonic waveguides.
A numerical study of the effects of tapering a hollow-core photonic bandgap fiber (HC-PBGF) on the spatial
parameters: effective area, nonlinear parameter and dispersion parameter is presented. The taper on the fiber is
modeled by scaling the cross section of the original fiber geometry. Both the air and the silica contribution to the
effective area and the nonlinear parameter are shown. The obtained results show a blueshift of the transmission
band and of the zero-dispersion wavelength. By tapering the fiber 30%, the transmission band and the zerodispersion
wavelength blueshift around 300 nm and 320 nm, respectively. HC-PBGFs have made possible the
study of nonlinear optical effects and by tapering the fiber, such nonlinear phenomena can be made stronger.
We present a new computational scheme to design supercontinuum spectra "à la carte" by means of Genetic Algorithms.
Due to the potentially large amount of computations required by this strategy, the deployment of these heuristic
algorithms is performed using distributed computing in the form of a Grid platform. The optimization procedure is
automated within the Grid platform and permits escalation to large computational Grids. Some examples of designed
supercontinua are given and potential applications for the design of future photonic devices are briefly described.
Using group theory arguments and numerical simulations we demonstrate the existence of spatial solitons in non linear photonic systems with discrete point-symmetry. This new approach permits a systematic classification of all non-linear solitonic solutions. New spatial effects can be derived and numerically tested in the context of two-dimensional photonic crystal fibers, optical lattices or, equivalently, in that of Bose-Einstein condensates in periodic potentials.
A square lattice photonic crystal fiber is described. The square lattice structures were fabricated, characterized and their polarization properties were investigated. The polarization properties of the fibers were not as strong as those reported previously in highly birefringent PCF, but these structures have considerable potential for high birefringence.
We study the group-velocity dispersion properties of a novel class of Bragg fibers. They are radially-symmetric microstructured fibers having a high-index core (silica in our case) surrounded by a cylindrical multilayer omnidirectional mirror as cladding, which is formed by a set of alternating layers of silica and a lower refractive-index dielectric. The interplay between the unusual geometric dispersion shown by the multilayer cladding of the fiber and the material dispersion corresponding to the silica core allows us to achieve an achromatic flattened dispersion behavior in the 0.8 μ<i>m</i> wavelength window and even an ultraflattened behavior in the 1.5 μ<i>m</i> range for some specific designs.
This paper gives the theoretical basis for the development of a novel modal method to describe 3D dielectric structure modes. To this end, the vector wave equation, which determines the magnetic field, is written in terms of a linear operator, whose eigenvectors satisfy orthonormality relation. The key of our method is to obtain a matrix representation of the wave equation in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to systems with arbitrary 3D real or complex refractive-index distributions. In this work we have focused on thin-film photonic crystal waveguides with an asymmetrical core.
A novel analysis of specially designed photonic crystal fibers accounts for the existence of endlessly single-mode structures with flattened dispersion. Our approach permits to control the fiber dispersion in terms of its geometrical parameters.