We discuss the complex dispersion relation of a one dimensional metallo-dielectric photonic crystal, produced by a
dielectric photonic crystal with extremely thin metallic inserts with the same periodicity. We have carried out the
analytical and numerical analysis. Also, we show a method to avoid the problem of solving the complicated system of
transcendental equations of the dispersion relation that was proposed previously for us and we extended it to the oblique
incidence, i.e., for calculating transversal electric and magnetic modes. Moreover, we demonstrated a metallic band gap
not only at the bottom but also at high frequencies.
Metallo Dielectric Photonic Crystals formed by same periodicity metallic inserts in a Dielectric Photonic Crystal show
three kind of band gaps, those at the well know dielectric band gap, the ones attributed to the absorption of metal to low
frequencies and a new class of metallic bandgaps. Numerical studies have confirmed that while the dielectric band gap
width is basically described by the refraction index contrast, the width of the metallic band is described by the thickness
of the metal inserts. In this work we carry on the corresponding analytical analysis of both band gaps for this one
dimensional ternary dielectric-dielectric-metal structure. The stack that we are proposing is a quarter-wave for the
dielectrics and the thickness of the metallic layers is changed as a free parameter. Using standard transfer matrix
formalism, we find a closed form of the dispersion relation and from it; we have analytically demonstrated the formation
and width of the dielectric band gap and its metallic perturbation, as well as those of the additional metallic band gap.
Abstract We introduce the simulation of a photonic crystal slab with a square lattice, whose basis elements are layered cylinders of an averaged refractive index <n>. We compare it with a similar photonic crystal with a basis of the same size and a refractive index matching to the average of the layered ones. Even when this is such a simple system with internal structure, we have found an interesting phenomenology: an increase in band gaps, flattening of the bands, degeneracy nodes, etc. We also introduce additional methods to fine tuning the design and analyze the inclusion of a plain cylinder defect within the slab.
We investigated numerically the TM electric field solutions of a dielectric slab formed by a photorefractive crystal with
diffusion-type nonlinearity and limited by two metallic films. This study allows us the analysis of nonlinear surface
optical waves as nonlinear solutions of the photorefractive crystal slab. Additionally, we analyzed the influence of these
nonlinear solutions to excite surface plasmon-polariton waves at the metallic interfaces. In this case, the coupling
between plasmons and nonlinear solutions it is possible because only TM electromagnetic waves are supported by a
metal-dielectric planar waveguide. Here, we solved the vectorial and nonlinear wave equation using an iterative method
based in self-autoconsistency. With this algorithm, the coupling between the waveguide modes and the surface plasmon-polariton
waves are systematically investigated. The results obtained in this work are reproducible and contributes with
new information for the design of tunable plasmonic devices based in nonlinear photorefractive crystals.
The Entanglement of quantum systems is a key aspect in order to understand the dynamics and behavior of mixed
systems (density matrix) as bipartite systems of quantum bits (q-bits). A quantifiable measure widely used is the
"entanglement of formation" of a mixed state, defined as the minimum number of singlets needed to create an ensemble
of pure states that represents the density matrix of the system. Considering a double quantum dot system coupled cavity
type Jaynes-Cummings investigate the entanglement between two quantum dots, immersed each in its own cavity,
showing analytically that entanglement has a very interesting effects such as temporal evolution including the so-called
sudden death effect.
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.
Spatial and temporal solitons are at the core of many physical, geological, biological, transmission and information
processing and other problems. However, in most cases we have focused on their steady behavior, and therefore on
homogeneous media and their single soliton eigenvalues spectrum. This has been done even in the case of an all optical
simultaneous loss and amplification, where we have assumed stability of those eigenvalues. However, the transient
behavior has received little attention, often disregarded under a generic pulse reshaping or experimentally diafragmed as
often occurs in large amplifiers. But such transient behavior can be frozen in a periodic nonhomogenous media, tandems,
where such behavior corresponds to the soliton convergence in each tandem media, producing a regular but not steady
behavior. We discuss the resonant pulse propagation in a two level atom media tandem, described by a real convergence
and a Kerr intensity dependent nonlinearity, described by a complex convergence.
Waveguides coupling have been widely studied; however, nanowaveguides of high refraction index contrast open the
opportunity of studying the nonlinear dynamics of coupled waveguides, in particular those filled with metallic
nanaoparticles composites. Those composites show a Quantum Mechanical Kerr Nonlinearity and a classical field
amplitude nonlinearity that are compared by using a iterative WKB to introduce the field nonlinearity and based in the
ensuing M matrix. The produced nonlinear supermodes show a confinement of the pulse in the waveguides and a
breaking of the coupling at small and large core waveguides.
We present the characterization of a photonic crystal slab with a square lattice, whose basis elements are layered
cylinders. The cylinders are conceived as glass cores and subsequent layers of two alternating media with different
refractive indices, the thickness of each layer is a quarter of a tuning wavelength within the media. The band
structure in the dispersion relation is computed by means of numerical simulation and compared to the band
structure of a square lattice with plain cylinders, with the same size, and refractive index equal to the average
index of the layered ones. We have found that the band structure shrinks to lower frequencies as the number
of full periods of layers increases, although keeping the average refractive index and filling factor. This shrink
occurs even when the index contrast is kept constant.
CQED has been an active field of research for the last three decades, describing the intimacy of the interaction of radiation and matter in small volumes λ3, and have demonstrated that modifies not only the nature of this interaction, but also atomic characteristic that often were thought intrinsic, such as spontaneous emission or the very quantum nature of the interaction. These conditions have acquired quite an importance for the current activity on Quantum computation and Information. However, most of that activity has been developed in the conceptual and experimental framework of atomic systems. There is evidence that such features also occurs in Quantum Dots. We compare the Dicke and Jaynes Cummings dynamics of atoms described by the Hamiltonian of Quantum Dots, and develop the SU(2) perturbative approach in the regimen where the excitation number (atoms + photons) is larger than the number of atoms L. We exhibit the dynamical detuning produced by the Forster interaction.