A perturbative analysis of dispersion-managed solitons

We study soliton solutions of the path-averaged propagation equation governing the transmission of dispersion-managed (DM) optical pulses in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. In the case of small dispersion map strengths, the averaged pulse dynamics is governed by a perturbed form of the nonlinear Schrödinger equation; applying a perturbation theory – elsewhere developed – based on inverse scattering theory, we derive an analytic expression for the envelope of the DM soliton. This expression correctly predicts the power enhancement arising from the dispersion management. Theoretical results are verified by direct numerical simulations.

A perturbative analysis of dispersion-managed solitons

We study soliton solutions of the path-averaged propagation equation governing the transmission of dispersion-managed (DM) optical pulses in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. In the case of small dispersion map strengths, the averaged pulse dynamics is governed by a perturbed form of the nonlinear Schrödinger equation; applying a perturbation theory – elsewhere developed – based on inverse scattering theory, we derive an analytic expression for the envelope of the DM soliton. This expression correctly predicts the power enhancement arising from the dispersion management. Theoretical results are verified by direct numerical simulations.

The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.

Global Waves with Non-Positive Energy in General Relativity

2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.

CHARACTERIZATION OF THE ATMOSPHERIC EFFECTS ON THE TRANSMISSION OF THERMAL RADIATION

Atmospheric scattering plays a crucial rule in degrading the performance of electro optical imaging systems operating in the visible and infra-red spectral bands, and hence limits the quality of the acquired images, either through reduction of contrast or increase of image blur. The exact nature of light scattering by atmospheric media is highly complex and depends on the types, orientations, sizes and distributions of particles constituting these media, as well as wavelengths, polarization states and directions of the propagating radiation. Here we follow the common approach for solving imaging and propagation problems by treating the propagating light through atmospheric media as composed of two main components: a direct (unscattered), and a scattered component. In this work we developed a detailed model of the effects of absorption and scattering by haze and fog atmospheric aerosols on the optical radiation propagating from the object plane to an imaging system, based on the classical theory of EM scattering. This detailed model is then used to compute the average point spread function (PSF) of an imaging system which properly accounts for the effects of the diffraction, scattering, and the appropriate optical power level of both the direct and the scattered radiation arriving at the pupil of the imaging system. Also, the calculated PSF, properly weighted for the energy contributions of the direct and scattered components is used, in combination with a radiometric model, to estimate the average number of the direct and scattered photons detected at the sensor plane, which are then used to calculate the image spectrum signal to- noise ratio (SNR) in the visible near infra-red (NIR) and mid infra-red (MIR) spectral wavelength bands. Reconstruction of images degraded by atmospheric scattering and measurement noise is then performed, up to the limit imposed by the noise effective cutoff spatial frequency of the image spectrum SNR. Key results of this research are as follows: A mathematical model based on Mie scattering theory for how scattering from aerosols affects the overall point spread function (PSF) of an imaging system was developed, coded in MATLAB, and demonstrated. This model along with radiometric theory was used to predict the limiting resolution of an imaging system as a function of the optics, scattering environment, and measurement noise. Finally, image reconstruction algorithms were developed and demonstrated which mitigate the effects of scattering-induced blurring to within the limits imposed by noise.

Analytical methods for modeling elastic metasurfaces

This dissertation aims at developing advanced analytical tools able to model surface waves propagating in elastic metasurfaces. In particular, four different objectives are defined and pursued throughout this work to enrich the description of the metasurface dynamics. First, a theoretical framework is developed to describe the dispersion properties of a seismic metasurface composed of discrete resonators placed on a porous medium considering part of it fully saturated. Such a model combines classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. Second, an exact formulation based on the multiple scattering theory is developed to extend the two-dimensional classical Lamb’s problem to the case of an elastic half-space coupled to an arbitrary number of discrete surface resonators. To this purpose, the incident wavefield generated by a harmonic source and the scattered field generated by each resonator are calculated. The substrate wavefield is then obtained as solutions of the coupled problem due to the interference of the incident field and the multiple scattered fields of the oscillators. Third, the above discussed formulation is extended to three-dimensional contexts. The purpose here is to investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces. Finally, the multiple scattering formulation is extended to model flexural metasurfaces, i.e., an array of thin plates. To this end, the resonant plates are modeled by means of their equivalent impedance, derived by exploiting the Kirchhoff plate theory. The proposed formulation permits the treatment of a general flexural metasurface, with no limitation on the number of plates and the configuration taken into account. Overall, the proposed analytical tools could pave the way for a better understanding of metasurface dynamics and their implementation in engineered devices.

Structure, stability, depolarized light scattering, and vibrational spectra of fullerenols from all-electron density-functional-theory calculations

We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C(60)(OH)(n)] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke's three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C(60)(OH)(36). Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1, 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C(60)(OH)(24) isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4, 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

alpha alpha scattering in halo effective field theory

We study the two-alpha-particle (alpha alpha) system in an Effective Field Theory (EFT) for halo-like systems. We propose a power Counting that incorporates the subtle interplay of strong and electromagnetic forces leading to a narrow resonance at an energy of about 0.1 MeV. We investigate the EFT expansion in detail, and compare its results with existing low-energy aa phase shifts and previously determined effective-range parameters. Good description of the data is obtained with a surprising amount of fine-tuning. This scenario can be viewed as an expansion around the limit where, when electromagnetic interactions are turned off, the (8)Be ground state is at threshold and exhibits conformal invariance. We also discuss possible extensions to systems with more than two alpha particles. (c) 2008 Elsevier B.V. All rights reserved.

Release of Cyanopyridine from a Ruthenium Complex Adsorbed on Gold: Surface-Enhanced Raman Scattering, Electrochemistry, and Density Functional Theory Analyses

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Virtual Compton scattering in baryon chiral perturbation theory

This thesis is concerned with the calculation of virtual Compton scattering (VCS) in manifestly Lorentz-invariant baryon chiral perturbation theory to fourth order in the momentum and quark-mass expansion. In the one-photon-exchange approximation, the VCS process is experimentally accessible in photon electro-production and has been measured at the MAMI facility in Mainz, at MIT-Bates, and at Jefferson Lab. Through VCS one gains new information on the nucleon structure beyond its static properties, such as charge, magnetic moments, or form factors. The nucleon response to an incident electromagnetic field is parameterized in terms of 2 spin-independent (scalar) and 4 spin-dependent (vector) generalized polarizabilities (GP). In analogy to classical electrodynamics the two scalar GPs represent the induced electric and magnetic dipole polarizability of a medium. For the vector GPs, a classical interpretation is less straightforward. They are derived from a multipole expansion of the VCS amplitude. This thesis describes the first calculation of all GPs within the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. Because of the comparatively large number of diagrams - 100 one-loop diagrams need to be calculated - several computer programs were developed dealing with different aspects of Feynman diagram calculations. One can distinguish between two areas of development, the first concerning the algebraic manipulations of large expressions, and the second dealing with numerical instabilities in the calculation of one-loop integrals. In this thesis we describe our approach using Mathematica and FORM for algebraic tasks, and C for the numerical evaluations. We use our results for real Compton scattering to fix the two unknown low-energy constants emerging at fourth order. Furthermore, we present the results for the differential cross sections and the generalized polarizabilities of VCS off the proton.