<p> The rapid increasing bandwidth requirement of communication systems demands powerful numerical simulation tools for optics fiber. The computational efficient, memory saving and stable are of the most important characteristics for any simulation tools used for long-haul and broadband optics fiber. An optimized split-step digital filtering method is developed in this paper. The concept of Fourier integral and Fourier series are used in extracting a FIR filter which is used to fit the original transfer function. A further optimization process which employs windowing technique to improve computation efficiency had also been done. Compared with split-step frequency method, our method improves the computation efficiency. Only simple shifts and multiplications are needed in our method. This optimized digital filtering method differs from the former digital filtering method in a sense that the filter length of the FIR filter we extracted is reduced to a very small number. The computation time can be saved as much as 96% than before. This method can also be used to solve coupled nonlinear Schrodinger equation which governs polarization mode dispersion effect in fibers. A new simulation scheme for PMD is proposed to save computation time. The propagation results shows good accordance to those already published results. </p> / Thesis / Master of Applied Science (MASc)

Arterial pulse pressure is critically important to a number of diseases such as isolated systolic hypertension, coronary artery disease and heart failure. Determining the cause of increased pulse pressure has been hampered for two reasons. First, pulse pressure results from contraction of the heart and the load formed by the complex arterial tree. Pressure pulses travel from the heart to the peripheral arteries. As they reach a bifurcation or change in arterial wall properties, some of the pulses get reflected and propagate retrograde towards the heart. Second, two different modeling approaches (0-D and 1-D) describe the arterial system. The Windkessel model ascribed changes in pulse pressure to changes in total arterial compliance (Ctot) and total arterial resistance, whereas the transmission model ascribed them to changes in the magnitude, timing and sites of reflection. Our investigation has addressed both these limitations by finding that a complex arterial system degenerates into a simple 2-element Windkessel model when wavelength of the propagated pulse increases. This theoretical development has yielded three practical results. First, isolated systolic hypertension can be viewed as a manifestation of a system that has degenerated into a Windkessel, and thus increased pulse pressure is due to decreased Ctot. Second, the well-discussed Augmentation Index does not truly describe augmentation of pulse pressure by pulse reflection. Third, the simple 2-element Windkessel can be used to characterize the interaction among heart, arterial system and axial-flow left ventricular assist device analytically. The fact that arterial systems degenerate into Windkessels explains why it becomes much easier to estimate total arterial compliance in hypertension?total arterial compliance is the dominant determinant of pulsatile pressure.

Arterial pulse pressure is critically important to a number of diseases such as isolated systolic hypertension, coronary artery disease and heart failure. Determining the cause of increased pulse pressure has been hampered for two reasons. First, pulse pressure results from contraction of the heart and the load formed by the complex arterial tree. Pressure pulses travel from the heart to the peripheral arteries. As they reach a bifurcation or change in arterial wall properties, some of the pulses get reflected and propagate retrograde towards the heart. Second, two different modeling approaches (0-D and 1-D) describe the arterial system. The Windkessel model ascribed changes in pulse pressure to changes in total arterial compliance (Ctot) and total arterial resistance, whereas the transmission model ascribed them to changes in the magnitude, timing and sites of reflection. Our investigation has addressed both these limitations by finding that a complex arterial system degenerates into a simple 2-element Windkessel model when wavelength of the propagated pulse increases. This theoretical development has yielded three practical results. First, isolated systolic hypertension can be viewed as a manifestation of a system that has degenerated into a Windkessel, and thus increased pulse pressure is due to decreased Ctot. Second, the well-discussed Augmentation Index does not truly describe augmentation of pulse pressure by pulse reflection. Third, the simple 2-element Windkessel can be used to characterize the interaction among heart, arterial system and axial-flow left ventricular assist device analytically. The fact that arterial systems degenerate into Windkessels explains why it becomes much easier to estimate total arterial compliance in hypertension?total arterial compliance is the dominant determinant of pulsatile pressure.

We simulate ultrashort pulse propagation through water by numerical methods, which is a kind of optical communication research. Ultrashort pulses have been known to have non Beer-Lambert behavior, whereas continuous waves (CW) obey the Beer-Lambert law. People have expected that the ultrashort pulse loses less intensity for a given distance in water than CW which implies that the pulse can travel over longer distances. In order to understand this characteristic of the pulse, we model numerically its spectral and temporal evolution as a function of traveling distance through water. We achieve the pulse intensity attenuation with traveling distance, obtain the temporal envelope of the pulse and compare them with experimental data. This research proves that the spectral and temporal profile of a pulse can be predicted knowing only the intensity spectrum of the input pulse and the refractive index spectrum of water in the linear regime. The real feasibility and the advantage of using an ultrashort pulse as a communication carrier will also be discussed.

This doctoral dissertation focuses on the nonlinear optical response of water vapour as well as some solids at terahertz (THz) frequencies. In this study, the propagation of broadband single-cycle THz pulses through a medium with the third-order nonlinear optical response is theoretically investigated. Also, a technique to measure the nonlinear response of transparent materials based on the time-domain THz spectroscopy is developed, which provides frequency dispersion curves of the nonlinear Kerr coefficient (n₂). A numerical model is used to simulate the THz pulse propagation. This model takes into account non-paraxial effects, self-focusing, and diffraction, as well as dispersion, in both the linear and nonlinear optical regimes. The contribution of non-instantaneous Kerr-type nonlinearity to the overall instantaneous and delayed Kerr effect at the THz frequencies is investigated. It is shown how increasing the nonlinear relaxation time and its dispersion modifies the THz pulse after the propagation through a transparent medium. The effect of linear dispersion on self-action during pulse propagation is also discussed. Moreover, the nonlinear spectroscopy of water vapour at THz frequencies is reported. Atmospheric water vapour has a rich spectrum with several strong resonances at frequencies below 3 THz, falling within the range of operation of most existing THz sources. An extremely large nonlinear response to THz radiation is observed at the positions of these resonances. Using the optical Kerr model for the nonlinear response, a minimum nonlinear refractive index of the order of 10² m²/W is estimated. The results provide insight into the energy levels of the water molecule and give a more accurate picture of its response to electromagnetic radiation, paving the way to more accurate THz spectroscopy, imaging, and sensing systems, and thereby facilitating future emerging THz technologies. Finally, the nonlinear response of solids at THz frequencies is studied. It has been shown that a phonon-induced THz Kerr effect can result in a larger nonlinear refractive index than the nonlinear refractive index at the visible or near-infrared range (optical Kerr effect). This pronounced nonlinear optical behavior is verified using a time-domain characterization approach. The results indicate a large delay occurred to the THz fields as they transmit through some of the material samples. In the frequency domain, the induced nonlinear phase shift of the intense THz field is shown to be relatively large of the order of 0.1 rad. From the phase information, the nonlinear phase is extracted by which the dispersion profile of n₂ is obtained.

No description available.

With the recent resurgence of interest in double negative (DNG) materials and the reported construction of a metamaterial with DNG characteristics, applications of these materials become feasible and examination of the behavior of systems and devices a potentially fruitful topic. The most promising area of research, upon inquiry into past work related to DNG materials, proves to be dielectric waveguides. The present investigation, then, focuses on the inclusion of DNG materials in various planar dielectric waveguide configurations. These waveguides involve a core region surrounded by various numbers of symmetrically-placed cladding layers. The present investigation involves the review of the electromagnetic properties of DNG materials by a thorough analysis based on Maxwell's equations. The use of a negative index of refraction for these materials is justified. These results are then used to perform a frequency domain analysis of an N-layer formulation for dielectric waveguides which is general for any combination of DNG and double positive (DPS) materials. This N-layer formulation allows for the derivation of the characteristic equation, which relates the operating frequency and the propagation constant solutions, along with the cutoff conditions and field distributions. A causal material model which obeys the Kramers-Kronig relations and which is based on measurements of a realized metamaterial is studied and used in the investigation in order to produce realistic results. The N-layer formulation is then applied to the three-layer (slab) waveguide and known results are reviewed. A new interpretation of intramodal degeneracy is given, whereby degenerate modes are split into two separate modes, one with positive phase velocity and one with negative phase velocity but both with a causal positive group (energy) velocity. Next, the formulation is applied to the five-layer waveguide. New behaviors are observed in this case which are not seen for the three-layer waveguide, including the return of the fundamental mode in some cases, whereas it is never present for the three-layer guide, the absence of certain higher-order modes in some situations and the appearance of new modes. Additionally, for some configurations the order of the even and odd modes in the DNG frequency range is found to be reversed from that of conventional waveguides. The photonic crystal waveguide, which involves an infinite number of periodically placed cladding layers, is next studied using ray analysis, and a slight variation of the N-layer formulation is used to compare these results with those of the pseudo-photonic crystal waveguide. The pseudo-photonic crystal waveguide is identical to the photonic crystal waveguide with the exception that it has only large but finite number of layers. It is seen that the results of these two cases are similar for conventional modes, but the photonic crystal waveguide allows for new modes called photonic crystal modes which are inaccessible through conventional waveguides. Interesting phenomena such as mode crossings among the photonic crystal modes are observed and discussed. Using the results from the frequency domain analysis of the five-layer waveguide, a Fourier transform technique is used to study pulse propagation in a waveguide containing DNG materials. A Gaussian pulse is launched in the waveguide over the frequency range covering a portion of the positive- and negative-phase-velocity fundamental transverse electric (TE) modes. Splitting of the input pulse into two separate pulses is observed, where both of these new pulses have a causal, positive energy velocity. The interpretation of intramodal degeneracy given in previous discussions is buttressed with evidence from this portion of the investigation, thus completing the analysis and bringing the present study to its conclusion. / Ph. D.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In this thesis, a femtosecond electron diffraction (FED) set-up that is capable of investigating the photo-induced switching of Cu(DCNQI)2 from being an insulator to being a conductor is presented. Movies of atomic structural changes with temporal resolution within the typical photo-switching transition timescales (sub-picoseconds) are obtainable with this set-up by employing a femtosecond laser. The experimental technique and the design of a crucial instrument of the machine, the electron gun, are extensively described and characterised both numerically and experimentally. The interest in observing atomic structural changes of Cu(DCNQI)2 in real time is because of the rich variety of the radical salts available that show alloy-specific Charge Density Wave (CDW) transitions. Valuable insights about the driving mechanisms behind these structural changes that are responsible for a change in conductivity are obtainable, as well as the relation between crystal alloys and their transition characteristics. Electron diffraction patterns of crystals in their metallic phase (room temperature) are shown in this thesis, but diffraction patterns of cryo-cooled Cu(DCNQI)2 in its insulating phase are still to be acquired. The temporal resolution of the atomic movie can be improved by recompression of electron pulses that are debunched due to Coulomb repulsion and electron energy spread within a pulse. Numerical and preliminary experimental results presented in this work expose the potential of a simple compression technique. In this way, more electrons in a single electron pulse can be afforded which allows to perform experiments at shorter integration time or lower repetition rate. / AFRIKAANSE OPSOMMING: In hierdie tesis word ’n femtosekonde elektron diffraksie opstelling aangebied wat daartoe in staat is om die foto-geïnduseerde omskakeling in Cu(DCNQI)2 van nie-geleier tot geleier te ondersoek. Deur gebruik te maak van ’n femtosekonde laser in hierdie opstelling, is ’rolprente’ van strukturele veranderinge op atoomskaal met ’n tyd resolusie beter as die tipiese foto-omskakelings tydskaal (sub-pikosekonde) verkrygbaar. Die eksperimentele tegniek en die ontwerp van ’n noodsaaklike instrument van die masjien, die elektron geweer, word breedvoerig beskryf en numeries en eksperimenteel gekenmerk. Die belangstelling om strukturele veranderinge in Cu(DCNQI)2 op atoom skaal in reële tyd waar te kan neem is as gevolg van die ryke verskeidenheid van radikale soute, wat allooispesifieke ladings digtheid golf (CDW) oorgange toon, wat beskikbaar is. Waardevolle insigte oor die meganismes wat hierdie strukturele veranderinge wat ’n verandering in geleiding veroorsaak dryf is verkrygbaar, sowel as die verwantskap tussen die kristal allooi en die oorgang kenmerke. Diffraksie patrone van kristalle in die metaalagtige fase (kamer temperatuur) word in hierdie tesis getoon, maar diffraksie patrone van cryo-verkoelde Cu(DCNQI)2 in die niegeleier fase moet nog verkry word. Die tyd resolusie van die atomiese rolprent kan verbeter word deur die elektron puls — wat deur Coulomb afstoting en elektron energie spreiding versprei is — weer saam te pers. Numeriese en voorlopige eksperimentele resultate toon die potensiaal van ’n eenvoudige kompressie tegniek. Hierdeur kan meer elektrone in ’n elektron puls gegun word en so die integrasie tyd of die herhalingstempo van die eksperimente verkort kan word.

Este trabalho tem por objetivo o estudo de dispersão de pulsos ultracurtos em estruturas metamateriais para a faixa de micro-ondas. Como é bem sabido, os metamateriais são estruturas altamente dispersivas em qualquer faixa de frequências. Essas características dispersivas são normalmente tratadas como deletérias para a propagação de pulsos. Entretanto, nesta dissertação é demonstrado que essas mesmas características podem produzir efeitos benéficos em certas aplicações. Para isso é realizada uma análise teórica detalhada das características de dispersão de células metamateriais de diferentes geometrias. Adicionalmente, é investigada a propagação de um pulso gaussiano em meios metamateriais infinitos com o objetivo de melhor compreender fenomenologia por trás dos efeitos de dispersão nesses materiais. É também apresentado um novo procedimento de homogeneização de metamateriais que permite descrever estes meios de maneira mais precisa e com menor custo computacional que métodos encontrados na literatura. Esse método é baseado em modelos materiais conhecidos, como os de Lorentz e Drude. Este trabalho também apresenta uma nova abordagem para compressão de pulsos e compensação de dispersão por meio da propagação de pulsos de micro-ondas chirpados em metamateriais no regime de refração negativa. Para conseguir esse efeito, são investigadas placas de metamateriais com espessuras de 1, 3, 5 e 7 células metamateriais utilizando o método das diferenças finitas no domínio do tempo (FDTD) juntamente com técnicas de extração de parâmetros. É demonstrado que com o controle do chirp inicial do pulso, em associação com a densidade/geometria das células metamateriais e de sua resposta em frequência, é possível não só compensar o alargamento temporal desses pulsos devido à dispersão cromática como também realizar a compressão temporal por um fator de 2. / The goal of this work is to study the dispersion of ultra-short microwave pulses in metamaterials structures. It is well known that metamaterials are highly dispersive structures in any frequency range. These dispersive characteristics are normally treated as deleterious to pulse propagation. However, in this dissertation it is demonstrated that these characteristics can produce beneficial effects in certain applications. This assertion is addressed through a theoretical analysis of the dispersion of metamaterials cells of different geometries. In addition, it is investigated the propagation of a gaussian pulse through an infinite homogeneous metamaterial structure aiming at improving our understanding of the phenomenology behind dispersion effects in such media. It is also presented a new homogenization procedure for metamaterials that allows these media to be described in a more realistic manner and with computational cost lower than those currently found in the literature. This procedure is based on well known material models, such as Drude and Lorentz models. This work also introduces an efficient technique for pulse compression and dispersion compensation via propagation of chirped microwave pulses through metamaterials in the negative refraction regime. To accomplish this, it is investigated infinitely wide metamaterial slabs with thicknesses of 1, 3, 5, and 7 cells with a finite difference in time domain method together with a parameter extraction technique. It is demonstrated that by controlling the chirp of the initial pulse, in association with the metamaterial cell density/geometry and frequency response, it is possible not only to compress the pulse (by a factor of 2), but also to compensate pulse broadening due to chromatic dispersion.

New generations of ultrashort and intense laser pulses as well ashigh power synchrotron radiation sources and x-ray free electronlasers have promoted fast developments in nonlinear optics andx-ray spectroscopy.The new experimental achievements and the appearance of varieties of novelnonlinear phenomena call for further development of theories. The objective of this thesis is to develop and apply thetheories to explain existing experimental data and to suggest new experiments. The first part of the thesis is devoted to nonlinear propagation of optical pulses. It is shown that the vibrational levels can be selectively populated by varying the duration, shape and intensity of the pump pulse. We obtained a strict analytical solution for the resonant two-photon interaction in a multilevel system beyond rotating wave approximation. Simulations show that the polarization anisotropy of the two-photon excitation affects strongly the anisotropy of photobleaching.The two-photon area theorem is reformulated with taking into account the dynamical Stark shift and the contribution from the permanent dipole moments. In general the dynamical Stark shift does not allow complete population of the excited state, but it can be compensated by detunings in atoms. A dynamical theory of the sequential two-photon absorption of  microsecond pulses  is developed to explore the role of transverse inhomogeneity of the light beam on optical limiting properties.  The propagation of ultrashort laser pulses in nondipolar and dipolar media is investigated with special attention to the generation of superfluorescence and supercontinuum and the formation of attosecond pulses. The second part of the thesis addresses the interaction of molecules with x-ray radiation.  We explore here the role of nuclear dynamics in resonant Auger scattering. Multimode simulations of the Auger spectra of ethylene molecule explain the main spectral features of the experimental spectra and show that the spectral profiles are formed mainly due to six vibrational modes. We predict the Doppler splitting of the atomic peak in resonant Auger scattering from SF6 molecule for circularly polarized x-rays. This effect is confirmed by the recent experiment. A new scheme of x-ray pump-probe spectroscopy, namely, resonant inelastic x-ray scattering accompanied by core-hole hopping induced by strong laser fields is suggested. The laser-induced promotion of core holes opens the symmetry forbidden scattering channels and gives rise to new spectral lines in the x-ray scattering spectrum. The strength of the symmetry forbidden lines becomes strong when  the time of Rabi flopping is shorter than the lifetime of the core-excited state. We study the role of propagation of femtosecond x-ray free-electron pulses on the Auger process. Simulations show  that there exists a strong competition between Auger decay and stimulated emission. The Auger yield and Auger branching ratio are strongly suppressed in the course of pulse propagation. / QC 20100729