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Recent experimental realizations of single-cycle pulses in the terahertz, infrared, and optical regions provide promising light sources for applications in telecommunication, medical imaging, spectroscopy, and coherent control. In the resonant regime, the short duration of such pulses imply that they may escape certain effects that are detrimental to coherence; spontaneous emission is one such example. In combination with an octave-spanning spectral bandwidth, an adequate theoretical approach necessitates a semiclassical coherence model outside the conventional few-level, rotating wave, and slowly varying envelope approximations. The evolution equations that govern the underlying dynamics of such systems are inherently nonlinear and possess solutions only in certain idealized, limiting cases. In this thesis we investigate the viability of obtaining general-purpose numerical solutions to such problems. A computational approach based on Maxwell’s equations coupled with a multi-level quantum mechanical model for homogeneously and inhomogeneously broadened media is reported. The formulation leads to a numerical algorithm applicable to bi-directional propagation of pulses of arbitrary duration along all three spatial coordinates. For sufficiently dense inhomogeneously broadened materials we show, numerically, that when the forward propagation approximation of Maxwell’s wave equation is not valid, certain types of optical solitons may lose a significant amount of energy with increasing propagation distance through the co-excitation of a backward mode. A second set of computational routines is based on neglection of optical backpropagation in Maxwell’s wave equation. The resulting propagation equation generalizes the paraxial wave equation to the single-cycle pulse regime and is shown to be susceptible to numerical integration in conjunction with quantum theory. Our computer code is applied to femtosecond conical emission in atomic sodium. We find that cone emission occurs together with spatiotemporal pulse breakup analogous to the soliton-type splitting observed in self-induced transparency. We furthermore support these results by presenting complementary numerical calculations of the same phenomenon in the picosecond pulse regime. The angular structure of the conical emission observed numerically agrees with expermental measurements performed by others. Our computational results resolve some of the underlying questions surrounding conical emission in alkali metal vapors. Consideration of optical selection rules in rigid-rotor molecules is shown to greatly simplify the numerical evaluation of single-cycle pulse propagation in multi-level molecular systems. Numerical application of linearly polarized single-cycle terahertz pulses in rigid rotor molecular media, incorporating a full rotational manifold, shows that coherent bleaching effects ultimately lead to self-steepening of the driving pulse. A possible practical consequence of these results is that coherent, nonlinear saturation effects may partially cancel dispersion-induced temporal broadening of single-cycle pulses, opening up the possibility of increased energy transmission of terahertz pulses through molecular media. PhD i elektronikk og telekommunikasjon PhD in Electronics and Telecommunication

Avhandlingen undersøker hvordan streamerutbredelse langs en dielektrisk overflate påvirkes av profilen på overflaten. Et eksperimentelt oppsett er utformet for å etterligne en 2D modell som også simuleres. Simuleringsprogramvaren er et avansert program som beregner utladningsdynamikken i gassen. Tre forskjellige dielektriske overflater er maskinert med en bestemt overflateprofil. Den ene er glatt (høyde = 0 um) og de to andre har en profil med høyden 200 um og 500 um. Streamerutbredelsen dokumenteres ved å bruke et høyhastighetskamera og ved å måle spennings- og strømutviklingen under forsøkene. Lynimpulser påføres med to forskjellige spenningsnivåer (14 kV og 35 kV), slik at streamer vil stoppe i det ene tilfelle og gå helt til jord i det andre tilfellet. Hastigheten og utbredelsesavstanden til streamerene reduseres betydelig når den beveges langs de profilerte overflatene. Jo høyere overflateprofilen er, desto mer blir streamer bremset og rekkevidden reduseres. Simuleringene gir innsikt i hvorfor dette skjer. De profilerte flatene har lengre overflatelengde per lengde i x-retning, men dette forklarer ikke hele reduksjonen i forplantningshastighet eller lengde. Hastigheten til streameren blir kraftig redusert når den klatrer opp mot toppene på overflateprofilen. Den beveger seg raskere på vei ned, men gjennomsnittshastigheten blir fortsatt redusert som en konsekvens av toppen. E-feltet på streamerhodet er rettet inn mot det dielektriske planet når det klatrer toppen, og dette er vist at begrenser elektronskredene på streamerhodet. For høye spenninger kan det også forekomme at negativ overflateladning forandrer hastighetsforløpet til streameren. Allikevel er gjennomsnittshastigheten ikke veldig påvirket av denne effekten. Reduksjonen i streamerhastighet og rekkevidden ved bruk av profilerte overflater kan være av interesse for bruk i høyspenningskomponenter. The thesis investigates how streamer propagation along a dielectric surface is affected by the profile of the surface. An experimental setup is designed to reassemble a 2D model, which is also simulated. The simulation software is an advanced program that calculates the discharge dynamics in the gas. Three different dielectric surfaces are machined with specific surface profiles. One is smooth (height = 0 um) and the two others have a profile with a height of 200 um and 500 um. The streamer propagation is documented by using a high-speed camera and by measuring the voltage and current evolution during the experiments. Lightning impulses are applied with two different voltage levels (14 kV and 35 kV),and they are chosen so that the streamer will stop in one case and reach ground in the other case. The speed and propagation distance of the streamers are significantly reduced when moving along the profiled surfaces. The higher the surface profile, the more the streamer is slowed down, and the propagation is reduced. The simulations give insight into why this is. The profiled surfaces have a longer surface length per length in x-direction, but this does not explain the whole reduction in either propagation speed or length. The streamer is greatly slowed down when climbing the peaks on the surface profile. It moves faster on the way down, but the average speed is still reduced as a consequence of the peak. The E-field on the streamer head is directed into the dielectric plane when it is climbing the peak, and this is shown to limit the electron avalanches on the streamer head. For high voltages, negative surface charging can also occur, which alters the propagation of the streamer. However, the average speed is not affected greatly by this effect. The reduction in streamer speed and propagation distance when using profiled surfaces can be of interest for high voltage engineering.

A novel numerical fluid model for simulating streamer discharges has been tested and utilized with a two-diemnsional triple junction configuration. The triple junction was located at the upper end of a 1 cm dielectric rod, and positive streamers were initiated by applying a constant voltage of 18.5 kV to the triple junction anode. After inception, propagation along the dielectric rod was investigated, and the streamer velocities was estimated to be about 0.05 mm/ns. The streamers was found to be very thin, only spanning across three layers of cells, if the charge density was used as a measurement. This was unexpected, and as far as the author is concerned, such a result has not been reported elsewhere. In the layer of cells closest to the dielectric, a very high charge density with a maximal value of 158.3 micro C/cm$ was seen. Simulations have also been performed using a 0.5 mm rod-plane gap configuration with a grounded dielectric barrier, displaying similar results for streamers propagating along the dielectric surface. With this configuration, multiple simulations were performed in order to probe how various electron yield coefficients for photoemission from the dielectric rod affected the dynamics of the streamers. With a coefficient value of 10, the discharge behaved quantitatively different than what was observed when a value of 0.1 and 1 was used. All simulations were performed in a nitrogen-oxygen mixture under normal conditions. Due to use of an explicit second order Runge-kutta method for advancing the hydrodynamic equations in time, restrictions on the sizes of the time steps had to be followed to avoid instability. Because of stiffness in the equation set, time steps of the order of 1e-13-1e-15 was found to be required for stability. Another issue with the numerical code was uncovered in form of memory leakage, causing the simulations to crash after approximately 13 000 time-iterations. With these limitations, full simulations of streamer propagation along the entire lengths of the dielectric surfaces could not be done. Also experimental work has been performed with a triple junction configuration similar to that used in the simulations. By means of a high-speed camera with a minimal exposure time of 10 ns, streamer discharges along the dielectric rod was attempted arrested. Based on the experimental data, a lower propagation speed of 1 mm/ns is estimated. It must however be noted that excess charge present on the rod from earlier experiments could have influenced the estimated lower bound propagation speed.