Spatiotemporal evolution of non-diffracting plasmonic pulses

Beugung ist ein allgegenwärtiges Phänomen in der Optik. In den späten 80er Jahren wurden zur Auslösung der Beugung Bessel-Strahlen vorgeschlagen und beobachtet. Bessel-Strahlen breiten sich im freien Raum ohne Beugung aus, sie können jedoch nur in drei Dimensionen existieren. Im letzten Jahrzehnt hat sich nach der bahnbrechenden Arbeit von Siviloglou und Christodoulides über Airy-Strahlen erhebliches Interesse an nicht-beugenden Strahlen entwickelt. Da die Airy-Strahlen auch in zwei Dimensionen existieren können, eignen sie sich besonders für die planarephotonik, z. B. an Metall-Dielektrikum-Grenzflächen. In dieser Doktorarbeit wird die Erzeugung von Airy-Strahlen und deren Eigenschaften an der Metall-Dielektrikum-Grenzfläche eingehend untersucht. Der Kern dieser Arbeit untersucht die räumliche und raum- zeitliche Entwicklung von Airy-Plasmonen. Ausreichendes Hintergrundwissen über elektromagnetische Theorie und numerische Methoden wurde dafür benötigt. Wir haben die räumlichen Eigenschaften von Airy-Plasmonen mit Hilfe der Photoemissions- Elektronenmikroskopie untersucht und eine rigorose Finite-Di erenzen-Zeitbereichsm- ethode angewendet. Die Ergebnisse wurden auch durch die Verwendung einer Strahl- propagationsmethode (BPM) bestätigt. Die BPM bietet eine Simulationsmethode zur schnelleren Optimierung der Struktur des anregungsgitters der Airy-Plasmonen. Diese Arbeit quantifiziert weiter die Erzeugungse zienz der nichtparaxialen Airy-Plasmonen eines Beugungsgitters. Es wurde eine breitbandige Erzeugungsbandbreite von Airy- Plasmonen gefunden, was einen gangbaren Weg zur Untersuchung von ultrakurz ge- pulsten Airy-Plasmonen darstellt. Das Beugungsgitter wurde optimiert, um die ultra- kurzen Airy-Plasmonenpulse zu erzeugen. Die raumzeitliche Entwicklung von Airy- Plasmonenpulsen wurde numerisch untersucht. Ein analytisches, semi-analytisches und numerisches Modell wurden eingesetzt, um die Trajektorie der zeitgemittelten Airy-Plasmonenpulse zu untersuchen

Simulating Maxwell–Schrödinger Equations by High-Order Symplectic FDTD Algorithm

A novel symplectic algorithm is proposed to solve the Maxwell–Schrödinger (M–S) system for investigating light–matter interaction. Using the fourth-order symplectic integration and fourth-order collocated differences, M–S equations are discretized in temporal and spatial domains, respectively. The symplectic finite-difference time-domain (SFDTD) algorithm is developed for accurate and efficient study of coherent interaction between electromagnetic fields and artificial atoms. Particularly, the Dirichlet boundary condition is adopted for modeling the Rabi oscillation problems under the semiclassical framework. To implement the Dirichlet boundary condition, image theory is introduced, tailored to the high-order collocated differences. For validating the proposed SFDTD algorithm, three-dimensional numerical studies of the population inversion in the Rabi oscillation are presented. Numerical results show that the proposed high-order SFDTD(4, 4) algorithm exhibits better numerical performance than the conventional FDTD(2, 2) approach at the aspects of accuracy and efficiency for the long-term simulation. The proposed algorithm opens up a promising way toward a high-accurate energy-conservation modeling and simulation of complex dynamics in nanoscale light–matter interaction

An explicit and symmetric exponential wave integrator for the nonlinear Schr\"{o}dinger equation with low regularity potential and nonlinearity

We propose and analyze a novel symmetric exponential wave integrator (sEWI) for the nonlinear Schr\"odinger equation (NLSE) with low regularity potential and typical power-type nonlinearity of the form $f(\rho) = \rho^\sigma$, where $\rho:=|\psi|^2$ is the density with $\psi$ the wave function and $\sigma > 0$ is the exponent of the nonlinearity. The sEWI is explicit and stable under a time step size restriction independent of the mesh size. We rigorously establish error estimates of the sEWI under various regularity assumptions on potential and nonlinearity. For "good" potential and nonlinearity ($H^2$-potential and $\sigma \geq 1$), we establish an optimal second-order error bound in $L^2$-norm. For low regularity potential and nonlinearity ($L^\infty$-potential and $\sigma > 0$), we obtain a first-order $L^2$-norm error bound accompanied with a uniform $H^2$-norm bound of the numerical solution. Moreover, adopting a new technique of \textit{regularity compensation oscillation} (RCO) to analyze error cancellation, for some non-resonant time steps, the optimal second-order $L^2$-norm error bound is proved under a weaker assumption on the nonlinearity: $\sigma \geq 1/2$. For all the cases, we also present corresponding fractional order error bounds in $H^1$-norm, which is the natural norm in terms of energy. Extensive numerical results are reported to confirm our error estimates and to demonstrate the superiority of the sEWI, including much weaker regularity requirements on potential and nonlinearity, and excellent long-time behavior with near-conservation of mass and energy.Comment: 35 pages, 10 figure

Numerical and Analytical Methods in Electromagnetics

Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics

Self-Induced Transparency Solitons in Nanophotonic Waveguides

This thesis explores the existence and properties of self-induced transparency (SIT) solitons in nanophotonic waveguides. SIT solitons are shape-preserving solutions of the semi-classical Maxwell-Bloch equations, a system of nonlinearly coupled differential equations. In a first investigation, collisions of counterpropagating simultons (SIT solitons in absorbing three-level systems) are studied numerically in the plane-wave approximation and a polarisation- and group-velocity dependent soliton birth is uncovered. Apart from their fundamental interest, such light-light interaction effects may be of use for optical computing applications if they can be transferred to tightly confined light pulses. Confining light is usually achieved by using dielectric waveguides that exhibit group velocity dispersion leading to chirped pulses, which experience absorption when entering an absorbing medium. If the chirp is strong enough and the pulse intense enough, they can even completely invert an absorber. When investigating chirped pulse propagation through a dense ensemble of two-level system it is found that the chirped pulses dynamically reshape into unchirped pulses experiencing transparency. Furthermore, the conditions on the waveguide geometry to enable SIT are analysed, identifying a nanophotonic slot waveguide with a low-index gap, exhibiting high electric field enhancement and a homogeneous field profile, as the ideal candidate system for guided SIT solitons. This analysis is supported by two-dimensional numerical calculations that show the solitary character is maintained during propagation if the absorber density is high enough to ensure a slow-down of the pulse and to thus counteract the waveguide dispersion. Finally, the soliton birth due to simulton collisions and optical memory schemes proposed for plane-wave SIT are investigated in the two-dimensional slot waveguide and found to also be possible in this geometry

Optical near-field dynamics of active 2D semiconductors

When structures with a strong confinement of the electromagnetic fields are considered, the near-field dynamics becomes integral to the description of a semiconductor. Not only it provides feedback from the environment, as is the case in a laser system, but it further mediates the interaction between different, otherwise independent, positions. In such a context, a full-field spatio-temporal description is essential to faithfully describe the dynamics of either an extended semiconductor system or a set of spatially separated emitters. This thesis highlights the importance of combining a complex (many-body and band-resolved) model of semiconductor carrier dynamics with a full-field description of the electromagnetic fields by presenting some applications. With the recent rise in popularity of atomically thin materials, semiconductors can be embedded in increasingly smaller optical environments, whose properties can only be studied by self-consistently combining carrier and field dynamics. The ability to calculate the linear and non-linear response of a system under arbitrary excitation conditions is shown. This is performed without any prior knowledge of the electromagnetic environment and can thus be extended to complex geometries. By embedding active materials in a tailored environment, the complex interaction of the two can be exploited to engineer the optical response of the system by using a self-consistent modelling technique. The complex dynamical interaction between field and gain in a semiconductor laser is another example of a system in which a self-consistent model is required. Here, a set of one-dimensional simulations is reported showing how the output of a semiconductor laser is highly sensitive to perturbation arising from sub-wavelength dynamics of the gain medium. By introducing a random patterning of the laser cavity, a novel approach to the suppression of dynamical instabilities in a laser output is demonstrated. This scheme, based on complex wave interference, is introduced by spatially perturbing the optical environment.Open Acces

Optical Communication

Optical communication is very much useful in telecommunication systems, data processing and networking. It consists of a transmitter that encodes a message into an optical signal, a channel that carries the signal to its desired destination, and a receiver that reproduces the message from the received optical signal. It presents up to date results on communication systems, along with the explanations of their relevance, from leading researchers in this field. The chapters cover general concepts of optical communication, components, systems, networks, signal processing and MIMO systems. In recent years, optical components and other enhanced signal processing functions are also considered in depth for optical communications systems. The researcher has also concentrated on optical devices, networking, signal processing, and MIMO systems and other enhanced functions for optical communication. This book is targeted at research, development and design engineers from the teams in manufacturing industry, academia and telecommunication industries