Comparison of a one and two parameter family of transmission conditions for Maxwell's equations with damping

Transmission conditions between subdomains have a substantial influence on the convergence of iterative domain decomposition algorithms. For Maxwell's equations, transmission conditions which lead to rapidly converging algorithms have been developed both for the curl-curl formulation of Maxwell's equation, see [2, 3, 1], and also for first order formulations, see [7, 6]. These methods have well found their way into applications, see for example [9, 11, 10]. It turns out that good transmission conditions are approximations of transparent boundary conditions. For each form of approximation chosen, one can try to find the best remaining free parameters in the approximation by solving a min-max problem. Usually allowing more free parameters leads to a substantially better solution of the min-max problem, and thus to a much better algorithm. For a particular one parameter family of transmission conditions analyzed in [4], we investigate in this paper a two parameter counterpart. The analysis, which is substantially more complicated than in the one parameter case, reveals that in one particular asymptotic regime there is only negligible improvement possible using two parameters, compared to the one parameter results. This analysis settles an important open question for this family of transmission conditions, and also suggests a direction for systematically reducing the number of parameters in other optimized transmission conditions

Rigorous numerical study of strong microwave photon-magnon coupling in all-dielectric magnetic multilayers

We demonstrate theoretically a strong local enhancement of the intensity of the in-plane microwave magnetic field in multilayered structures made from a magneto-insulating yttrium iron garnet (YIG) layer sandwiched between two non-magnetic layers with a high dielectric constant matching that of YIG. The enhancement is predicted for the excitation regime when the microwave magnetic field is induced inside the multilayer by the transducer of a stripline Broadband Ferromagnetic Resonance (BFMR) setup. By means of a rigorous numerical solution of the Landau-Lifshitz-Gilbert equation consistently with the Maxwell's equations, we investigate the magnetisation dynamics in the multilayer. We reveal a strong photon-magnon coupling, which manifests itself as anti-crossing of the ferromagnetic resonance (FMR) magnon mode supported by the YIG layer and the electromagnetic resonance mode supported by the whole multilayered structure. The frequency of the magnon mode depends on the external static magnetic field, which in our case is applied tangentially to the multilayer in the direction perpendicular to the microwave magnetic field induced by the stripline of the BFMR setup. The frequency of the electromagnetic mode is independent of the static magnetic field. Consequently, the predicted photon-magnon coupling is sensitive to the applied magnetic field and thus can be used in magnetically tuneable metamaterials based on simultaneously negative permittivity and permeability achievable thanks to the YIG layer. We also suggest that the predicted photon-magnon coupling may find applications in microwave quantum information systems

Characterization of multi-wall carbon nanotubes and their applications

PhDCarbon nanotubes (CNT) and their applications is a field which has attract a lot of interest in the past two decades. Since the first invention of CNTs in 1991, and in view of utilising nanoantennas, the focus in many laboratories around the world has shifted to trying to lengthen nanotubes longer from nanometers to few centimeters. Eventually this could lead to CNTs’ use in sub-millimeter, millimiter wave and microwave antenna applications. In this thesis, fundamental properties of carbon nanotube films are investigated, and some applications such as the use of CNTs as absorbers or CNT doped liquid crystals are considered. The concept of frequency tunable patch antennas is also presented. Simulation and measurement results of the liquid crystal based antenna show that frequency tuning is possible, through the use of a liquid crystal cell as a substrate. Additionally, greater tuning can be achieved using liquid crystals with higher dielectric anisotropy at microwave frequencies. This can be achieved by using CNT doped liquid crystals. As mentioned, microwave and terahertz measurements of vertically aligned carbon nanotube arrays placed on the top surface of a rectangular silicon substrate are presented. The S-parameters are calculated allowing the extraction of the complex permittivity, permeability and conductivity of the samples. Theoretical models are being introduced delineating the behaviour of the multi-walled nanotube (MWNT) samples. The material properties of this film provide useful data for potential microwave and terahertz applications such as absorbers. Finally, finite-difference time-domain (FDTD) modelling of CNTs is introduced, verifying the measurements that have been performed, confirming that CNT arrays can be highly absorptive. A novel estimation of the permittivity and permeability of an individual carbon nanotube is presented and a periodic structure is simulated, under periodic boundary conditions, consisting of solid anisotropic cylinders. In addition, the optical properties of vertically aligned carbon nanotube (VACNT) arrays, when the periodicity is both within the sub-wavelength and wavelength iii regime are calculated. The effect of geometrical parameters of the tube such as length, diameter and inter-tube distance between two consecutive tubes are also examined

Nonlinear optics

Nonlinear light-matter interactions have been drawing attention of physicists since the 1960's. Quantum mechanics played a significant role in their description and helped to derive important formulas showing the dependence on the intensity of the electromagnetic field. High intensity light is able to generate second and third harmonics which translates to generation of electromagnetic field with multiples of the original frequency. In comparison with the linear behaviour of light, the nonlinear interactions are smaller in scale. This makes perturbation methods well suited for obtaining solutions to equations in nonlinear optics. In particular, the method of multiple scales is deployed in paper 3, where it is used to solve nonlinear dispersive wave equations. The key difference in our multiple scale solution is the linearity of the amplitude equation and a complex valued frequency of the mode. Despite the potential ill-posedness of the amplitude equation, the multiple scale solution remained a valid approximation of the solution to the original model. The results showed great potential of this method and its promising wider applications. Other methods use pseudo-spectral methods which require an orthogonal set of eigenfunctions (modes) used to create a substitute for the usual Fourier transform. This mode transform is only useful if it succeeds to represent target functions well. Papers 1 and 2 deal with investigating such modes called resonant and leaky modes and their ability to construct a mode transform. The modes in the first paper are the eigenvalues for a quantum mechanical system where an external radiation field is used to excite an electron trapped in an electrical potential. The findings show that the resonant mode expansion converges inside the potential independently of its depth. Equivalently, leaky modes are obtained in paper 2 which are in close relation to resonant modes. Here, the modes emerge from a system where a channel is introduced with transparent boundaries for simulation of one-directional optical beam propagation. Artificial index material is introduced outside the channel which gives rise to leaky modes associated with such artificial structure. The study is showing that leaky modes are well suited for function representation and thus solving the nonlinear version of this problem. In addition, the transparent boundary method turns out to be useful for spectral propagators such as the unidirectional pulse propagation equation in contrast to a perfectly matched layer

The analysis of dielectric-loaded ferrite phase shifters including the effects of losses

Ph.D.F. Kenneth Hur

Wave propagation through soils in centrifuge testing.

International audienceWave propagation phenomena in soils can be experimentally simulated using centrifuge scale models. An original excitation device (drop-ball arrangement) is proposed to generate short wave trains. Wave reflections on model boundaries are taken into account and removed by homomorphic filtering. Propagation is investigated through dispersion laws. For drop-ball experiments, spherical wave field analysis assuming linear viscoelasticity leads to a complete analytical description of wave propagation. Damping phenomena are examined and evaluated using this description