We present detailed theoretical and experimental analysis of the magneto-optic transverse Kerr effect in magnetic multilayers. The theoretical model is based upon a phenomenological permittivity tensor. From the general result, suitable only for numerical calculations, we derive several approximate analytical expressions in order to make a qualitative discussion. The theoretical predictions are compared with experimental results in Y/Co bilayers, and the good agreement found allows for an accurate determination of the magneto-optical constants of the material. Then, the theoretical model is applied to make a detailed study of interface magnetism in Y 1Ϫx Co x alloys, and to perform numerical simulations in Co/Cu and Fe/Cu multilayers. The results in multilayers highlight the complex behavior of the magneto-optic transverse Kerr effect, in which the contributions of the individual layers are never strictly additive. This nonlinearity is found to be strongly dependent on the 3d magnetic metal present and could be used to probe the alignment of the layers even in a configuration of vanishing magnetic moment.
A unified and generalized formulation for the complexspatial point source beam solutions of the Helmholtz wave equation in the spatial and the Fourier-spectral domains for both, 3D and 2D scenarios, is presented in this paper. This general formulation is based on the description of the solutions in terms of complex distances and complex angles, emphasizing the physical meaning of these complex quantities and the relationship between spatial and spectral representations.
The well known 2D complex-point-source beam presents undesired field characteristics. This paper proposes some combinations of simple complex beams which allow the construction of well behaved fields.
The definition of a complex polar coordinate system that unifies complex distances and complex angles together with their relations with the real observation space is presented in this paper. Its utility is shown through some applications to electromagnetic problems: (i) new solutions are obtained from well-known solutions in real polar coordinates, (ii) the parameterization of the real space in terms of the complex polar coordinates helps to understand the physical behaviour of those solutions, and (iii) the results provide a better physical insight of the complex distances and angles.
Abstract-This paper is concerned with the analysis of the currents induced on a 2D infinite perfectly conducting plane illuminated by a complex beam obtained from the analytical continuation of the real location of a unit impulse source into a complex one. The main goal considering this well-known problem is to understand the meaning of the analytical continuation and the physical information underlying the complex quantities arising from it, and to investigate the capabilities of operating in complex spaces instead of the original real ones through a simple example. Several complex quantities directly related to this problem are analysed and translated into the real domain, leading to a clear and general description of all the possible behaviours of the currents. These results will provide some new insight to extend the complex analysis methodology to more complicated scattering problems. As expected, complex analysis appears to be a full-meaning tool to obtain parameterizations of EM problems, leading to more general solutions and their physical descriptions.
300González-Morales, Gago-Ribas, and Dehesa-Martínez
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