Stochastic electromagnetic fields can be described by the auto-and cross correlation spectra of the electric and magnetic field values at pairs of points in space. In this work the characterization of noisy electromagnetic fields by sampling the field values in pairs of sampling points is discussed. Sampling of the electric or magnetic field values in all pairs of a set of sampling points yields the correlation matrix of the field samples. If the near-field in a surface of reference enclosing the stochastic field sources is sampled and characterized by its correlation matrix the field radiated in the space outside the surface of reference can be calculated and described by the field correlation spectra. Depending on the number of statistically independent field sources the eigenvalue decomposition of the correlation matrix yields a compact description of the measured EM noise field. I. INTRODUCTIONNumerical values of noise amplitudes cannot be specified for stochastic signals. For numerical modeling of noisy circuits one has to deal with energy and power spectra. Correlation matrix based methods have been developed for the numerical simulation of noisy linear circuits [1]- [4]. Stochastic electromagnetic fields can be described by the auto-and cross correlation spectra of the electric and magnetic field values at pairs of points in space. In this work the characterization of noisy electromagnetic fields by sampling the field values in pairs of sampling points is discussed. Sampling of the electric or magnetic field values in all pairs of a set of sampling points yields the correlation matrix of the field samples. If the nearfield in a surface of reference enclosing the stochastic field sources is sampled and characterized by its correlation matrix the field radiated in the space outside the surface of reference can be calculated and described by the field correlation spectra. Depending on the number of statistically independent field sources the eigenvalue decomposition of the correlation matrix yields a compact description of the measured EM noise field.According to the uniqueness theorem the field in a sourcefree region outside a volume V enclosing electromagnetic radiation sources is determined in a unique way, if the tangential component of either the electric field intensity or the magnetic field intensity is known on the boundary surface ∂V of the volume V [5]. Therefore based on either the tangential electric field or the tangential magnetic field sampled on the boundary ∂V of the volume V enclosing the field sources allows to compute the electromagnetic field in the region outside V .

Abstract-We investigate the wave propagation properties in lossy structures with graded permittivity and permeability involving lefthanded metamaterials. An exact analytic solution to Helmholtz' equation for a lossy case with both real and imaginary parts of permittivity and permeability profile, changing according to a hyperbolic tangent function along the direction of propagation, is obtained. It allows for different loss factors in RHM and LHM media. Thereafter, the corresponding numerical solution for the field intensity along the composite structure is obtained by means of a dispersive numerical model of lossy metamaterials that uses a transmission line matrix method based on Z-transforms. We present the expressions and graphical results for the field intensity along the composite structure and compare the analytic and numerical solutions, showing that there is an excellent agreement between them.

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Abstract. Gradient refractive index metamaterials are of interest for various applications of transformation optics. Wave propagation through gradient index metamaterials using an exact analytical approach is investigated. Composite materials containing constituents with negative real and positive real indexes of refraction are considered. An exact analytical solution for the field distribution is obtained for the sinusoidal spatial variation of complex effective permittivity and permeability along a fixed direction, under the assumption that the wave impedance remains spatially uniform across the structure. Loss factors in the constituent materials can be different from each other corresponding to the realistic situations. Temporal dispersion can be arbitrary subject to the physical limitations imposed by the Kramers-Kronig relations. A numerical model based on the Z-transform is developed to verify the analytical results. The approach can be applied to arbitrary periodic refractive index profiles using the Fourier series method.

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