Magnetic permeability tensor

This defines the magnetic field intensity H /x is the 3x3 linear magnetic permeability tensor. Equation (2.7.13), linking B to H, is the "second constitutive equation." The magnetic field H is expressed explicitly by... 

Formally, if one has the experimental values of the dielectric tensor e, the magnetic permeability tensor /jl, and the optical rotation tensors p and p for the substrate, one can construct first the optical matrix M, then the differential propagation matrix A, and C, which, to repeat, is the x component of the wavevector of the incident wave. Once A is known, the law of propagation (wave equation) for the generalized field vector ift (the components of E and H parallel to the x and y axes) is specified by Eq. (2.15.18). Experimentally, one travels this path backwards. 

From equations (1) and (15), the change in magnetic permeability tensor due to a strong magnetic field is ... 

We can introduce now the transformed conductivity and magnetic permeability tensors as... 

The FDTD numerical scheme presented here uses the uni-axial PML (UPML) developed by Sacks et al. [23] to truncate the absorptive host medium in the FDTD calculation. The UPML is a physical model based on an anisotropic, perfectly matched medium. For a single interface, the anisotropic medium is uni-axial and is composed of both electric permittivity and magnetic permeability tensors. 

The magnetic induction B and magnetic field H are related through the magnetic permeability tensor as ... 

Table 11.4 Magnetic Permeability Dielectric Constant (at 0 Hz) s/e0 and Scalar Index of Refraction nD (Measured at the Yellow Na D-Line 590 nm) Or Tensor Components of the Index of Refraction n0, ne = nig, n7 for Some Gases, Liquids, and Solids ...

As noted above we treat only waves propagating along the helix axis z D and E are therefore confined to the xy- plane and are related by a two-dimensional, second-rank dielectric tensor In addition to this restriction, we neglect (1) the weak intrinsic optical activity of the constituent molecules which persists even in the isotropic phase, (2) energy dissipation by absorption, and (3) magnetic permeability (m = 1). Finally, we assume all waves to be of the form... 

The components of a symmetrical second-rank tensor, referred to its principal axes, transform like the three coefficients of the general equation of a second-degree surface (a quadric) referred to its principal axes (Nye, 1957). Hence, if all three of the quadric s coefficients are positive, an ellipsoid becomes the geometrical representation of a symmetrical second-rank tensor property (e.g., electrical and thermal conductivity, permittivity, permeability, dielectric and magnetic susceptibility). The ellipsoid has inherent symmetry mmm. The relevant features are that (1) it is centrosymmetric, (2) it has three mirror planes perpendicular to the... 

Here we have assumed a homogeneous isotropic material but in general the permeability is a second-rank tensor jt having 3x3 elements. The applied magnetic field is modified by the bulk magnetic properties of the substance and thus the magnetic field inside the sample becomes... 

E. However, developing this approach for practically important 3D anisotropic models with arbitrary tensors of electrical conductivity, magnetic and dielectric permeability happens to be very complicated. Yee s algorithm is based on calculation of different electric field components at different space points, but the electrical conductivity tensor relates these components taken at the same point. 

According to the classical theory, the electromagnetic free space permeability jUq and the magnetic susceptibility Xm scalars or tensors, depending on the anisotropy of the medium, that relate... 

Isolator Circulator Latching Temperature Switch 30MHz 30GHz MnMgAl YIG YIG MnCuZn Tensor permeability Magnetic flux density Resonance half-value width Curie Temperature... 

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