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On the other hand, a superposition of solutions with different frequencies leads to solutions with a more complex time dependence. , ones with a harmonic time dependence of a given frequency. In reality, the field variations are more appropriately described as quasimonochromatic, involving harmonic components with frequencies spread over a small interval. Monochromatic solutions to the Maxwell equations with the simplest spatial dependence, namely a harmonic one, are the plane waves. These will be considered in various aspects in sec.

In writing out these equations, I introduce for the sake of later use, fictitious magnetic charge- and current densities. Thus, we include the magnetic current density ( j(m) = dependent complex amplitude of (m)(r, t) = (m)(r)e−iωt (m)(r), the space ), and the corresponding magnetic charge density ( ρ(m) ). Evidently, such magnetic charges and currents do not correspond to real sources since observed fields are all produced by electric charge- and current distributions. , the sources producing the field are all located outside this region) then the field vectors can be equivalently expressed in terms of a set of fictitious charges and currents distributed over the boundary surface of the region, where these fictitious sources include magnetic charges and currents.

In the case of a linear anisotropic medium, the susceptibility is in the nature of a tensor, in terms of which the permittivity tensor is defined in an analogous manner. For a nonlinear medium, on the other hand, the polarization P depends on the electric intensity E in a nonlinear manner, giving rise to novel effects in optics. 6b) where χM is the magnetic susceptibility of the medium. 6c) where μr (= 1 + χM) is the relative permeability. In this book we will not have occasion to refer to magnetic anisotropy or magnetic nonlinearity.

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Basic Optics I-II by Avijit Lahiri

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