We recalled Maxwell's equations in the most general form (presence of medium, external charges and currents). We then retrieved the solution in vacuum without sources, recalling the concept of plane wave, Poynting vector, Fourier transform (derivative and convolution theorem). We then moved to the case of a dielectric medium (non magnetic), introducing within the linear approximation the time-dependent (non local) relation between polarization and electric field in the homogeneous and isotropic case. This implies a convolution in time domain. For example under an impulsive electric field (Dirac-delta(t)) the material response occurs even at finite times as P(t)=eps0*chi(t). Moving to the frequency domain, we derived the Helmotz equation in which the material properties enter via the (generally complex) frequency dependent dielectric constant. Pay attention to the way we treat the real (Taylor expansion) and imaginary (constant absorption at w_0) part of beta(w).
Please install MATLAB on your laptops (freely distributed by Sapienza: https://www.uniroma1.it/it/pagina/software-gratuito), which we will soon use to simulate pulse propagation.
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