Maxwell equation, in integral or differential form. Complex numbers.

Lectures

Mathematical introduction: divergence and rotor and its use in electrodynamics. Complex numbers: Euler identity and symbolic representation of oscillating quantities. Fasors.

Maxwell equations in linear isotropic media and their solution in vacuum. Wave equation and plane wave propagation; complex notation for the fields.

Linear and circular polarization of the e.m. (electro-magnetic) waves; time averages with phasor notation. Dissipated power in alternate circuits with real and imaginary impedance. The damped harmonic oscillator with a periodic external force: resonance curve, phase delay and dissipated power.

Plane waves in dielectric media; e.m. energy density and Poynting vector; vacuum impedance and intrinsic impedance in a dielectric medium.

E.m. energy conservation and the Poynting theorem; the dumped harmonic oscillator with a periodic external force and the Drude-Lorentz model for dielectrics; effective dielectric constant in conductive materials; electrical susceptivity and complex refractive index; absorption coefficient, absorbance and transmittance, Lambert-Beer law; electrical conduction in metals and the Drude model; frequency dependent complex conductivity and its low frequency limit; Ohm law; effective dielectric constant; high frequency limit; skin depth in metals; plasma frequency and plasma oscillations. Larmor formula and the static and radiating fields generated by an accelerated charged particle.

Larmor formula and the oscillating dipole; the Poynting vector and total emitted power; comparison between the far and near field. Maxwell equations and dielectric interfaces.

Dielectric/Dielectric and Dielectric/Metallic interface at normal incidence; Snell Law from Maxwell equations; Critical angle and evanescent transmitted wave.

Cauchy model for the refractive index, dispersive media and geometrical configuration for spectral analysis; Snell laws derived from the Fermat principle. Reflection and transmission coefficients for TE polarized field.

Reflection and transmission coefficients for TM polarization; Brewster angle and polarization by reflection; interference: superposition of scalar fields with the same or different frequency; phase mismatch and interference; conditions to observe interference effects; interference and polarization; optical path coherence time and length; coherent sources. Huygens principle and diffraction from a slit.

More on the interference with the double slit Young's experiment; interference effects with thin multilayers, multiple internal reflections; antireflection coating.

Michelson and Mach-Zehnder interferometers. The concept of optical path. Introduction to diffraction phenomena. Fresnel-Kirchhoff diffraction formula and the Huygens-Fresnel principle.

Extended coherent optical sources, Fresnel and Fraunhofer diffraction condition. Single slit diffraction pattern in the Fraunhofer limit. Geometrical interpretation with phasors sum. Solution of the wave equation for the single slit as boundary condition. Diffraction pattern for a circular hole and Airy fringes. Angular resolutive power.

Hallyday - Resnick - Fundamentals of Physics (for the beginning)

John David Jackson - Classical electrodynamics (for more advanced items)

Lessons are recorded.

Oral exam. Usually it start with an exercise: if difficulties arise, there will be questions about theory. If the student shows apoor knowledge of the theory, he would be asked to repeat the exam. Exams should not last more than 45 minutes.