![]() ![]() Maxwell-Lorentz equations: Microscopic Maxwell equations for a system of point charges, Newton-Lorentz equations for the motion of the charges, conservation laws for energy and momentum for the Maxwell-Lorentz system.Fresnel’s equations: Forms of Fresnel’s equations, reflectivity for s- and p-polarizations, reflection of unpolarized light, critical angle for internal reflection and Brewster’s angle, Brewster windows, critical angle and total internal reflection (TIR), TIR and optical waveguiding in fibers, phase of reflected field in TIR and the Goos-Haenchen shift for confined beams, evanescent waves in TIR and frustrated TIR, transmissivity and conservation of energy.Reflected and refracted fields: Helmholtz equations for the electric and magnetic fields and boundary conditions, TE or s-polarization and TM or p-polarization, reflection and transmission coefficients, normal incidence.Plane-wave relations: Plane-wave incident on a dielectric interface, reflected and refracted fields, energy and momentum relations, law of reflection and Snell’s law of refraction, admittance, external and internal reflection.Electromagnetic boundary conditions: General boundary conditions, application to a dielectric interface.Other solutions of the Helmholtz equation: Spherical waves, Bessel beams solutions in cylindrical coordinates, standing wave modes in an electromagnetic box.Spatial Fourier transform: Maxwell’s equations and the wave equation in reciprocal space, electric and magnetic fields for plane-waves, Poynting vector and time averaged intensity.Plane-wave propagation in conducting media: Telegrapher’s equation, absorption coefficient and Beer’s law. ![]() Wave equation: Maxwell’s wave equation in linear isotropic media, one-dimensional case, counter-propagating waves, refractive-index and the speed of light, temporal Fourier transform and the complex representation for a monochromatic field, Helmholtz equation, dispersion relation for plane-waves, linearly and circularly polarized fields, complex basis vectors, phase and group velocities.Electromagnetic field energy and momentum: EM field energy, Poynting vector, non-uniqueness of the Poynting vector, Lorentz force on charges, mechanical energy exchanged with charges, radiation pressure force on atoms and mirrors, expression for the EM field momentum and mometum density.ģ.Macroscopic electrodynamics: Macroscopic Maxwell equations in the MKSA system of units, definitions, constitutive relations in media, bound and free charges, charge conservation and the continuity equation, symmetries under space inversion and time reversal.Vector integration: Line, surface, and volume integrals, divergence of a vector field, flux of a vector field, the divergence theorem, curl of a vector field, circulation density, Stokes theorem, uniqueness theorem.Vector fields: div and curl operators, form in different coordinate systems, variety of second order derivatives of vector fields, transverse (solenoidal) and longitudinal (irrotational) fields, Helmholtz theorem.Scalar fields: Gradient operator as a vector operator and its interpretation, Laplacian operator as a scalar operator, grad and Laplacian operators in different coordinate systems.Basic vector algebra: Addition of vectors, parallelogram law, product of scalars and vectors, dot and cross products, vector identities, coordinate inversion, polar vectors and pseudo or axial vectors. ![]()
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