. – Optics
PROF. FRANCESCO BANFI
COURSE AIMS
Prof. Francesco Banfi is available to meet with students after lectures or by
appointment.
COURSE CONTENT
Maxwell’s equations in vacuum (review).
Maxwell’s equations in matter: constitutive equations, D and H vectors (review).
Conservation laws: charge (continuity equation), energy (Poynting theorem),
linear momentum (the Maxwell stress tensor).
Wave equations for E and B fields,
general and plane wave solution. Complex notation and time averages.
Constraints imposed by Maxwell’s equations: transverse fields, orthogonal K-E-B
triplet. Poynting vectors, energy transported by a wave.
Dispersive media, relaxation times, dispersion of refractive index. Definitions of
phase and group velocity.
Reflection and refraction on dielectric surfaces, boundary conditions, derivation of
the laws of geometrical optics.Amplitude of incident, reflected and refracted fields:
the Fresnel equations. Calculation of reflectivity and transmittance, Brewster’s
angle.
Total internal reflection, inhomogeneous waves, evanescent wave, phase shifts
between s and p polarizations.
Linear, circular and elliptical polarization of light, and importance of phase shift
between linearly and orthogonally polarized waves.
Maxwell’s equations in ohmic metals, approximation of the relaxation time, wave
equation for propagation in metals, complex wave vectors, damping and skin
depth.
Wave equation for the potentials, gauge transformations, Green’s theorem, solution
of the inhomogeneous wave equation. Volume integral and surface integral.
Surface integral: the radiation condition (behaviour of the fields at infinity) and
Kirchhoff’s integral. Volume integral: retarded-time potentials and the
information-propagation sphere.
Scalar approximation for diffraction phenomena. The Huygens Principle and
Kirchhoff’s integral. Kirchhoff’s hypotheses.
The Fresnel-Kirchhoff equation and the electromagnetic definition of the Huygens
principle. Diffraction in Fraunhofer approximation, condition on the curvature of
the wavefront, Fresnel-Kirchhoff formula in the Fraunhofer approximation,
diffraction by a rectangular aperture.
Complementary screens and Babinet’s principle. Fresnel diffraction (principles),
area of the Fresnel zones, Poisson’s spot. Screen zones.
Derivation of radiation fields starting from the retarded potentials. Spatial
derivatives for the approximation of radiation. Derivation of the magnetic field and
the electric field by radiation approximation. Approximation of radiation fields of
point dipole, the oscillating dipole. Radiation fields produced by the oscillating
dipole and the Poynting vector. Formula for total dipole radiation.
Fourier analysis. Fourier optics. Spatial filtering. Abbe’s theory of image
formation. Diffraction limit.
READING LIST
D.J. GRIFFITHS, Introduction to electrodynamics, Prentice Hall, USA
FOWLES, Introduction to modern optics, Dover, USA
JOHN DAVID JACKSON, Classical Electrodynamics (Third Edition)
R.P. FEYNMANN, Feynmann Lectures Voll. I e II.
BORN & WOLF, Principles of Optics, Cambridge University Press, Cambridge
JOSEPH GOODMAN, Introduction to Fourier Optics , Roberts & Company, Englewood, Colorado.
EUGENE HECHT, Optics (4th Edition).
TEACHING METHOD
Lectures and tutorial sessions, notes distributed in class, and topic-specific seminars taught by
other lecturers. The tutorial exercises will focus on specific aspects of the theory covered in the
lectures, with examples and comments.
ASSESSMENT METHOD
Students will be asked to submit a dissertation on a topic of particular interest (to be
agreed with the lecturer), and to sit an oral examination.
NOTES
The prerequisites for understanding the subject matter are the courses in
Electromagnetism.
Prof. Francesco Banfi is available to meet with students after class or by appointment.