. – Optics
PROFESSOR GABRIELE FERRINI
COURSE AIMS
The course is intended as an introduction to the fundamental principles of optics.
COURSE CONTENT
Maxwell's equations in vacuum, Maxwell's equations in matter:
constitutiveequations and vectors D and H. Charge conservation (continuity
equation), conservation of energy (Poynting's theorem), conservation of linear
momentum(Maxwell's stress tensor).
Wave equation for fields E and B, general and plane wave solutions.
Complexnotation and time averages. Constraints arising from Maxwell's equations:
transverse fields and orthogonal k-E-B reference frame. Poynting vector andenergy
carried by a wave.
Dispersive media, relaxation times and dispersion of refractive index. The
conceptsof phase and group velocities.
Reflection and refraction on dielectric surfaces, boundary conditions and
derivationof the laws of geometrical optics. Amplitudes of incident, reflected and
refractedfields: Fresnel's equations. Calculation of transmissivity and reflectivity,
Brewster'sangle. Total internal reflection, inhomogeneous waves, evanescent
waves, andphase shift between s- and p-polarized light.
Linear, circular and elliptical polarization of light. Maxwell's equations in
ohmicmetals, relaxation time approximation, wave equations for propagation in
metals, complex wave vectors, damping and skin depth. Wave equation for
potentials, gauge transformations, Green's theorem, and the solution of the
inhomogeneouswave equation. Surface integral: the radiation condition (behaviour
of fields atinfinity) and the Kirchhoff integral. Volume integral: retarded potentials
and theinformation sphere.
Scalar approximation for diffraction phenomena. Huygens' principle and
theKirchhoff integral. Kirchhoff's hypotheses. Fresnel-Kirchhoff equation and
theelectromagnetic definition of Huygens' principle.
Diffraction in the Fraunhofer approximation, wavefront curvature, the FresnelKirchhoff formula in the Fraunhofer approximation, rectangular slit diffraction.
Complementary screens and Babinet's principle. Fresnel diffraction (principles),
Fresnel zone area and Poisson spot. Zone plate.
Derivation of radiation fields from retarded potentials. Space derivatives
inradiation approximation. Derivation of magnetic and electric fields in
radiationapproximation. Radiation fields in the point dipole approximation and
theoscillating dipole. Total dipole radiation formula.
Fourier Analysis, Fourier Optics, spatial filtering, Abbe theory of image formation,
diffraction limit.
READING LIST
essential:
D. J. GRIFFITHS, Introduction to electrodynamics, Prentice Hall, USA
FOWLES, Introduction to modern optics, Dover, USA
advanced:
FEYNMAN LECTURES, Vol. I and II
BORN & WOLF, Introduction to Optics
PAULI, Lectures on Physics Vol. 1 and 2.
TEACHING METHOD
Lectures, notes handed out in class and seminars.
ASSESSMENT METHOD
An in-depth account of a subject chosen by the student (to be agreed upon) and an oral
examination.
NOTES
In order to understand the material presented in the course, the student must have
previously attended the electromagnetism I and electromagnetism II courses.
Prof. Ferrini receives in his office every day by appointment.