This exam is present in the following Optional Group


The course aims to introduce the physics of light and electromagnetic waves and their technological application. Starting from Maxwell's equations, the course introduces electromagnetic waves and their solutions in terms of plane or spherical waves. Particular attention is given to the interpretation of the refractive index in a microscopic key, as an active and reactive interaction of the polarization dipoles with the electromagnetic field. This approach aims to explain the slowing down of light in media, giving the cultural tools to understand all linear and nonlinear interaction effects between light and materials.

The course will therefore analyze the reflection and refraction of light and all associated phenomena, a fundamental part for understanding both how the different optical devices currently used (mirrors, lenses, complex optical systems, optical fibers) act. The course also introduces issues related to solar panels and the conversion of solar energy. The wavy aspects of light will be analyzed both in relation to interference and optical resonators, and in relation to diffraction, introducing the Huygens-Fresnel principle and its applications in the near and far fields. These studies will allow to introduce the basic concepts of nano-optics and associated simulation techniques.

The final part of the course will introduce nonlinear materials and associated phenomena. The nonlinear view of the second and third order will be discussed. Particular attention will be paid to second order phenomena both of a catalytic nature (generation of second harmonic and generation of harmonic difference) and of refractive nature (Kerr effect and photorefractivity). By exploiting photorefractive nonlinearities it will be shown how neuromorphic circuits can be produced whose response has a similar behavior to biological neurons. These neural circuits are able to recognize optically coded information (machine learning) and memorize it (RAM and ROM memories). Neuromorphic circuits are the fundamental elements for building a hardware Photonic Artificial Intelligence.




Electromagnetic waves and light
Maxwell equations and EM wave equation. Spherical and plane waves. Frequencies and wavelengths of EM waves. Microscopical interpretation of the refractive index. Active and reactive polarisation and the complex refractive index. Sellmeyer equation for the refractive index dispersion. Abbe number and Abbe space for glasses. Poynting vector and light energy. Lightning quantities.
Reflection and refraction
Fermat “minimal action” principle and Snell’s Laws. Fresnel coefficients. Critical angle and total reflection regime. Evanescent waves and Goos-Hänchen phase shift. Geometrical interpretation of optical fibres and waveguides.
Geometrical Optics
Short wavelength approximation. Reflection and mirrors. Refraction and dioptric surfaces. Thin lenses. Thick lenses and principal planes. Centred optical systems. Pupils/stops/f-number/numerical aperture. Vignetting and cosine-to-the-fourth-power law. Principal optical aberrations. Chromatic aberration and achromatic doublet. Fundamental refractive systems. Ray-tracing and ABCD matrices.
Interference and interferometers
Interference of 2 co-propagating waves. Wave beating. Continuous waves and pulses. Phase and group velocities. Spatial and temporal interference. Young’s experiment. Interference of 2 contra-propagating waves: stationary waves and resonators. Fabry-Perot resonator. Optical fibres as transverse resonators. Multilayer interferent systems. Design of dielectric mirrors and band-pass filters. Michelson and MachZehnder interferometers.
Huygens-Fresnel principle and integral. Near field regime and Fresnel Integral. Far field and Fraunhofer integral. Diffraction from a slit. Focusing limit of a lens. Diffraction from a stop. Diffraction from a grating. Harmonic and anharmonic gratings. Nano-optics.
Anisotropic optics
Anisotropic crystals. Index Ellipsoid. Uniaxial and biaxial crystals. Dichroism. Retardation plates.
Nonlinear Optics
Nonlinear response. Anharmonic oscillator. Second order effects. The nonlinear optical tensor. Optical harmonic generation. Parametric effects. The Pockels electro-optic effect. Electro-optic modulators. Photorefractivity and self-assembling optical structures. Spatial solitons and solitonic waveguiding. Smart systems, Machine Learning and Photonic Artificial Intelligence.

Adopted texts

M. Born & E. Wolf, Principles of Optics, Pergamon Press
F. Gori, Elementi di Ottica, Accademia
K.D. Moller, Optics, Springer
G. Chartier, Introduction to Optics, Springer


Students must know the physics of electricity and magnetism as it is done in the courses of Physics 2. The course is delivered in English so they must know the English language well.

Frequency modes

Attendance is not compulsory although it is highly recommended in order to fully understand the program topics. During the lessons a special effort is made to explain all the mathematical passages necessary for the development of the topic.

Exam modes

The student's ability to reason on electromagnetic waves will be evaluated, to have understood the main phenomena of light and to be able to discriminate between them in a real case presented. The evaluation test consists of an oral interview.

Exam reservation date start Exam reservation date end Exam date
27/09/2021 07/06/2022 10/06/2022
27/09/2021 08/07/2022 11/07/2022
27/09/2021 07/09/2022 12/09/2022
23/09/2022 23/10/2022 29/10/2022
Course sheet
  • Academic year: 2021/2022
  • Curriculum: Particle and Astroparticle Physics (Percorso valido anche fini del conseguimento del titolo multiplo italo-francese-svedese-ungherese) - in lingua inglese
  • Year: First year
  • Semester: Second semester
  • SSD: FIS/01
  • CFU: 6
  • Attività formative affini ed integrative
  • Ambito disciplinare: Attività formative affini o integrative
  • Exercise (Hours): 36
  • Lecture (Hours): 24
  • CFU: 6
  • SSD: FIS/01