Degree course: 
Corso di Second cycle degree in PHYSICS
Academic year when starting the degree: 
Academic year in which the course will be held: 
Course type: 
Compulsory subjects, characteristic of the class
First Semester
Standard lectures hours: 
Detail of lecture’s hours: 
Lesson (48 hours)

Basic knowledge of classical electromagnetism (provided by the course of Electromagnetism). However, no pre-requisites are required.

Final Examination: 

The exam is oral and is initially based on the discussion of the report containing the exercises that were assigned during the course. This allows an initial verification of the knowledge, the ability to apply them to reproduce some known results and the ability to draft a text. Following are asked questions on some specific topics dealt with during the course, for which a general classification is asked and the ability to derive the mathematical formulas that describe the phenomenon. The understanding of some research articles that have been discussed during the course is also verified.

Voto Finale

The aim of the course is to introduce the student to the working principles of metamaterials and their applications. At the end of the course the student will have acquired the techniques on which the so-called "theories of effective medium" are based and will therefore be able to calculate the actual parameters of different metamaterials.
During the course, exercises are assigned that allow students to check the level of knowledge achieved. Moreover, these exercises sometimes require the use of calculation software such as Matlab, of databases on the network and the study of basic articles in English.
At the end of the course these exercises are organized in a written report that constitutes the starting point of the exam.
The autonomy of judgment is also expressed in the evaluation of teaching by completing the prepared questionnaires.

The first part of the course (20 h) is devoted to a review of the fundamental concepts of electromagnetism, particularly those relating to the interaction between an electromagnetic wave and a material, insulator or metal.

Maxwell equations and monochromatic plane waves (4 h)
Poynying theorem for non-dispersive and dispersive media (2 h)
Light polarization (2 h)
Fresnel's laws, transmission and reflection coefficients of a layer of material (4 h)
Formulas for relative permittivity and permeability based on reflection and transmission coefficients (2 h)
Lorentz-Drude's model of complex susceptibility, Kramers-Kronig relations (4 h)
Metals, plasma oscillations (2 h)

In the second part of the course (28 h), we introduce the "effective medium theories" needed to describe the metamaterials and consider some particular configurations.

Maxwell-Garnett's theory (4 hrs)
Bruggeman's effective medium theory (4 hrs)
Corrections to the theory for ellipsoid inclusions (4 h)
Wiener bounds (2 h)
Metal wire arrays (2 h)
Split ring resonators (2 h)
Some experiments (2 h)
Condition necessary and sufficient to obtain a left-handed material (2 h)
Super-lenses (2 h)
Hyperbolic Metamaterials (2h)
Hyper-lenses (2 h)

W. Cai and V. Shalaev, Optical Metamaterials – Fundamentals and applications, Springer 2010
Notes provided by the teacher


Frontal teaching (48 h)

The teacher receives the students by appointment by writing to