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 (60 hours)

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

Final Examination: 

The exam consists at first in the preparation of a written work that requires the student to reproduce analytically and numerically some results published in research articles. The elaborate is then discussed in an oral test in which the knowledge gained on other topics developed during the course is also verified.

Voto Finale

The purpose of the course is to acquaint the student with the principles of operation of the metamaterials and their applications. At the end of the course, the student will acquire the techniques on which so-called "effective medium theories" are based and will then be able to calculate the actual parameters of different metamaterials.

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

Frontal teaching (48 h)