Modern Optics: Theory and Applications

Course: The course consists of a basic part, which provides all the background needed to study the advanced applied topics, and of a second part where we discuss advanced subjects, which are barely encountered in any textbook but that are of vital importance for any modern applications of optics.
In the first part of the course we discuss some of the foundations of optics, embedded in the more general context of electromagnetic theory. Here below some more detail on the content.

1. The basic part provides rigorous (namely at a higher and deeper level than usually treated in other courses and books) treatments of the basic theoretical aspects of optics. This material can be found scattered in different references, but we also provide lecture notes where the theory is described. The material contained in those lecture notes is much more extensive than we can cover in the course. During the first lectures, we start with the electromagnetic theory of optics. We will focus on how to formulate and solve scattering problems in optics using the Lippmann-Schwinger equation. We will discuss how to solve that fundamental equation using perturbation methods (the Born series) and we will explain why this method seems to fail in practice and what can be done about it. We will recall diffraction theory and we will make use of the stationary phase method to approximate rapidly oscillating integrals, which are often encountered when dealing with propagation problems. The plane wave expansion method to propagate optical fields through homogeneous space is derived. That method is important as it will give us the chance to understand the fundamental limit that exists for the amount of spatial information about an object that can be transferred by any monochromatic light wave (although to really understand why such a resolution limit exists we will need to discuss on inverse problems, ill-posedness, regularization techniques etc, which will do as well). Equipped with this knowledge, you will be able to also understand the true origin of classical resolution limit of optical imaging, which is instrumental to trying to figure out ways to overcome that limit. Then, depending on the applied topics which we will choose to study in the second half of the course, we discuss one or a few topics out of:
a) optical beams;
b) Parameter estimation and inference;
c) partial coherent light and statistical optics;
d) holography and phase sensitive imaging;
Which of these subjects is covered depends, among other things, on the knowledge and interest of the students taking the course how long and how extensive the basic theory will be treated.

2. In the second half of the course we will apply the theory to study advanced applications. Examples are new (proposed) methods to achieve super-resolution by using meta-materials or by exploiting multiple scattering. Plasmonic waves and their role in achieving high sensitivity will be treated as well as the concepts of a perfect and super lens are explained. Furthermore, regularization methods in parameters retrieval and inverse scattering problems are discussed. Also new ways of imaging, such as lensless imaging using phase retrieval techniques and ghost imaging are discussed. Optical beams with special properties (non-diffracting beams, beams carrying an orbital angular momentum, phase singularities) may be also discussed. More advanced topics, such as non-trivial symmetries and conservation laws in optics can also be discussed. In many cases, the topics are treated by studying scientific papers together which will be made available. The particular choice of topics will also depend on the preference of the students.

Finally, the course is made of tutorials (typically 1 hour a week), exercise sessions (1 hour/week) and normal lectures (2 hours/week). In the tutorial we will show the detailed solution to problems while the exercise sessions are mostly meant to gain practical experiences in solving problems.

Application fields of the course: The material covered in the course finds a direct applications in several fields, such as dimensional nanometrology for the semiconductor sector, imaging and microscopy for biology, instrumentation design, space research.