# Laser Matter Interaction

“*Most important part of doing physics is the knowledge of approximations*.”

L. D. Landau

Dear Students,

I see this course as an opposition to a very popular today’s trend to substitute theoretical physics with computational one. Ever increasing power of computers and algorithms has made possible simulation of very complex problems starting from the basic laws of physics. Although this approach can reproduce and even predict physical phenomena, I am convinced that a physicist must have a good intuitive understanding of the studied subject. Without intuitive understanding one cannot test the validity of computational results and it is difficult for an experimentalist to identify new and interesting physics in tons of experimental results.

An intuitive understanding is normally based on a simple model and in order to develop such a model one must invent suitable approximations. The goal of this course is to show the main approximations and the basic models allowing to describe interaction of light and matter. One of the most important breakthroughs in physics of the 20^{th} century was the development of laser. Such a source of light facilitated many discoveries and forced to reconsider models of light-matter interaction. During my lectures after an introduction of the main approximations and the simplest models of light-matter interaction, I am planning to emphasize the physics which each of the made approximations overlooks or ignores.

The course will consist of four parts: lectures, exercise classes, students seminars and practicum.

Presently I am aiming at 12 lectures and 7 exercise classes, 2 afternoons for practicum and student seminars. The latter depends on the number of students, obviously.

With kind regards

Alexey Kimel

Lecture notes all lectures (pdf, 2,2 MB)

## Lecture 1

At the lecture we will discuss the main approximations which allow us to build an adequate model of light-matter interaction. The material of the lecture is discussed in chapter 1 of the lecture notes.

For those who want to study the topic in more details, I can advise the following paragraphs from L.D. Landau and E. M. Lifshitz, "Electrodynamics of continuous media" (Elsevier, 2006):

- Paragraph 75. The field equation in a dielectric in the absence of dispersion
- Paragraph 77. The dispersion of the permittivity
- Paragraph 83. A plane monochromatic wave

For hystorical aspects of the discovery that light is an electromagnetic wave see J. Clerk Maxwell, A dynamical theory of the electromagnetic field, Phil. Trans. R. Soc. London 155 459-512 (1865).http://www.bem.fi/library/1865-001.pdf

Powerpoint presentation (pdf, 1,1 MB)

## Lecture 2

It will be shown how one can use the concept of harmonic oscillator for the development of intuitive understanding of light-matter interaction. Using the model we will show how light matter interaction changes upon inclusion of dissipations. The material described during the lecture is described in chapter 2 of the lecture notes.

- For hystorical aspects of the developemnt of the classical electronic theory of light-matter interaction see H. Lorentz, The theory of electrons and the propagation of light", Nobel lecture (1902). https://www.nobelprize.org/nobel_prizes/physics/laureates/1902/lorentz-lecture.html

Powerpoint presentation (pdf, 939 kB)

## Lecture 3

At the previous lecture we noticed that the real and the imaginary parts of the dielectric permittivity are mutually dependent. At this lecture it will be shown that based on the causality the real and the imaginary parts of the dielectric permittivity must be mutually dependent. A pictorial proof of the Kramers-Kronig ratio (as the one at https://www.uzh.ch/cmsssl/physik/dam/jcr:bd4a04bb-a526-465c-bf79-0f95884ddb1a/KramersKronig.pdf) is discussed.

The material discussed in the lecture is covered by chapter 3 of the lecture notes.

The paragraphs from L.D. Landau and E. M. Lifshitz, "Electrodynamics of continuous media" (Elsevier, 2006) relevant to the discussed subjects:

Paragraph 77.The dispersion of the permittivity

Paragraph 78. The permittivity at very high frequencies

Paragraph 80. The field energy in dispersive media

Paragraph 82.The analytical properties of epsilon (omega)

For the conventional proof of the Kramers-Kronig ratio see, for instance, J. D. Jackson ”Classical Electrodynamics (2nd ed.)” New York: Wiley (1975)).

(Much) more about properties of susceptibilities in physics, in general, can be found in D. Landau and E. M. Lifshitz, "Statistical physics. Part I" (Elsevier, 2006) in the paragraph "The generalized susceptibility" (see, for instance, paragraph 125 in https://archive.org/details/ost-physics-landaulifshitz-statisticalphysics)

Powerpoint presentation (pdf, 1 MB)

## Lecture 4

At the lecture we will show that if a medium is anisotropic, linear optical properties of the latter are described by a matrix of the optical susceptibility or by a matrix of the dielectric permittivity. In the case of non-dissipative approximation, the matrices are Hermitian. If light propagates through or bounces from an anisotropic medium, the original polarization state of light changes. In order to predict the change, one should define the eigen vectors of the dielectric permittivity matrix. Afterwards one should represent the electric field of the incoming light as a superposition of the eigen vectors of the matrix. Consequently, the problem of light-matter interaction should be treated as a problem of interaction of light components having the electric fields which corresponds to the eigen states. We will show that anisotropic media can be used to manipulate polarization state of light. The effect of polarizers, phase plates and rotators on the polarization of light can be described in terms of Jones matrices. Using such matrices and linear algebra, one can predict the polarization state of light after interaction with series of optical elements even in the cases when the outcome is counter-intuitive.

The lecture is summarized in chapter 4 of the lecture notes.

Powerpoint presentation (pdf, 909 kB)

## Lecture 5

Powerpoint presentation (pdf, 1,4 MB)

## Lecture 6

Powerpoint presentation (pdf, 1,1 MB)

## Lecture 7

Powerpoint presentation (pdf, 2,2 MB)

## Lecture 8

Powerpoint presentation (pdf, 1,2 MB)

Excersises

## Lecture 9

Powerpoint presentation (pdf, 1,3 MB)

Excersises

## Lecture 10

Powerpoint presentation (pdf, 2,2 MB)

Excersises

Lecture 11

Powerpoint presentation (pdf, 1,1 MB)

Excersises

## Lecture 12

Powerpoint presentation (pdf, 1 MB)

Excersises