# Photonics for Materials

## Objectives

The aim of the *Photonics in Materials* discipline is to teach the basic concepts of applied physics and materials science related with light-matter interaction. The discipline introduces the students to the areas of wave optics, quantum mechanics and solid state physics, so that they gain fundamental knowledge in such domains which will later be developed in subsequent disciplines in the next years of their degree.

The discipline has a strong practical character, since the topics lectured in the classes are presented in the context of current research and technological development in related scientific fields. For instance, the lesson on numerical simulation and the laboratory work highly contribute in that respect, as they allow the students to follow a real R&D experiment in nano-photonics and execute the inherent steps of design, fabrication, characterization and results interpretation.

The lessons are divided in 6 modules:

*1) **Introduction – *presentation of the discipline and what is expected from the students. Introductory seminar about the main historical developments related with the fields of the discipline.

2) *Applied Optics* – fundamental concepts of classical optics, electromagnetism and wave-nature of light, starting by introducing analogous principles of classical mechanics (oscillators and waves).

3) *Quantum Mechanics* – introduction to quantum physics, with focus in the aspects related with particle-wave duality and photonics.

4) *Solid State Physics* – basic fundaments of solid state physics with the aim of describing and deriving the properties of matter (i.e. band structure, refractive index, etc) that explain its interaction with light.

5) *R&D Topics* – scientific and technological principles involved in the current research work related with photonics for photovoltaics (i.e. light management in solar cells), optical measurement methods, and computational simulation, under development in CENIMAT-CEMOP and covering main aspects of the R&D activities performed in the group: modeling, experimental development, device fabrication and characterization.

6) *Laboratory* – lessons conducted in the laboratories of CENIMAT-CEMOP where the students participate in an experiment covering the characterization of two different types of light trapping structures for solar cells: a plasmonic back reflector and a dielectric wave-optical micro-structure, aimed to be integrated in the rear and front contacts of thin film photovoltaics devices, respectively.

## General characterization

##### Code

11509

##### Credits

6.0

##### Responsible teacher

Manuel João Dias Mendes

##### Hours

Weekly - 4

Total - 82

##### Teaching language

Português

### Prerequisites

Análise Matemática I, Física I.

### Bibliography

*Physics for Scientists and Engineers* – by P. M. Fishbane, S. Gasiorowicz, S. T. Thornton. Prentice Hall, 1996

*Physics for Scientists and Engineers, with Modern Physics* – by R. A. Serway & J. W. Jewett. Brooks/Cole, Boston USA, 2014

*Óptica* – de Eugene Hecht. Fundação Calouste Gulbenkian, 2002

* Introduction to Solid State Physics – *by C. Kittel. Wiley, 2004

Additional:

* Absorption and Scattering of Light by Small Particles –* by C. F. Bohren & D. R. Huffman. John Wiley & Sons, 1983

*Solar Cells & Light Management – *by F. Enrich & G. C. Righini. Elsevier, 2020

### Teaching method

The discipline is chiefly composed of theoretical-practical lessons, giving emphasis on a regular engagement of the students via oral discussion and problem solving. The lessons are presented in power-point slides containing comprehensive text and eye-catching images, in accordance with the material transmitted orally by the tutor, as well as several exercises presented after each topic for the students to solve in class. Each exercise is solved in the blackboard by a different volunteer student, under the guidance of the tutor.

The discipline motivates the continuous participation of all the students in the exercise solving activities, as well as oral discussion during the lectures, simulation lessons and lab classes, by assigning a classification to their class participation performance which can benefit their final grade.

### Evaluation method

Evaluation methods:

- Average of 2 Tests of continuous evaluation (no minimum grade required to do exam) or Exam (75% of grade)

- Computational modelling work (15% of grade)

- Class participation (10% of grade)

Minimum grade to pass: 9.5

[updated for the Covid-19 period, via remote evaluation]

## Subject matter

**Introduction:**

Objectives and Program. Discipline organization. Evaluation methods.

Historical description of main developments leading to the present fields of photonics and quantum mechanics.

**Electromagnetism and classical optics:**

Harmonic oscillator (simple, damped and forced), resonances, and general applications.

Wave equation. Stationary and propagating waves in 1, 2 and 3 dimensions. Energy in waves.

Electromagnetic (EM) waves. Poyinting vector and energy transfer via EM waves. Dipole antenna and radiation of EM waves.

Geometric (ray) optics. Wave nature of light. Fresnel laws. Young double and multiple slits. Light wave interference.

Thin-film interference. Interferometers. Single-slit diffraction. Diffraction gratings. Bragg’s law. X-ray diffraction.

EM in complex notation. Propagation of light in matter. Refractive index. Lambert-Beer law. Rayleigh and generic particle scattering.

**Quantum Mechanics:**

Introduction to Quantum Mechanics. Planck’s law and Black body radiation. Quanta of light and the Photo-electric effect.

Compton shift effect. Wave properties of particles. Revised Double-slit. Quantum particles. Uncertainty principle.

Wave function. Particle in a box. Schrödinger equation. Potential wells. Tunnel effect. Harmonic oscillator.

**Solid State Physics:**

Periodic crystals. Atomic Bonding. Free-electrons in metals. Band theory. Electric conduction. Semiconductor physics.

Lorenz and Drude models. Band structure in solid state physics. Thin film optical and electrical characterization methods.

**Seminars:**

Photonic nano/micro-structures for light trapping in solar cells.

Fundaments and applications of Surface-enhanced Raman scattering (SERS) for molecular detection.

Tutorial and numerical (FDTD) simulations performed in class to compute the opto-electronic response of photonic-enhanced thin film solar cells.

Quantum mechanics technology for light-to-electricity conversion. Multi-band solar cells and other novel quantum-related concepts for photovoltaics.

**Laboratory:**

Analysis of light trapping structures developed in CENIMAT-CEMOP, via their morphological (SEM imaging) and optical (Spectrophotometry) characterization. Presentation of fabrication techniques.

## Programs

Programs where the course is taught: