Numerical Methods in Optics

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The student should have basic knowledge in the field of mathematical analysis and algebra. Exercises do not require prior knowledge of Matlab or Mathematica programs.

Classroom

Lecture with tutorials (exercises) on basic optics, numerical methods and computer modeling of physical phenomena.

The aim of the lecture is to introduce students to the subject of numerical methods and computer modeling of physical phenomena on the example of basic problems related to optics. The student will develop practical computing skills during numerical exercises conducted using Matlab and Mathematica environments. The lecture is an introduction course for Photonics (5-th semester) .

Lecture and exercise program:

Numerical topics:

1. Introduction to Matlab and Mathematica

2. Data visualization, 2D and 3D plots, animations

3. Data managment

4. Selected problems of algebra and mathematical analysis

Optical topics:

1. Introduction to optics

2. Interaction of light with matter (Fermat principle, refraction, reflection, dispersion, absorption, dispersion)

3. Geometric optics (matrix optics, lenses, mirrors, prisms)

4. Wave motion (harmonic waves, phase and phase velocity, superposition principle, complex form, plane waves, wave equation)

5. Interference and Diffraction (Young's experiment, diffraction grating, elements of Fourier's optics)

6. Spectral analysis (time and spatial signals, light pulses, group velocity).

7. Polarization (polarization states, birefringence, optical elements)

8. Theory of electromagnetism (Maxwell equations, boundary conditions, Fresnel equations)

Photonic projects:

1. Modeling of lens systems

2. Analysis of sub-wave systems

3. Image processing

4. Design of diffraction objects

5. Machine learning

In general, the lecture and exercises are in Polish. However, it is possible to personalize the exercises for English-speaking students.

1. Web page https://www.igf.fuw.edu.pl/pl/courses/lectures/metody-numerycz-72041g/

2. E. Hecht, Optyka, WN PWN

3. J. Brzózka, L. Dorobczyński, MATLAB: środowisko obliczeń naukowo-technicznych, Wydawnictwo Naukowe PWN

4. Stephen Wolfram, The Mathematica Book, Wolfram Media

5. D. Griffiths, Podstawy elektrodynamiki, PWN

1. Mastering Matlab and Mathematica programming environments at the basic level, enabling data visualization and creating simple functions and scripts.

2. Knowledge of basic optical phenomena and related concepts

3. Ability to use mathematical formalism associated with electromagnetic waves

4. Ability to numerically model light propagation in optical elements

60% of total number of points can be obtained by solving numerical problems during the tutorials. The final exam will have a form of a test checking the student knowledge about the optical phenomena discussed during the lecture (40%).

The mark can be improved during the exam retake session. Two unexcused absences are allowed. Number of allowed excused absences will be determined individually.