Subjects

Advanced course of optics which broadens knowledge gained in the basic course of optics. Synopsis: Electromagnetic waves and their characteristics, basic equations of electromagnetic theory, polarization of light, instrumental optics, light waves in absorbing medium, optical coherence, Fourier optics, Gaussian beams and optical resonators.

Last update: Kapsa Vojtěch, RNDr., CSc. (22.06.2021)

The aim of the course is to provide a broad background in optics to students that intend to work in this field. In particular, it is intended as an introductory course for starting Ph.D. students, which do not have detailed knowledge of optics from their previous studies.

Last update: Němec Petr, prof. RNDr., Ph.D. (23.06.2021)

At the end of the course, the students have to pass through a written test where the ability to solve practical problems, which were discussed during the tutorials, is checked. The successful passing of this test is required before the actual oral exam, where the theoretical knowledge acquired in the course is tested.

Last update: Němec Petr, prof. RNDr., Ph.D. (23.06.2021)

B. E. A. Saleh, M.C, Teich: Fundamentals of Photonics, John Wiley & sons, inc., New York, 1991.

E. Hecht: Optics, Addison Wesley, 4th edition, San Francisco. 2002.

M. Born, E. Wolf: Principles of Optics, Cambridge University Press, 7th extended edition, Cambridge 2003.

Last update: Kapsa Vojtěch, RNDr., CSc. (22.06.2021)

The examination is oral, the requirements corresponds to the syllabus.

Last update: Němec Petr, prof. RNDr., Ph.D. (23.06.2021)

1. Basic equations of electromagnetic theory.

Electromagnetic origin of light, Maxwell equations, boundary conditions.

Wave equation, Helmoltz equation. Phase and group velocity of light.

Energy, intensity, radiation pressure and momentum of electromagnetic wave.

2. Polarization of light.

Polarization ellipse, linear and circular polarization. Angular momentum of electromagnetic wave.

Propagation of light in anisotropic media. Polarization devices - polarizers, wave plates, polarization rotators.

Mathematical description of polarization - Jones vectors and matrices, Stokes parameters, Poincaré sphere.

3. Instrumental optics.

Geometrical optics, light rays. Optical imaging by reflection and refraction on a spherical interface, mirrors, lenses. Ray transfer matrix analysis. Aberrations (monochromatic and chromatic).

Fresnel and Fraunhofer diffraction on slit, rectangular and spherical aperture; implications for a construction of optical instruments. Optical diffraction grating.

Optical imaging instruments (magnifier glasses, microscope, telescope). Spectral instruments - spectrometers (prism and grating) and interferometers.

4. Light waves in absorbing medium.

Propagation of light in conductive medium, complex index of refraction.

Reflection and refraction of plane waves on interfaces, Fresnel formulae.

Kramers-Kronig dispersion relation.

5. Introduction to theory of optical coherence.

Complex representation of monochromatic and polychromatic waves, Fourier transformation, complex analytical signal. Statistical optics, ergodicity principle.

Time coherence, correlation function, power spectrum, Wiener-Chinčin theorem. Spatial coherence.

Interference of partially coherent light, Michelson interferometer, Fourier spectrometers.

Partial polarization, coherence matrix, degree of polarization.

6. Fourier optics.

Two-dimensional Fourier transformation, spatial frequencies.

Optical transfer function of imaging system, impulse response.

Optical computation of Fourier transform, spatial filtration.

7. Gaussian beams and optical resonators.

Paraxial Helmholtz equation. Gaussian beam - complex amplitude, intensity, radius, divergence, wavefronts. Transformation of Gaussian beam by optical elements, transformation of terahertz waves, ABCD law.

Optical resonators - resonant frequencies, longitudinal and transversal modes. Losses in resonators. Boyd-Kogelnik stability diagram.

Last update: Němec Petr, prof. RNDr., Ph.D. (23.06.2021)

1. Basic equations of electromagnetic theory.

Students will understand the nature and mutual relation between the main physical quantities used in the Maxwell equations.

Students will derive the general wave equation from the Maxwell equations, apply several approximations and calculate the velocity of light in a medium.

Students will understand the amount of energy and angular momentum carried by an electromagnetic wave and apply it to practical examples.

2. Polarization of light.

Students will understand the nature of polarization of light and the emergence of elliptically polarized modes from the addition of phase-shifted components of the vector of electric field.

Students will get an overview of different practical ways to polarize light and to control the polarization, including a deeper explanation of physical principles in typical polarization devices.

Students will learn to use the mathematical apparat to describe and calculate polarization states.

3. Instrumental optics.

Students will apply the principles of geometrical optics to model light propagation and imaging through spherical interfaces, mirrors, and thin lenses.

Students will master the ray transfer matrix analysis (ABCD matrix) to calculate the properties of complex paraxial optical systems.

Students will identify and describe various types of optical aberrations (monochromatic and chromatic) and evaluate their impact on image quality.

Students will analyze Fresnel and Fraunhofer diffraction patterns for different apertures and understand how diffraction limits the resolving power of optical instruments.

Students will understand the design and function of advanced optical systems, including microscopes, telescopes, spectrometers, and interferometers.

4. Light waves in absorbing medium

Students will describe the propagation of light in conductive and absorbing media using the concept of the complex refractive index.

Students will apply the Fresnel formulae to determine the reflection and transmission coefficients at various interfaces and understand the fundamental difference between reflection on dielectric and absorbing media.

Students will understand the physical significance of the Kramers-Kronig dispersion relations and their role in connecting the real and imaginary parts of the refractive index.

5. Introduction to theory of optical coherence

Students will utilize complex analytic signals and Fourier transformations to represent and analyze monochromatic and polychromatic waves.

Students will understand the statistical nature of light, including the concepts of ergodicity and stationarity in optical fields.

Students will relate temporal and spatial coherence to experimental observations in interferometry and be able to explain the Wiener-Khinchin theorem.

Students will characterize partially polarized light using the coherence matrix and the degree of polarization.

6. Fourier optics

Students will apply Fourier transforms to introduce and analyze spatial frequencies in optical signals and imaging.

Students will evaluate the performance of imaging systems using the Optical Transfer Function (OTF) and the impulse response.

Students will learn how optical systems can be used for spatial filtering and the optical computation of Fourier transforms and be part of an experimental demonstration of the procedure.

7. Gaussian beams and optical resonators

Students will solve the paraxial Helmholtz equation to derive the properties of Gaussian beams, including beam waist, divergence, and wavefront curvature.

Students will apply the ABCD law to predict the transformation of Gaussian beams (and terahertz waves) through various optical elements.

Students will calculate resonant frequencies and identify longitudinal and transversal modes in optical resonators.

Students will evaluate the stability of resonators using the Boyd-Kogelnik stability diagram and estimate energy losses within the system.

Last update: Nádvorník Lukáš, RNDr., Ph.D. (11.02.2026)