Statistical Optics

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Lecturer:

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Department of Laser Physics and Photonics

Synopsis:

The lecture covers both the basics and advanced topics in statistical optics, i.e. the classical theory of optical coherence. It reviews the basics of probability theory and statistics, random variables, random stochastic processes, together with the complex analytical and quasimonochromatic signals. It futher systematically discusses especially the statistical properties of radiation, in terms of the classical scalar 2nd order theory of optical coherence, including elementary concepts and definitions, correlation functions and their properties, time domain, interference law, complex degree of coherence, frequency domain, coherence time, area, volume, spectral degree of coherence, and Wiener-Khinchin theorem. It also introduces special types of fields (coherent, cross spectrally pure) and radiation from primary sources (Schell model sources). The attention is further given both to the dynamics of correlation function (Wolf equations, Van Cittert - Zernike theory) and to applications of the coherence theory (Michelson stellar interferometer, correlation spectroscopy). The course is further devoted to vectorial aspects of coherence theory (standard statistical theory of polarization, using either polarization matrices or Stokes parameters), together with the unified treatment of polarization and coherence aspects, and general vectorial correlation matrices and tensors. The final attention is given to higher order correlation functions.

Requirements:

Basic course of optics.

Syllabus of lectures:

1. Introduction - classical theory of coherence, basics of probability theory and statistics, random variables

2. Random stochastic processes, complex analytical signal, quasimonochromatic signal

3. Classical 2nd order theory of optical coherence, elementary concepts and definitions, correlation functions and their properties, time domain, interference law, complex degree of coherence

4. Classical 2nd order theory of optical coherence - frequency domain, coherence time, area, volume, Wiener-Khinchin theorem

5. Theory of partial coherence, radiation from partially coherent sources, nonclassical sources

6. Special types of fields - coherent, cross spectrally pure

7. Dynamics of correlation function - Wolf equations, Van Cittert - Zernike theory

8. Radiation from primary and secondary sources, Schell model sources

9. Applications of the 2nd order theory of coherence, Michelson stellar interferometry, correlation spectroscopy

10. Vectorial aspects of coherence theory, statistical theory of polarization, unified theory of polarization and coherence

11. General vectorial coherence theory, correlation matrices and tensors

12. Higher order correlation functions, intensity interferometry

Syllabus of tutorials:

Study Objective:

Knowledge: solid basic and advanced knowledge of classical statistical optics, theory of random processes, with the classical 2nd order theory of optical coherence and its applications, both in time and frequency domains, with standard and unified statistical theory of polarization, as well as basics of higher-order correlation theory.

Skills: orientation in the field of statistical optics, its methods and procedures, skills in its practical usage, understanding and applications.

Study materials:

Compulsory literature:

[1] Mandel L.: Wolf E.: Optical Coherence and Quantum Optics, Cambridge University Press, 1995.

Supplementary literature:

[2] J. W. Goodman, Statistical Optics, John Wiley & Sons, 2000.

[3] J. Peřina, Coherence of Light, Dordrecht Reidel Publishing Company, 1985.

[4] E. L. O'Neill, Introduction to statistical optics, Dover Publications, 1992.

[5] Ch. Brosseau, Fundamentals of polarized light: a statistical optics approach, J. Wiley & Sons, 1998.

[6] M. Bass, Ed., Handbook of Optics I and II, McGraw-Hill, 1995.

[7] M. Born, E. Wolf, Principles of Optics, Pergamon Press, 1993 (sixth edition).

[8] B. E. A. Saleh, M.C. Teich, Fundamentals of Photonics, J. Wiley & Sons, 1991; Czech translation Základy fotoniky. Matfyzpress, Praha, 1995.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Fyzikální elektronika - Fotonika (PS)
• Fyzikální elektronika - Laserová fyzika a technika (elective course)
• Kvantové technologie (elective course)