Code: 12NLOP Nonlinear Optics
Lecturer: prof. Dr. Ing. Ivan Richter Weekly load: 3+1 Completion: A, EX
Department: 14112 Credits: 5 Semester: S
Description:
The lecture covers both the basic and advanced topics of nonlinear optics, both from classical and quantum viewpoint, consequentially to the previous courses of Physical optics. From a classical viewpoint, the attention is given to optical processes in dielectric media, macroscopic polarization vector, and microscopic description of polarization vector. Further, it deals with dispersion properties of nonlinear susceptibilities (2nd order nonlinearity for noncentrosymmetric media, 3rd order nonlinearity for centrosymmetric media), and with symmetries of nonlinear susceptibility tensors. From a quantum (poloclassical) viewpoint, the attention is given to derivation of linear, quadratic, and cubic susceptibility, and particularly to the resonant process in two-level media. The processes are classified to nonresonant (parametric) and resonant ones, conservation laws, as well as Manley-Rowe relations, phase matching and synchronisms are discussed. The lecture then separately discusses three-wave mixing (second harmonic generation, sum and difference frequency generation), four wave mixing, optical Kerr effect, third harmonic generation. Concentration is given to light induced refractive index changes, selffocusation and automodulation effects, electrooptical and photorefractive effects, nonlinear light scattering, optical phase conjugation, nonlinear absorption effects, and to nonlinear effects with short pulses. The lecture is conluded with applications of selected nonlinear optical effects.
Contents:
1. Introduction - approximation of nonlinear systems with linear ones.
2. Induced oscillations of nonlinear systems, linear and nonlinear wave in infinite medium.
3. Helmholtz coupled wave equation, microscopic description of polarization vector, dielectric polarizability.
4. Classical description of susceptibility, 2nd order nonlinearity, 3rd order nonlinearity.
5. General symmetry laws of the nonlinear susceptibility tensors.
6. Quantum description of susceptibility, linear, quadratic, and cubic susceptibility, nonlinear resonant process.
7. Nonresonant wave coupling in nonlinear media, Manley-Rowe relations, phase matching and synchronism.
8. Three-wave mixing with 2nd order nonlinearity, four wave mixing with 3rd order nonlinearity, optical Kerr effect.
9. Light induced refractive index changes, selffocusation and automodulation effects, spatial and temporal solitons.
10. Electrooptical effect, photorefractive effect, two and four wave mixing in nonlinear media.
11. Nonlinear light scattering, classification of scattering, physics of Raman and Brillouin scattering.
12. Optical phase conjugation, holographic model, phase conjugation generated with nonlinear processes.
13. Nonlinear absorption effects, spectral line broadening, saturable absorption, two-photon absorption.
14. Nonlinear effects with short pulses, nonlinear Schrödinger equation, impuls selffocusing.
15. Applications of selected nonlinear optical effects.
Seminar contents:
1. Generalization of complex representation, equivalence of complex and classical approach.
2. Mechanical analogy of nonlinear equations - a pendulum with large amplitude of deviation.
3. Helmholtz coupled-wave equations, application to systems with second and third order nonlinearity
4. Anisotropic materials - coefficients of nonlinear susceptibility tensor.
5. Practical approach to Manley-Rowe relations.
6. A difference between selffocusation a selfguiding.
7. Electrooptical effect - transverse, of higher order,essentials of photorefractive effect.
8. Nonlinear scattering processes.
Recommended literature:
Key references:
[1] P. Fiala, I. Richter, Nelineární optika, Skriptum FJFI ÈVUT, 2009 (in Czech).
[2] R.W. Boyd, Nonlinear Optics, 2nd edition, Academic Press, London, 2003.

Recommended references:
[3] B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, J. Wiley & Sons, 1991.
[4] G.S. He, S.H. Liu, Physics of Nonlinear Optics, Word Scientific, Singapore, 1999.
[5] R.L. Sutherland, Handbook of Nonlinear Optics, 2nd edition, Dekker, 2003.
Keywords:
Nonlinear optical medium, polarization vector, susceptibility, polarizability, parameteric interaction, Manley-Rowe relations, phase synchronism, three and four wave mixing, second and third harmonic generation, sum and difference frequency generation, selffocusation and automodulation effect, soliton, electrooptical effect, photorefractive effect, nonlinear light scattering, Raman and Brillouin scattering, optical phase conjugation, nonlinear absorption optical bistability, optical limitation.

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