4. Conclusions

We briefly discussed the fundamentals of nonlinear optics. The nonlinear optical phenomena are caused by the interaction between light and matter. Generally, all media are nonlinear. However, optical nonlinearity is extremely weak, and the observation of the nonlinear optical effects became possible only after invention of lasers as the sources of the strong enough coherent optical radiation. The nonlinear optical processes are described by Maxwell's equations with the nonlinear polarization of the medium. The coupled equations for the interacting electromagnetic and material waves are usually solved by using SVEA. Typically, the secondand third-order polarizations are considered. The nonlinear polarization and the optical field in the medium are related by the nonlinear susceptibilities which in general case can be evaluated by the quantum mechanical methods. In some simple cases, the classical model of anharmonic oscillator also can be used. We briefly discussed the fundamental nonlinear phenomena related to the second- and thirdorder susceptibilities. The former exists only in the media without the inversion symmetry, while the latter exists in any medium.

Author details

Boris I. Lembrikov

11

Technology (HIT), Holon, Israel

\*Address all correspondence to: borisle@hit.ac.il

Introductory Chapter: Nonlinear Optical Phenomena DOI: http://dx.doi.org/10.5772/intechopen.83718

provided the original work is properly cited.

Department of Electrical Engineering and Electronics, Holon Institute of

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

The typical nonlinear optical phenomena related to the second-order susceptibility are the sum-frequency generation, difference-frequency generation, and SHG. The typical nonlinear optical phenomena related to the third-order susceptibility are self-focusing, SPM, optical soliton formation and propagation, different types of SLS such as SBS and SRS, and FWM. SBS involves the acoustic waves. SRS involves the material excitations such as molecular vibrations. We also discussed some peculiarities of nonlinear optical processes in optical fibers. The nonlinear optical effects are widely used in optical communications and optical signal processing.

Introductory Chapter: Nonlinear Optical Phenomena DOI: http://dx.doi.org/10.5772/intechopen.83718

wave, and the material excitation wave [1, 2]. The analysis of this problem can be found in Refs. [1, 2]. Usually, the anti-Stokes wave is attenuated [2]. SRS in optical fibers can be used for the development of Raman fiber lasers and Raman fiber

FWM is the nonlinear process with four interacting electromagnetic waves [1]. FWM is a third-order process caused by the third-order nonlinear susceptibility χð Þ<sup>3</sup> . It can be easily observed by using the high-intensity lasers, and it has been demonstrated experimentally [1]. FWM is a complicated nonlinear phenomenon because it exhibits different nonlinear effects for different combinations of the coupled wave frequencies, wave vectors, and polarizations. The analysis of FWM is based on the general theory of optical wave mixing [1, 2, 4]. For three input pump waves with frequencies ω1, <sup>2</sup>, 3, the singly resonant, doubly resonant, and triply resonant cases can occur [1]. They correspond to the situations when one, two, or three input frequencies or their algebraic sums approach medium transition frequencies [1]. In such cases the third-order susceptibility χð Þ<sup>3</sup> can be divided into a resonant part χ

Due to the wide range of the mixed frequencies, FWM can be used for the generation of the waves from the infrared up to ultraviolet range [1]. For instance, the parametric amplification can be realized when two strong pump waves amplify two counterpropagating weak waves [1]. The frequency degenerate FWM occurs when the frequencies of the four waves are the same. It is used for the creation of a phaseconjugated wave with respect to one of the coupled waves [2]. In such a case, the phase of the output wave is complex conjugate to the phase of the input wave [1, 2]. FWM in optical fibers can be used for signal amplification, phase conjugation, wavelength conversion, pulse generation, and high-speed optical switching [4].

We briefly discussed the fundamentals of nonlinear optics. The nonlinear optical phenomena are caused by the interaction between light and matter. Generally, all media are nonlinear. However, optical nonlinearity is extremely weak, and the observation of the nonlinear optical effects became possible only after invention of lasers as the sources of the strong enough coherent optical radiation. The

nonlinear optical processes are described by Maxwell's equations with the nonlinear polarization of the medium. The coupled equations for the interacting electromagnetic and material waves are usually solved by using SVEA. Typically, the secondand third-order polarizations are considered. The nonlinear polarization and the optical field in the medium are related by the nonlinear susceptibilities which in general case can be evaluated by the quantum mechanical methods. In some simple cases, the classical model of anharmonic oscillator also can be used. We briefly discussed the fundamental nonlinear phenomena related to the second- and thirdorder susceptibilities. The former exists only in the media without the inversion

The typical nonlinear optical phenomena related to the second-order susceptibility are the sum-frequency generation, difference-frequency generation, and SHG. The typical nonlinear optical phenomena related to the third-order susceptibility are self-focusing, SPM, optical soliton formation and propagation, different types of SLS such as SBS and SRS, and FWM. SBS involves the acoustic waves. SRS involves the material excitations such as molecular vibrations. We also discussed some peculiarities of nonlinear optical processes in optical fibers. The nonlinear optical effects are widely used in optical communications and optical signal

NR [1]. The FWM process has some important applications.

ð Þ3 R

amplifiers [4].

and a nonresonant part χ

4. Conclusions

processing.

10

ð Þ3

Nonlinear Optics ‐ Novel Results in Theory and Applications

symmetry, while the latter exists in any medium.
