Book contents
- Frontmatter
- Contents
- Preface to the Second Edition
- 1 Electromagnetic waves, light, and lasers
- 2 Optical frequency amplifiers
- 3 An introduction to two practical laser systems
- 4 Optical resonators containing amplifying media
- 5 Laser radiation
- 6 Control of laser oscillators
- 7 Optically pumped solid-state lasers
- 8 Gas lasers
- 9 Molecular gas lasers I
- 10 Molecular gas lasers II
- 11 Tunable lasers
- 12 Semiconductor lasers
- 13 Passive optical systems
- 14 Periodic optical systems, resonators, and inhomogeneous media
- 15 The optics of Gaussian beams
- 16 Optical fibers and waveguides
- 17 The optics of anisotropic media
- 18 The electro-optic and acousto-optic effects and modulation of light beams
- 19 Introduction to nonlinear processes
- 20 Wave propagation in nonlinear media
- 21 Detection of optical radiation
- 22 Coherence theory
- 23 Laser applications
- Appendix 1 Optical terminology
- Appendix 2 The ´-function
- Appendix 3 Black-body radiation formulas
- Appendix 4 RLC circuits
- Appendix 5 Storage and transport of energy by electromagnetic fields
- Appendix 6 The reflection and refraction of a plane electromagnetic wave at a boundary between two isotropicmedia of different refractive indices
- Appendix 7 The vector differential equation for light rays
- Appendix 8 Symmetry properties of crystals and the 32 crystal classes
- Appendix 9 Tensors
- Appendix 10 Bessel-function relations
- Appendix 11 Green's functions
- Appendix 12 Recommended values of some physical constants
- Index
- References
19 - Introduction to nonlinear processes
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Contents
- Preface to the Second Edition
- 1 Electromagnetic waves, light, and lasers
- 2 Optical frequency amplifiers
- 3 An introduction to two practical laser systems
- 4 Optical resonators containing amplifying media
- 5 Laser radiation
- 6 Control of laser oscillators
- 7 Optically pumped solid-state lasers
- 8 Gas lasers
- 9 Molecular gas lasers I
- 10 Molecular gas lasers II
- 11 Tunable lasers
- 12 Semiconductor lasers
- 13 Passive optical systems
- 14 Periodic optical systems, resonators, and inhomogeneous media
- 15 The optics of Gaussian beams
- 16 Optical fibers and waveguides
- 17 The optics of anisotropic media
- 18 The electro-optic and acousto-optic effects and modulation of light beams
- 19 Introduction to nonlinear processes
- 20 Wave propagation in nonlinear media
- 21 Detection of optical radiation
- 22 Coherence theory
- 23 Laser applications
- Appendix 1 Optical terminology
- Appendix 2 The ´-function
- Appendix 3 Black-body radiation formulas
- Appendix 4 RLC circuits
- Appendix 5 Storage and transport of energy by electromagnetic fields
- Appendix 6 The reflection and refraction of a plane electromagnetic wave at a boundary between two isotropicmedia of different refractive indices
- Appendix 7 The vector differential equation for light rays
- Appendix 8 Symmetry properties of crystals and the 32 crystal classes
- Appendix 9 Tensors
- Appendix 10 Bessel-function relations
- Appendix 11 Green's functions
- Appendix 12 Recommended values of some physical constants
- Index
- References
Summary
Introduction
In this chapter we shall begin our discussion of nonlinear phenomena that are important in optics. When one or more electromagnetic waves propagate through any medium they produce polarizations in the medium that, in principle, oscillate at all the possible sum and difference frequencies that can be generated from the incoming waves. These polarizations, which oscillate at these new frequencies, give rise to corresponding electromagnetic waves. Thus, we get phenomena such as harmonic generation, for example, when infrared light is converted into visible or ultraviolet light, and various other frequency-mixing processes. These nonlinear processes can be described by a series of nonlinear susceptibilities or mixing coefficients. These coefficients will be defined and their origin traced to the anharmonic character of the potential that describes the interaction of particles in the medium.
Anharmonic potentials and nonlinear polarization
When an electromagnetic wave propagates through a medium a total electric field acts on each particle of the medium. This total field contains components at all the frequencies contained in the input wave or waves. Each particle of the medium will be displaced from its equilibrium position by the action of this field. Positive ions and nuclei will be displaced in the direction of the field, while negative ions and electrons will be displaced in the opposite direction to that of the field. The resultant separation of centers of positive and negative charge creates dipoles in the medium.
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- Chapter
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- Lasers and Electro-opticsFundamentals and Engineering, pp. 622 - 639Publisher: Cambridge University PressPrint publication year: 2014