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Nonlinear Optics and Photonics$
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Guang S. He

Print publication date: 2014

Print ISBN-13: 9780198702764

Published to Oxford Scholarship Online: December 2014

DOI: 10.1093/acprof:oso/9780198702764.001.0001

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Nonlinear Polarization of an Optical Medium

Nonlinear Polarization of an Optical Medium

Chapter:
(p.18) 2 Nonlinear Polarization of an Optical Medium
Source:
Nonlinear Optics and Photonics
Author(s):

Guang S. He

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198702764.003.0002

In nonlinear polarization theory, the key issue is to establish the relationship between the optical electromagnetic fields and the induced electric polarization response of the medium. Furthermore, it is necessary to specify the nonlinear relations between the Fourier components of the induced polarization field and the corresponding Fourier components of the interacting optical fields. The connection between them is provided by the nonlinear susceptibilities of the medium, which characterize the nonlinearity of the medium and are functions of the various possible frequency combinations of the involved Fourier components of the optical fields. For this purpose, we need to introduce the definition and tensor formulation of various orders of nonlinear susceptibilities of the medium, and to derive the nonlinear coupled-wave equations that can be used to describe various nonlinear wave-mixing processes.

Keywords:   Nonlinear polarization, nonlinear susceptibility, Fourier component, wave-mixing process, induced electric polarization, coupled-wave equation

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