文档介绍：Chapter 2 Theory of Nonlinear Optical Susceptibility
Key words:
Electric polarization P(r, t) ;
Linear polarization P(1) ( r, t)
Nonlinear part PNL(r, t) of the material
Electric field E(r, t)
Linear susceptibility (1),
Quadratic/second order susceptibility (2)
Cubic/third order susceptibility (3)
This chapter contents: Discuss (NL)
By the theory of classical anharmonic oscillator model
By the semiclassical theory.
By the density operator theory.
(NL) is a tensor with many elements
Symmetry of (NL)
Some practical efforts of determining the NLO properties of materials.
§ Classical Model
The electric polarization
Nonpolar molecule
b. Polar molecule
Under the action of the electric field E
No the electric field E
Restoring
1. Harmonic Model
Let x0=0, then x is the displacement of electron
Let
where k is the restoring factor, is the dipole damping rate.
In linear optics, the electron moves near the equilibrium position x0.
E
damping
Thus, the Restoring force is
The damping force is
Thus
When applying an electric field.
Electric field force
By substituting Eq. () into Eq. (), we get
Let its solution as follows form:
The induced polarization
The induced polarization at a field frequency of in medium is
The electric dipole moment偶极矩of single atom
where N is the number density of electrons in the material.
Comparing Eq. () and ()
Based on the definition