Chapter 3 Coupled-Wave Equations and Second Harmonic Generation.ppt

Chapter 3 Coupled-Wave Equations and Second Harmonic Generation
Coupled-Wave Equations
Coupled-Wave Equations for Nonlinear Susceptibility
Maxwell's equations are valid for both the linear and nonlinear optical phenomena.
Mainly studying the ic here and ideal dielectric materials that contain no free charges and no free current.
Where 0 and 0 are the permeability and permittivity of free space, respectively.
Operating ▽×
The wave equation in NLO
Let
The nonlinear polarization of the medium acts as a source term. Lower E induces PNL=0
E is the total electric field in the medium
Let them to propagate along z direction, so
where kn is the wave vector of the electric field, and k'n is that of nonlinear electric polarization. Both the electric field and the polarization have the same frequency n and should satisfy the wave equation in NLO)
Then
It is usually permissible to neglect the first term if
(-24)
so is known as the slowly-varying-envelope approximation.
Coupled-Wave Equations for Second-Order Nonlinear Optics
Use the wave equations to study second-order NLO effects, such as second harmonic generation, sum-and difference-frequency generations.
Encountering three waves interacting with each other in the medium. 3 = 1 + 2
Let the two incident light fields, says e1 and e2, are propagating along z direction with frequencies 1 and 2, respectively