1. Nonlinear Optics Tobias J. Kippenberg tjk@mpq.mpg.de
T. Kippenberg (2006)
Nonlinear Optics
Tobias J. Kippenberg
T.W. Hänsch Division
Lecture 8

2. Slowly varying amplitude equation
T. Kippenberg (2006)
Lecture 8

3. Linear vs. Nonlinear Polarization
T. Kippenberg (2006)
Linear vs. Nonlinear Polarization
Lecture 8

4. Second harmonic Generation
T. Kippenberg (2006)
Second harmonic Generation
In general
For linear polarization
We can conclude that a second order nonlinearity acts as a source term in the wave equation and consequently produces radiation at the second harmonic frequency. Thus once can assume the presence of two waves:
Lecture 8

5. Second harmonic Generation
T. Kippenberg (2006)
Second harmonic Generation
The wave equation in the SVE approx. is given by: 2
Clearly the polarization terms couple the fields:
Collecting only resonant terms
Lecture 8

6. Second harmonic Generation
T. Kippenberg (2006)
Second harmonic Generation
The coupled wave equations are given by: 2
Lecture 8

7. T. Kippenberg (2006)
Phase matching
Lecture 8

8. Second harmonic Generation
T. Kippenberg (2006)
Second harmonic Generation
     
                                
(125)
                             
Lecture 7

9. Second harmonic Generation
T. Kippenberg (2006)
Second harmonic Generation
     
                                
(125)
                             
Lecture 7