Contents of the course :

1. Introduction to non linear optics

2. Nonlinear Susceptibilities
- Field notations
- Nonlinear susceptibilities tensor : definition
- Properties of the nonlinear susceptibilities
- Contracted notation for the 2nd order nonlinear susceptibility
- Spatial symmetries

3. Nonlinear wave equation
- Maxwell's equations
- Propagation in a linear anisotropic material
- Stationary nonlinear wave equation
- Nonlinear wave equation in a isotropic materials
- A physical picture : free and driven waves

3. Second order nonlinearities
- 2nd Harmonic generation
-> Undepleted pump approximation regime
->Phase matching considerations
->Depleted pump regime
- Frequency generation - Parametric processes
->optical parametric fluoresence and amplification
->optical parametric oscillation : OPO
- Quasi-phase matched materials

4. Third order nonlinearities
- Four-wave Mixing
- Optical Kerr Effect : self-focusing, nonlinear Shrödinger equation, self-phase modulation, solitons
- Raman Scattering : spontaneous and stimulated Raman scattering, Raman amplification, Raman laser
- Brillouin Scattering : spontaneous and stimulated Brillouin scattering
- Two photon absorption