Résumé de section

◄Lecture 6: 3rd order nonlinearities (part 1)
►Tutorial n°5 & 6 - Optical Kerr Effect

  • In a first part, we will describe the so-called Four-Wave Mixing (FWM) interactions occurring in lossless materials. Similarly to  parametric interactions in \chi^{(2)} materials, third order optical parametric amplification process can be exploited to amplify a signal beam by means of its interaction with a pump beam.

    Finally, we end the lecture by illustrating resonant nonlinear interactions involving a two-photon transition on the material. It focuses on Raman and Brillouin scattering effects involving the interaction of light respectevely with optical and acoustic phonons in materials.
    We first introduce a classical description of spontaneous Raman scattering which originates from the polarizibility fluctuations of molecules due to vibrating modes and provide a quantum description insight of Raman scattering. We will show that Raman scattering can be stimulated by through a double excitation at \omega_L and \omega_S, providing that \omega_L-\omega_S match with the Raman shift \omega_v of the molecular material. Under a stimulated regime, the Stokes beam at \omega_S is amplified at the expense of the pump beam at at \omega_L, leading to a cascading regime with the generation of successive Stokes peaks at \omega_{S1}=\omega_L-\omega_v, \omega_{S2}=\omega_{S1}-\omega_v, ..., . Such a Raman cascading effect is used in Raman fiber lasers.


    LEARNING OUTCOMES OF THE LECTURE

    By the end of this lecture, students will know...

    • the nonlinear effects that arise in a 3rd order nonlinear materials

    By the end of this course, students will be skilled at ...

    • Solving the nonlinear equation in parametric situations and derive analytical solutions under the undepleted pump approximation
    • Calculating nonlinear interaction performances/efficiencies in situations governed by analytical solutions or expressions

    By the end of this course, students will understand  ...

    • Nonlinear effects are a key points in the development of many applications in photonics (especially in relation with laser physics)

    • Nonlinear interactions lead to energy transfer between optical beams, and/or between matter and beams, enabling in some cases the realization of nonlinear optical amplification and/or oscillation.
    • Nonlinear optics is an essential tool to create novel optical frequencies generated through the interaction of incident beams within nonlinear materials
    • Nonlinear effects are subject to phase matching conditions

    By the end of this course, students will be able to  ...

    • Model 3rd order nonlinear effects, 
    • Evaluate nonlinear interaction performances/efficiencies under approximations that should be specified, explained and justified
    • Determine in a situation involving the propagation of at least one light beam through a dielectric material medium (solid or guided), whether non-linear effects can be neglected.
◄Lecture 6: 3rd order nonlinearities (part 1)
►Tutorial n°5 & 6 - Optical Kerr Effect