by Carla Figueira de Morisson Faria
Period: 01.2004 - 02.2004 (on Thursdays!)

1. Introduction
   1. How strong is a "strong laser field"?
      1. Different intensity regimes, in comparison to typical atomic parameters
      2. Ponderomotive energy, breakdown of perturbation theory
      3. Typical frequencies/intensities used
   2. How to obtain a strong laser field?
      1. Amplification techniques (especially Chirped Pulse Amplification)
   3. Examples of strong-field optical phenomena: first observations, key experiments, why they are counterintuitive, simple physical pictures, applications: applications
      1. High-order harmonic generation
      2. Above-threshold ionization
      3. Nonsequential double ionization
      4. Stabilization
   4. Perspectives
2. Theoretical Methods
   1. Framework: gauge-equivalent Hamiltonians (length, velocity, KH gauges)
   2. Perturbative methods
      1. Starting point: Dyson (DuHamel) Equation
      2. Standard ("weak-field")perturbation theory (emphasis on why it breaks down)
      3. The Gordon-Volkov series:
         1. Explanation/derivation of the Volkov solution
         2. Integral(Volterra) equations to sum up the whole series
      4. Strong-field (Keldysh-Faisal-Reiss) approximation:
         1. Main idea: modified perturbation theory
         2. Difference between K. F. and R.
         3. The Keldysh parameter
         4. Breaking the gauge invariance
   3. High-frequency approximations
   4. Purely numerical methods (TDSE)
3. Applications
   1. Analytical treatment of stabilization
      1. Influence of pulse shapes
      2. Extreme limits
   2. Quantum-orbit analysis of ATI and NSDI
      1. The SFA S-Matrix (derivation, different formulations and physical interpretation)
      2. Saddle-point approximation (connection with path integrals and classical models, applicability; examples of interference effects)
      3. Uniform approximation (derivation)