Antonio Politi: A New Interpretation of Laser Instabilities

Title: A New Interpretation of Laser Instabilities

Abstract: An accurate mathematical model to describe laser instabilities is available since more than 50 years.
However, a detailed comprehension of the resulting dynamical behaviour is still missing.
In particular, the reason why atomic polarization cannot be adiabatically eliminated even in the presence of very fast relaxation processes is puzzling.
I revisit the dynamical equations by first transforming the original model into an equation with delay much easier to simulate numerically and then implementing a multi-scale perturbative approach, which reintroduced a space-time representation.
As a result, I am able to show that the laser dynamics is unexpectedly nearly Hamiltonian, the underlying equation being nonlinear wave equation of Klein-Gordon type in the presence of a Toda potential.
The closeness to a Hamiltonian dynamics explains a posteriori the singularity of the original model, including the difficulty of adiabatically eliminating the polarization.