טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKreiserman Roman
SubjectWavepackets in Dynamically-Evolving Disordered Potentials
DepartmentDepartment of Physics
Supervisor ? 18? Mordechai Segev
Full Thesis textFull thesis text - English Version


Abstract

My M.Sc. thesis research focuses on the analytical and numerical study of propagation of wavepackets in dynamically-evolving disordered potentials. I will present a new approach developed to describe and explain the interaction of waves with dynamically fluctuating disordered potential. The idea is to represent the disordered potential as a multi-frequency phase grating, where each frequency is accompanied by a random phase term. When a test wavepacket is launched into the disordered potential, the diffraction pattern at the exit of the lattice can be explained as a multiple scattering events from the net effect of these phase gratings.

In our spectral wave theory, we distinguish between two regimes. For low potential energies, i.e. potential with slow dynamics, the interaction between the wavepacket and the disorder is dominated by conservation of momentum (phase matching). Momentum conservation in  (transverse direction) is due to the grating momentum, with inherent momentum conservation in  (longitudinal direction) due to phase matching. On the other hand at high energies, for fast fluctuations in the disordered potential, it seems that the interaction does not conserve momentum (phase mismatch) momentarily. Here, momentum is being conserved in  (transverse direction) due to the grating momentum, while the phase mismatch is compensated by the presence of many longitudinal spectral components of the disordered potential. From simple considerations of momentum conservation and small angle assumption (using the paraxial approximation), we can extract the analytical prediction for the width of spectrum of the waves at saturation in the limit of weak disordered potential. Hereby we are able to demonstrate the profound difference between the regime of slow dynamics (Bragg regime) and the regime of fast dynamics (Raman-Nath regime).

 We test the spectral theory by solving numerically the paraxial wave equation and comparing the dynamics of waves to the dynamics of classical Newtonian particles in a one dimensional potential that is random both in space and in time. We find that, in the case of a dynamic disordered potential with high energies, both the waves and the particles exhibit the same global behavior, conforming on the Correspondence Principle. Nonetheless, we test our analytical predictions in some physical scenarios (such as Bragg resonances, spectral tunneling etc.) and show features of distinct wave character, that cannot be predicted by any particle theory, since such theories can give estimates and equivalences between the dynamics of waves and particles only at the major observables.