Lez #23+24 Radiation - matter, rabi oscillations, perturbative expansion

 Today we recalled the basic concepts of quantum mechanics, introducing the density matrix. We stressed the importance  of density matrix to describe statistical mixtures, and how this is not possible through an eigenstates superposition (for instance a two level system).

We discussed how to solve Bloch equation and Rabi oscillation, introducing the rotating wave approximation to neglect some terms in the integration.

We then introduced Shroedinger, Heisenberg and Interaction schemes (in this latter both eigenfunctions and operators evolve, and the temporal evolution related to the unperturbed Hamiltonian is removed from the wavefunction). Then it makes sense a perturbative expansion of the eigenfunctions and of the density matrix in the Interactions scheme. Finally, we went back to the Shroedinger scheme.

Please refer to the first part of the notes added to classroom.

Lez #21+22 Introduction to 3rd order spontaneous vs stimulated processes, classical approach

We introduced the field-induced polarization, in both the spontaneous and stimulated cases. We discussed the origin of spontaneous Raman, and why it is incoherent, linear and homodyne. As for the selection rules we recalled some basic notions from struttura della materia class. Then we moved to the stimulated Raman, a third order process for which we evaluated different contributions to the polarization. See the material on classroom.

Lez #19+20 wavemixing and OPA II

We derived the solution in the general case of non perfect phase matching, providing the acceptance bandwidth of the signal for given thickness, non linearity and group velocity mismatch. I commented on the need of having large bandwidth to preserve short pulse durations, but also on the opportunity to use long crystals to obtain efficient spectral filtering for example via second harmonic generation (in which w1=w2 and it acts as a pump, while w3 is the generated signal). We understood how to realize the phase matching in the collinear and non collinear case, dealing with walk off. In the non collinear case it is possible to amplify a wide bandwith with a wise choide of the incidence geometry and cristal orientation.

Lez #17+18 Wavemixing and OPA

We first finalized the laser lecture introducing mode locking for pulsed laser generation, active and passive methods, gain and losses compensation.  

Starting from Maxwell equation in presence of a dielectric, non magnetic  we re-derived the differential equation for the pulse envelope in presence of linear polarization in a slightly different way.

We then extended to a non linear term, considering the specific case of second order. The most general case is here a three waves mixing, approximating one beam (the pump) much more intense then the others, the signal (initially weak) and the idler (initially empty). We derived the gain expression in the case of perfect phase matching.

Primo esonero

Lez #15+16 Experimental techniques for pulsed laser characterisation

 We discussed different type of autocorrelation techniques for measuring the duration of ultrashort pulses, namely linear autocorrelator, non-collinear SHG autocorrelator and collinear SHG autocorrelator, discussing the different advantages/disadvantages. We also introduced FROG (frequency-resolved optical gating) as a convenent approach to characterize an optical pulse.