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.

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.

Lez #13+14 Principles of Laser

 Recap on Absorption, Spontaneous and stimulated emission. Laser principles. Passive resonator. Is a laser superior to a conventional sources? Trading spatial and temporal coherence with flux. Statistical properties of light. How to make a laser: 2/3/4 level systems. Different type of lasers, He-Ne, ruby, excimers, p-n junctions and semiconductor based photonic devices.

Lez #11+12 Propagation in non-linear media: Kerr effect

 We discussed non linear effects. At first, we observed as in the very common case of centro symmetric materials even susceptibilities must be zero. Therefore, the most general, lowest order non linear effect is the third order (Boyd 1.5.10 and this link). Such an effect can be introduced in terms of a non linear, intensity dependent refractive index. We solved the equation in time domain, obtaining a z-independent temporal profile and a z dependent phase term. It can be shown (numerically) how the resulting spectrum broadens with z. We then combined the two effects and derived the soliton solution arising when (anomalous) GVD and Kerr compensate for LD=Lnl and qualitatively explained the wave breaking phenomenon.

Lez #9+10 Helmotz solution in linear dispersive (beta2) regime I: CHIRPED gaussian pulse

  We discussed as, in linear regime, the presence of a beta2 (GVD) affects a pulse initially chirped in time domain (i.e. adding a phase in time domain). In such case, the pulse can indefinitely broaden upon traveling along z into the material OR, it can get narrower down to a minimum and then broaden again. Hence, providing some chirp it can be useful, for instance, if one aims to get a minimum beam waist at a given point in space (the sample) and NOT in the z position where the pulse is generated (the laser output). Note that starting with a pulse chirped in time domain, the initial bandwidth is also broadened with respect to 1/T0, i.e. the pulse is initially non fourier Transform limited. In principle, one could start with a pulse chirped in frequency domain (only a phase factor in frequency domain) hence modifying the initial time duration. This situation is similar to what is done pre-compensating pulse broadening. See for instance Chirped Pulse Amplification.