The most studied solution of the Helmholtz equation is, in the paraxial approximation, the Gaussian beam. This partial description of the optical propagation drastically reduces the possibility of optical schemes and imaging. Overcoming this limit is crucial to developing innovative devices. Although many studies have started to explore the field of non-paraxial optics, much still has to be developed and understood.
The aim of this project is to explore, experimentally and numerically, the behaviour of non-gaussian beams, such as Bessel, Airy, and vortex beams when these propagate in photorefractive crystals, with specific focus on samples at the phase transition from the paraelectric to the ferroelectric phase. The photorefractive nonlinearity is strong also with low intensity fields, so we can easily access the study of extreme events and we can observe the time dynamics of the system. Our preliminary results show that, using non-gaussian beams, new and exotic phenomena are observed.
The main goal of this research project is a significant advancement in the understanding of the behaviour of non-paraxial (non-gaussian) beams when they propagate in very strong non-linear media. This field is only partial explored due to the intrinsic difficulties given by the lack of an analytic theory, as instead is available for paraxial beams. Furthermore, the need for high intensity optical fields, due to the low Kerr nonlinearities commonly exploited, fundamentally limits the experiments to pulsed laser beams. This reduces the generality of the phenomena and does not allow a careful analysis of the temporal evolution of the beams. Lastly the use of crystals with non-linear periodicity, that have already revealed unusual behavior for gaussian beams, has never been employed, to our knowledge, for non-gaussian beams.
All of the previous statements motivate this research project to pursue the following innovations:
1-The exploitation of strong nonlinearity that does not need intense light beam through the photorefractive effect. This possibility opens an unprecedented avenue to study nonlinear non-gaussian beams. Furthermore, it is necessary for developing devices, because a low field guarantees the reversibility of the phenomenon (ensuring to not permanently modify the samples and the devices);
2-The adoption of continuous light beams to study the non-linear propagation of non-gaussian beam. This will allow the stable observation of the temporal dynamics of the beam evolution;
3-The study of different light beams in the same photorefractive nonlinearity. This allows us to create of a comprehensive treatise of the nonlinear propagation of several non-gaussian beams helping to include some of the missing elements in the present theory.
4-The interaction between non-gaussian beams and non-linear lattice crystals. This enables us to correlate the nonlinear effects with the scales of the periodic non-linear pattern embedded in the sample.