Mistura não-linear de feixes paraxiais

Abstract

The mode generation through sum-frequency processes occurs when we consider two beams mixing inside a medium with a second order nonlinearity. A study based on both a theoretical and an experimental analysis of this process was done, considering, as initial beams, the families of Ince-Gaussian beams (IG) and Helical Ince-Gaussian beams (HIG). As a theoretical basis, the paraxial equation was solved using the Green function method, and the result made possible the development of a numerical simulation for the mode generation inside the medium. Experimentally, the assembled setup used a BBO crystal as the nonlinear medium, and enabled the observation and detection of this mixture. Through these two methodologies, the study considered all the possible parity combinations of two IG beams with defined parity (even-even, even-odd, odd-odd), as well as multiple combinations of HIG beams carrying orbital angular momentum (OAM). In all these cases, a very good agreement between the experimental and the theoretical results was observed, and for the beam carrying OAM, it was possible to verify the conservation of momentum in the resulting beam. Furthermore, analyzing the obtained results, it was possible to find, for the first time, the selection rule that controls the creation of modes inside the medium, and lastly, the transition between the different families of paraxial beams was observed by changing the eccentricity parameter E. These results form a good study basis for applications such as optical communication, micro-manipulation and optical tweezers.