Nonlinear frequency conversion under general phase mismatched condition: the role of phase locking and random nonlinear domains
Authors:   , Vito Roppo 
Published: October 2023

In the field of second harmonic (SH) generation most studies have been concerned with maximizing conversion efficiencies, generally achievable at the phase matching (PM) condition. Outside of the PM the conversion efficiency drastically decreases. This has caused that the possible working conditions out of PM to remain largely unexplored.
In this thesis work we initiated a systematic study of the SH behavior in under conditions of large phase mismatch. When a pump pulse crosses an interface between a linear and a nonlinear medium there are always two generated SH components. These components may be understood on the basis of the mathematical solution of the inhomogeneous wave equations at the SH frequency. The homogeneous (HOM) solution is a component with wave-vector k(2¿) as expected from the dispersion relation and exchanges energy with the pump until the inevitable walk-off. The inhomogeneous (INH) solution is a component with a wave-vector 2k(¿), twice the pump wave-vector, and travels locked to the pump pulse. We divide our work in two parts, one for each generated component.
Inhomogeneous component.
We start a systematic study of the behavior of the generated INH component, phase locked to the pump. The consequences of phase locking (PL) can guide us towards new scenarios by allowing working conditions hitherto assumed inaccessible for absorbing materials. We show that while the HOM component travels with the group velocity given by material dispersion, the IHN component is captured by the pump pulse and experiences the same effective dispersion of the pump. It does not follow the PM condition. It naturally follows that the suppression of absorption at the SH wavelengths will occur if the pump is tuned to a region of transparency. We extended the same theory for the generated third harmonic (TH). We then studied the surprising behavior of SH and TH INH components with frequencies above the absorption edge when the material is placed inside a cavity resonant only at the fundamental frequency. We have shown that the PL mechanism not only inhibits absorption but also fosters the enhancement of harmonic generation by several orders of magnitude compared to the no-cavity case. Finally, we tested the INH SH and TH behaviors in metallic frequency regime of material.
Homogeneous component.
The techniques used to PM the nonlinear interaction enable efficient nonlinear interactions but drastically limit the spectral bandwidth of the nonlinear optical process, making the designed frequency converter only suitable for a fixed input wavelength and single interaction only.
It has been shown that the use of disordered nonlinear media relaxes the PM condition thus allowing one to achieve relatively efficient broad bandwidth regime of the frequency conversion. An example of a quadratic nonlinear medium with a disordered domain structure is an un-poled Strontium Barium Niobate (SBN) crystal. It is composed of a system of random size anti parallel ferroelectric domains that allow to phase-match any second-order parametric process over a broad range of wavelengths without any poling.
We have initiated an experimental and theoretical investigation of the properties of the SH waves generated in SBN crystals, with an extension to the generated TH. This study covers the coherence and polarization properties of the generated signal, as well as its spatial distribution.
In addition, we have made an experimental study of the noncollinear interaction of short optical pulses in a SBN crystal by using two fundamental waves intersecting inside the crystal. We have shown that this effect may be employed as a simple tool for monitoring both the pulse duration and initial chirp. This method offers a simple and economic alternative to the existing methods for pulse characterization.