AbstractQuadratic solitons have ridden the wave of recent interest in applications of frequency conversion and supercontinuum generation in particular. In recent years advances in fabrication of smaller Χ(2) waveguides with lower loss has made experimental quadratic soliton research more feasible, stoking significant theoretical interest in them.
Here we will start by studying solitons due to quadratic nonlinearity only. We derive soliton existence criteria which allow us to identify five regimes of soliton existence. Using perturbation theory we predict the emission of non-solitonic radiation from these solitons due to their interaction with the linear dispersion of the system and other dispersive waves. We investigate two distinct lithium niobate nanowaveguide structures and analyse their modelled dispersion to assess their potential for quadratic soliton research. We find our two candidate waveguides provide all five existence regimes making them ideal for experimental investigation. Our numerical simulations of pulse propagation in these structures show good agreement with our analytic predictions for soliton existence and their dynamics.
We improve the generality of our work by including cubic nonlinear terms in our next model. We show that two-component solitons supported by quadratic and cubic nonlinearity may undergo soliton self-frequency shift due to the Raman effect in lithium niobate. Our analytic predictions of temporal and spectral shifts match up remarkably closely with numerical simulations of soliton propagation. In some cases we see that extreme Raman shifting brings about instabilities in the soliton not reported elsewhere. These instabilities are associated with the two-component soliton shifting towards the boundary of its existence, a process that we show does not happen in Kerr solitons.
In our final model we highlight a particular feature of lithium niobate nanowaveguides that we have observed while researching them. The focus of this work is the avoided crossings found between certain mode pairs in these waveguides. We therefore introduce an additional mode to our model such that the second harmonic component of the soliton can exist in the avoided crossing between the two modes centred at this frequency. The key advantage that these avoided crossings offer is the opportunity for modal group velocity matching which is essential for low power soliton existence and efficient frequency conversion in short pulses. This model also automatically includes the dispersion of nonlinearity seen in the modelled system. Continuous wave solutions are found to exist in this system and exhibit modulation instability over the majority of their existence domain. We find soliton solutions in this system and make comparisons between their existence and that of the continuous wave solutions. In general the spectral structure of these solitons is not simple and we find the core and tail frequencies often differ.
|Date of Award||23 Mar 2022|
|Supervisor||Andriy Gorbach (Supervisor) & Dmitry Skryabin (Supervisor)|
- Nonlinear optics