1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Photonics Engineering, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
The focal point of the research presented here is all-optical signal processing via nonlinearities. The objective has been to investigate the interaction between optical signals via nonlinearities and how these nonlinearities can be engineered to serve specific purposes. The nonlinear response of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH). During this project the interaction between such spatial solitons has been investigated theoretically through perturbation theory and experimentally via numerical simulations. The outcome of this research isnew theoretical tools for quantitatively predicting the escape angle, i.e. the angle of incidence below which the solitons will fuse and above which they will move apart. Head-on collision experiments are not comprised within the model assumptions, but even so expressions predicting the so-called inwards escape angle are proposed and numerically veriÝed for certain cases. Chapter 2 and paper 1 are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW and the SH. Via quasi-phase-matching (QPM) the phase mismatch and hence the nonlinearity is eÙectively brought under control through periodic sign reversal of the nonlinearity. On theaverage QPM changes the quadratic nonlinearity and induces new cubic nonlinearities in the system. The engineering and exploitation of these cubic nonlinearities in two-period QPM wave-guides has been another area of investigation. Introducing the second period might make practical engineering of the nonlinearities possible. A major result is the discovery that cubic nonlinearities leads to an enhancement of the bandwidth for soliton generation. This part of the research is presented in Chapter 3 and paper 2.