The following contains a more detailed description for the proposed projects.

When phase-mismatched (cascaded) second-harmonic generation of fs pulses takes place, the quadratic nonlinear interaction can effectively be modelled with a cubic nonlinearity. A recently developed theory at DTU Fotonik showed that this effective cubic nonlinearity is nonlocal. The presence of dispersion, in particular group-velocity mismatch (GVM) between the pump and the generated second harmonic, implies that the effective cubic nonlinear response is not instantaneous, but is delayed. This nonlocal effect has many similarities to the Raman effect known, e.g., from silica fibers. However, there are many interesting aspects that are yet to be understood in this system, where ultra-short fs pulses interact at extreme intensities. The project is mainly theoretical, and numerical simulations using an advanced code for describing ultra-short fs pulses must be performed.

Fiber lasers have a huge market potential as they are cheap, rugged, effective, and have a small footprint. High-power pulsed fs lasers are at the moment unable to compete with state-of-the-art solid-state amplifier systems, however. In particular, the pulse duration is typically 300-700 fs, and getting sub-50 fs pulses from fiber laser amplifiers would constitute a huge break-through. This project investigates the potential of using cascaded quadratic soliton compression to achieve this goal. The compression can take place in bulk nonlinear crystals, or in nonlinear waveguides. The project requires a detailed study of various nonlinear crystals, the dispersion properties, and the nonlinear performance, and extensive numerical simulations are required.

Group-velocity mismatch (GVM) is an obstacle for efficient compression of fs pulses using cascaded quadratic nonlinearities. The compression occurs as trade-off between GVM and the quadratic nonlinear strength of the material. A low GVM is required in order to compress to sub-10 fs duration in typical nonlinear crystals, and in particular for visible and near-IR pulses the crystals become too dispersive for this to occur. This project will investigate techniques to reduce GVM in order to get efficient compression with lower nonlinearities, or to achieve compression in regimes, that today are inaccessible.

Recently, it was discovered that dispersive waves appear when extremely short 10-20 fs solitons are generated with cascaded quadratic nonlinearities in nonlinear crystals. These dispersive waves are typical when generating broad-band radiation (i.e. ultra-short pulses), but the novelty here is the extreme tunability of the dispersive wave appearing in nonlinear crystals. This project will perform a detailed analysis of the strength, conditions for occurring and spectral location of these dispersive waves.

Soliton compression in cascaded quadratic nonlinear systems is a successful way of generating ultra-short fs pulses. However, as it is a nonlinear effect, only the most intense part of the beam is compressed, i.e. the central part of the pulse. The wings of the pulse are not compressed, and this leaves an unwanted “pedestal”. A typical commercial use of the compressed pulses would require that the pedestal be reduced. This can be done by adiabatically compressing the pulse, which requires a chirped quasi-phase matched grating. This project will investigate the potential in this method by using theory and numerics.

Compression of fs pulses with low-energies can be done in phase-mismatched second-harmonic generation in waveguides. The waveguide confines the pump and the generated second-harmonic, so much lower pulse energy is needed in order to achieve the compression. The downside is that the second harmonic will typically be multi-moded. This project investigates in detail for the first time the modes of a waveguide, their dispersion, and the impact this has on generating ultra-short fs pulses.

The cascaded quadratic soliton compressor is a unique method for compressing high-energy fs pulses in bulk nonlinear crystals to sub-20 fs duration. Diffraction is avoided by defocusing the beam so the Rayleigh length is much longer than the crystal. However, only the central part of the transverse beam has high enough intensity to compress, and the wings are therefore left uncompressed. A faithful description of the dynamics as the ultra-short fs solitons are generated therefore requires a full 3+1D numerical code (transverse part plus time propagating along the crystal). The purpose of this project is to develop such a numerical code, which requires parallel programming and large-scale computing. The code will then be used to model actual experimental conditions.

Nanowires are extremely small waveguides whose diameter is smaller than the guided light. In nanowires the dispersion can be modified to a very large degree, and the confinement of light is very strong allowing for large nonlinear effects. Silica nanowires can be made by tapring silica fibers, either standard telecom fibers or microstructured fibers. Because of the strong nonlinearity and dispersion control, silica nanowires can be used for soliton compression of fs pulses. This project will investigate such possibilities both theoretically and also experimentally.