Probing Nonlinear Optical Instabilities in Gas-filled Hollow-core Photonic Crystal Fibre

In this thesis, different techniques to study instabilities caused by ultrashort pulses propagating in confined gaseous media are explored. Gas-filled hollow-core photonic crystal fibres provide a unique platform in which to study such effects as they provide a degree of control of their dispersion and optical nonlinearity, which is imperative to exploring a variety of nonlinear optical dynamics of femtosecond pulses in gasbased systems. Changes of polarisability, for instance, due to photoionisation of the gas by ultrashort pulses or due to coherent excitation of molecular gases, can be monitored and studied in such systems by using techniques that are developed to take advantage of the wave-guidance properties of hollow-core fibres. To begin with, different optical modes that can be guided by these fibres are used to study the transverse dynamical effects of a gas undergoing ionisation at the temporal compression focus point of an ultrashort pulse. Plasma recombination which lasts for a few nanoseconds as well as hydrodynamic and thermodynamic effects which carry on for hundreds of microseconds induce phase changes which are picked up by the different transverse probes, allowing these effects to be studied. Following this, the self-compression of optical solitons in these fibres is used to generate a phase-matched dispersive wave in the ultraviolet, that is used as a probe that counter-propagates against an ionising pulse. The longitudinal profile of the plasma within the emission length of the dispersive wave is reconstructed, based on the shifting of the dispersive wave in the presence of the free electrons. Both these techniques to study photoionisation are robust against perturbations due to air fluctuations and vibrations of mirrors which techniques such as interferometry are usually susceptible to, as they are phase-matched processes. The third project shifts the focus of the thesis to investigating the coherent excitation of vibrational modes in molecular gas by covariance spectroscopy. This is done with broadband noisy pulse bursts generated by modulational instability in a separate fibre, which are then sent to a short fibre that holds the sample gas to be studied. This scan-free technique identifies the signatures of nonlinear interactions imprinted on incoherent pulse bursts by calculating the intensity correlations between the optical frequencies in the pulse bursts. To conclude, two numerical studies that can be pursued experimentally in the future are discussed. The first explores the use of tapered hollow-core fibres to generate broadband incoherent ultraviolet light for a resonance-enhanced implementation of the Raman covariance spectroscopy discussed in the last project. The second introduces the idea of using molecular gases as the medium of choice for pulse compression with hollow-core fibres. Throughout the thesis, different types of instabilities caused by optical nonlinearities are studied. At the end, the idea proposed is that although often more energy is lost from a pulse propagating in molecular media, by using appropriately delayed pulses, the energy that is deposited into a molecular oscillation Raman mode could be re-extracted. Such a method could suppress long-lived effects of energy deposition into the medium and in some cases, might be a preferable alternative to losing pulse energy as thermal energy (as occurs, for instance, during ionisation).