Since the birth of mode-locking the temporal duration of optical pulses has radically
diminished. In parallel to this, bandwidths have grown so large that almost entire
frequency octaves are present in today’s few-cycle pulses.
This thesis investigates the character of ultra-wideband pulses in nonlinear environments.
Because of the growth in optical bandwidths, traditional definitions and propagation
models break down, requiring newer more accurate numerical techniques. A
novel approach capturing the uni-directionality of pulses is presented in the form of Gvariables
by combining the electric and magnetic field descriptions. These G-variables
have the advantage of both an accurate spectral representation and a reduced computational
overhead, making them significantly more efficient than existing direct Maxwell
solvers. Such approaches are particularly important where large propagation distances
and/or transverse dimensions are concerned.
Pseudo-spectral techniques play a key role in the success of these wideband models
enabling sub-cycle dynamics to be studied. One such phenomenon is Carrier Wave
Shocking (CWS), where the optical carrier undergoes self-steepening in the presence of
third-order nonlinearity. This process is carefully studied, focussing on the effect of dispersion
and the feasibility of its physical realisation. The process is then generalised to
arbitrary nonlinear order, where the quadratic form finds potential applications in High
Harmonic Generation (HHG). Shock detection schemes are also developed, and agree
with analytical solutions in the dispersionless regime.
To fully characterise few-cycle pulses, the absolute Carrier Envelope Phase (CEP)
must be known. A novel 0 − f self-referencing scheme relying on wideband interference
is investigated. By applying robust frequency domain definitions a proposal is made to
convert this scheme into one that determines absolute CEP. The scheme maps the level
of spectral interference to absolute CEP using numerical simulations.